Recover mathematical assertions from the pre-rewrite SMF tests

roed314 · claude · roed314 · commit ea1ad6c56644 · 2026-08-04T17:20:56.000-04:00
Port every recoverable assertion from the old sample-based
test_siegel_modular_forms.py onto the new smf_* pages, with all values
re-verified against devmirror and against classical formulas:

- Igusa cusp forms chi_10/chi_12 (2.S.1.10.0.a.b, 2.S.1.12.0.a.c):
  Saito-Kurokawa spin coefficients 240/21960/1317900 and
  2784/107352/80234700, lifts of 1.18.a.a and 1.22.a.a
- Siegel Eisenstein series of weight 12 (2.S.1.12.0.a.a): eigenvalues
  2100225 = 1+2^10+2^11+2^21 etc., porting the old Sp4Z.24_E test
  (weight 24 no longer in the data)
- Klingen-Eisenstein series in M_{10,2} and M_{10,10} (from Delta and
  1.20.a.a), recovering the old Sp4Z_2/Sp4Z_j browse checks
- the old Sp4Z.18_Maass sample: defining polynomial x^2 - x - 589050
  and the 1.34.a.a lift on 2.S.1.18.0.a.c
- paramodular level 277: dim S_3(K(277)) = 56 = 33 (P) + 23 (G),
  Atkin-Lehner split 1/55, and the rational eigenform's Dirichlet series
- numeric dimension tables: Igusa's dim M_k(Sp(4,Z)) sequence on both
  dimension-search routes (values match the retired dimensions.py
  formulas exactly), weight-3 paramodular dims at levels 270-280, and
  dim S_{14,2}(Gamma_0(2)) = 16 from the old Gamma0_2 table
- header comment cataloguing what is NOT recoverable (smf_samples pages,
  weight-24/56 samples, weight-2 Poor-Yuen paramodular forms, degree 3/4
  data, Gamma1_2/Gamma0_4*/psi/half-integral tables) and two data
  discrepancies found while verifying: the stored lambda_p of
  2.S.1.18.0.a.c adds the Eisenstein summand 196608 to both coordinates,
  and new Gamma_0(3) totals are 3 short of the classical dimensions at
  even weights (Eisenstein types beyond F/Q not counted)

The deleted test_smf.py needed no recovery: it was a byte-identical
stray copy of classical_modular_forms/test_cmf.py (GL2 content only).

25 tests pass (was 17), pyflakes clean.

Co-Authored-By: Claude Fable 5 &lt;noreply@anthropic.com&gt;
diff --git a/lmfdb/siegel_modular_forms/test_siegel_modular_forms.py b/lmfdb/siegel_modular_forms/test_siegel_modular_forms.py
@@ -4,6 +4,60 @@
 The data on devmirror is provisional and only partially loaded, so tests
 that depend on database content use runtime skip guards rather than
 failing when a table or label has not been loaded yet.
+
+Recovered content from the pre-rewrite tests
+--------------------------------------------
+The old test_siegel_modular_forms.py exercised the smf_samples-based pages
+(families Sp4Z, Sp4Z_2, Sp4Z_j, Gamma0_N, Kp, Sp6Z, Sp8Z).  Wherever the
+same mathematical object exists in the new smf_* tables, its assertions
+have been ported below with values re-verified against the database and
+against the classical formulas (see test_igusa_cusp_forms,
+test_eisenstein_series, test_klingen_eisenstein, test_maass_spezialschar,
+test_paramodular_277, test_sp4z_dimension_tables, test_gamma0_2_dimensions).
+The old Sp4Z scalar dimension table (Igusa's numbers) and the old
+M_{k,2}(Gamma_0(2)) table agree exactly with the new smf_newspaces data.
+
+Content of the old tests that is NOT recoverable on the new pages
+(re-add if/when the data or features return):
+ * Sample pages driven by db.smf_samples (129 samples: Sp4Z 97, Sp4Z_2 12,
+   Sp8Z 10, Sp6Z 2, Kp 8).  The rewrite has no sample routes; smf_samples,
+   smf_ev and smf_fc still exist on devmirror but are unused by the code.
+ * Sp4Z.24_E (weight 24 Siegel Eisenstein): eigenvalue 35184384671745
+   (= 1 + 2^22 + 2^23 + 2^45), the ev_index=19/fc_det UI, Fourier
+   coefficients such as (0, 0, 25), and mod-p reduction (1000000007 ->
+   384425457).  Scalar level-1 data now stops at weight 20; the same
+   eigenvalue formula is asserted at weight 12 in test_eisenstein_series.
+ * Sp4Z.18_Maass eigenvalue "-144a + 135840" (= 135768 - b with
+   b = 72*sqrt(2356201)): the newform 2.S.1.18.0.a.c exists (its defining
+   polynomial x^2 - x - 589050 is asserted below), but smf_hecke_nf stores
+   its lambda_2 as 135768 + 196607*b, i.e. the Eisenstein summand
+   2^16 + 2^17 = 196608 was added to BOTH coordinates instead of only the
+   rational one, so the displayed eigenvalue disagrees with the classical
+   value and is not asserted.  Its Fourier coefficients ("10a - 8340",
+   dets (1,1,1), (2,2,2)) and the modulus-reduction UI are also gone.
+ * Sp4Z.56_Ups ("interesting cusp form", "6085 bytes", "7912968 bytes"):
+   no weight-56 data.
+ * Kp weight-2 Poor--Yuen samples 2_PY2_{277,349,353,389,461,523,587+-}:
+   the new paramodular (K) data starts at weight (3, 0).
+ * Sp6Z (Miyawaki lifts, "Miyawaki (1)") and Sp8Z (Ikeda/Miyawaki lifts,
+   "Other_II (2)"): no degree > 2 data in smf_newforms/smf_newspaces.
+ * Old dimension-table families with no new counterpart: Gamma1_2 (no
+   Gamma_1(N) family), Gamma0_4 (dim M_20 = 192), Gamma0_4_psi_4
+   (dim M_40 = 495) and Gamma0_4_half (non-cusp 129 at k = 20): level 4,
+   characters and half-integral weight are absent; Gamma0_3_psi_3
+   (dim M_19 = 68): no nontrivial character orbits at level 3.
+ * Gamma0_3 totals (e.g. dim M_20(Gamma_0(3)) = 74): the new
+   2.S.3.20.0.a space has total_dim 71; the new tables are smaller by
+   exactly 3 at every even weight (Eisenstein series beyond the F/Q types
+   are not counted), so the old numbers are not asserted.
+ * Gamma_2 tables decomposed by Sp(4,F_2) = S_6 irreps (columns 111111,
+   3111, ...): the new principal-family (P) level-2 dimensions come from a
+   different construction (total_dim in the tens of thousands) and do not
+   match dim M_{k,j}(Gamma(2)); nothing asserted.
+Additionally, the deleted lmfdb/siegel_modular_forms/test_smf.py was a
+byte-identical stray copy (commit c0fdb6f551, Aug 2022) of
+classical_modular_forms/test_cmf.py; all of its GL(2) assertions live on
+in lmfdb/classical_modular_forms/, so nothing Siegel was lost with it.
 """
 
 import re
@@ -278,3 +332,186 @@ def test_sidebar(self):
         self.check("Source", "Source of Siegel modular form data")
         self.check("Reliability", "Reliability of Siegel modular form data")
         self.check("Labels", "Labels for Siegel modular forms")
+
+    # ------------------------------------------------------------------
+    # Mathematical content recovered from the pre-rewrite sample pages
+    # (see the module docstring for the items that could not be ported).
+    # All eigenvalues below were re-verified against classical formulas:
+    # for a Saito-Kurokawa lift of f in S_{2k-2}(1) the spin coefficient
+    # is a_p(f) + p^{k-2} + p^{k-1}, for the Klingen-Eisenstein series of
+    # f in S_{k+j}(1) it is a_p(f)(1 + p^{k-2}), and for the weight-k
+    # Siegel Eisenstein series it is 1 + p^{k-2} + p^{k-1} + p^{2k-3}.
+    # ------------------------------------------------------------------
+
+    def test_igusa_cusp_forms(self):
+        """
+        The Igusa cusp forms chi_10 and chi_12 (the weight-10 and weight-12
+        cusp forms for Sp(4,Z)), which are Saito-Kurokawa lifts of the
+        elliptic newforms 1.18.a.a and 1.22.a.a
+        """
+        self.need_forms("2.S.1.10.0.a.b")
+        self.check("2/S/1/10.0/a/b/", [
+            "Newform orbit 2.S.1.10.0.a.b",
+            "Saito-Kurokawa Lift (P)",
+            # lambda_2 = -528 + 2^8 + 2^9, lambda_3 = -4284 + 3^8 + 3^9,
+            # lambda_5 = -1025850 + 5^8 + 5^9
+            "1 + 240 * 2^{-s} + 21960 * 3^{-s}",
+            "1317900 * 5^{-s}",
+            "Modular form 1.18.a.a",
+        ])
+        self.need_forms("2.S.1.12.0.a.c")
+        self.check("2/S/1/12.0/a/c/", [
+            "Newform orbit 2.S.1.12.0.a.c",
+            "Saito-Kurokawa Lift (P)",
+            # lambda_2 = -288 + 2^10 + 2^11, lambda_3 = -128844 + 3^10 + 3^11,
+            # lambda_5 = 21640950 + 5^10 + 5^11
+            "1 + 2784 * 2^{-s} + 107352 * 3^{-s}",
+            "80234700 * 5^{-s}",
+            "Modular form 1.22.a.a",
+        ])
+        self.check("download_traces/2.S.1.12.0.a.c",
+                   "[0, 1, 2784, 107352, -1778648202240, 80234700")
+
+    def test_eisenstein_series(self):
+        """
+        The Siegel Eisenstein series of weight 12 for Sp(4,Z).  This ports
+        the old Sp4Z.24_E eigenvalue test (weight 24 is not in the new
+        data): the eigenvalue formula 1 + p^{k-2} + p^{k-1} + p^{2k-3} gave
+        35184384671745 for k=24, p=2 and gives 2100225 for k=12, p=2.
+        """
+        self.need_forms("2.S.1.12.0.a.a")
+        self.check("2/S/1/12.0/a/a/", [
+            "Newform orbit 2.S.1.12.0.a.a",
+            "Siegel-Eisenstein (F)",
+            # 1 + 2^10 + 2^11 + 2^21 and 1 + 3^10 + 3^11 + 3^21
+            "1 + 2100225 * 2^{-s} + 10460589400 * 3^{-s}",
+            "476837216796876 * 5^{-s}",
+        ])
+
+    def test_klingen_eisenstein(self):
+        """
+        Klingen-Eisenstein series in the vector-valued spaces M_{10,2} and
+        M_{10,10} for Sp(4,Z), attached to the elliptic newforms 1.12.a.a
+        (Delta) and 1.20.a.a; this recovers the old Sp4Z_2/Sp4Z_j browse
+        pages with sharper content
+        """
+        self.need_forms("2.S.1.10.2.a.a")
+        self.check("2/S/1/10.2/a/a/", [
+            "Newform orbit 2.S.1.10.2.a.a",
+            "Klingen-Eisenstein (Q)",
+            # tau(2)(1 + 2^8) = -6168, tau(3)(1 + 3^8) = 1653624
+            "1 - 6168 * 2^{-s} + 1653624 * 3^{-s}",
+            "Modular form 1.12.a.a",
+        ])
+        self.need_forms("2.S.1.10.10.a.a")
+        self.check("2/S/1/10.10/a/a/", [
+            "Newform orbit 2.S.1.10.10.a.a",
+            "Klingen-Eisenstein (Q)",
+            # a_2(1.20.a.a)(1 + 2^8) = 456*257, a_3(1.20.a.a)(1 + 3^8) = 50652*6562
+            "1 + 117192 * 2^{-s} + 332378424 * 3^{-s}",
+            "Modular form 1.20.a.a",
+        ])
+
+    def test_maass_spezialschar(self):
+        """
+        The old Sp4Z.18_Maass sample: the weight-18 Maass spezialschar
+        (Saito-Kurokawa) eigenform with coefficient field
+        Q[x]/(x^2 - x - 589050), the lift of the elliptic newform 1.34.a.a.
+        (Its stored Hecke eigenvalues are not asserted; see the module
+        docstring.)
+        """
+        self.need_forms("2.S.1.18.0.a.c")
+        self.check("2/S/1/18.0/a/c/", [
+            "Newform orbit 2.S.1.18.0.a.c",
+            "(18, 0)",
+            "Saito-Kurokawa Lift (P)",
+            "x^{2} - x - 589050",
+            "Modular form 1.34.a.a",
+        ])
+
+    def test_paramodular_277(self):
+        """
+        Weight-3 paramodular forms of level 277 (the level emphasized on
+        the old Kp browse page): dim S_3(K(277)) = 56 = 33 (Saito-Kurokawa)
+        + 23 (general type), with Atkin-Lehner/Fricke split 1/55, and the
+        rational general-type eigenform 2.K.277.3.0.a.a
+        """
+        self.need_spaces("2.K.277.3.0.a")
+        self.check("2/K/277/3.0/a/", [
+            "S_{3,0}(K(277))",
+            "Cusp forms 56 0 56",
+            "Saito-Kurokawa lifts (P) 33 0 33",
+            "General type (G) 23 0 23",
+            r"\(+\) \(1\) \(1\) \(-\) \(55\) \(22\)",
+            "2.K.277.3.0.a.a",
+        ])
+        self.need_forms("2.K.277.3.0.a.a")
+        self.check("2/K/277/3.0/a/a/", [
+            "Newform orbit 2.K.277.3.0.a.a",
+            "General type (G)",
+            "1 - 5 * 2^{-s} - 10 * 3^{-s} + 7 * 4^{-s}",
+        ])
+
+    def test_sp4z_dimension_tables(self):
+        """
+        Numeric dimension tables for scalar-valued Siegel modular forms of
+        level 1 (Igusa's classical dimensions, as served by the old Sp4Z
+        dimension table): dim M_k(Sp(4,Z)) for k = 4..20 is
+        1,0,1,0,1,0,2,0,3,0,2,0,4,0,4,0,5 and the newform dimensions
+        include dim S_10 = dim S_12 = 1
+        """
+        self.need_spaces("2.S.1.12.0.a")
+        self.need_forms("2.S.1.12.0.a.a")
+        # space dimensions (full spaces M_{k,0}(Sp(4,Z)))
+        self.check("?search_type=SpaceDimensions&degree=2&family=S&level=1&weight=1-20", [
+            "The dimensions shown are for spaces of modular forms",
+            "(4, 0) 1 (5, 0) 0 (6, 0) 1 (7, 0) 0 (8, 0) 1 (9, 0) 0 (10, 0) 2 (11, 0) 0 (12, 0) 3",
+            "(14, 0) 2 (15, 0) 0 (16, 0) 4 (17, 0) 0 (18, 0) 4 (19, 0) 0 (20, 0) 5",
+        ])
+        # newform dimensions (including the odd-weight Saito-Kurokawa forms)
+        self.check("?search_type=Dimensions&degree=2&family=S&level=1&weight=6-20", [
+            "The dimensions shown below are for the space of newforms",
+            "(10, 0) 2 (11, 0) 1 (12, 0) 3",
+            "(16, 0) 4 (17, 0) 2 (18, 0) 4 (19, 0) 3 (20, 0) 5",
+        ])
+        # the weight-12 space page: 3 = Eisenstein (F) + Klingen (Q) + Maass (P),
+        # with the eigenvalue columns of the decomposition table
+        self.check("2/S/1/12.0/a/", [
+            "M_{12,0}",
+            "2.S.1.12.0.a.a", "2.S.1.12.0.a.b", "2.S.1.12.0.a.c",
+            "2100225",  # Siegel Eisenstein lambda_2
+            "-24600",   # Klingen-Eisenstein lambda_2 = tau(2)(1 + 2^10)
+            "2784",     # chi_12 lambda_2
+        ])
+        self.check("2/S/1/10.0/a/", [
+            "M_{10,0}",
+            "131841",   # Siegel Eisenstein lambda_2 = 1 + 2^8 + 2^9 + 2^17
+            "240",      # chi_10 lambda_2
+        ])
+        # old browse pages Sp4Z_2/10/ and Sp4Z_j/10/10/
+        self.need_spaces("2.S.1.10.2.a")
+        self.check("2/S/1/10.2/a/", "M_{10,2}")
+        self.need_spaces("2.S.1.10.10.a")
+        self.check("2/S/1/10.10/a/", "M_{10,10}")
+
+    def test_paramodular_dimension_table(self):
+        """
+        Weight-3 paramodular newform dimensions around level 277
+        """
+        self.need_spaces("2.K.277.3.0.a")
+        self.check("?search_type=Dimensions&degree=2&family=K&weight=3&level=270-280", [
+            "Level 270 271 272 273 274 275 276 277 278 279 280",
+            "(3, 0) 16 48 19 31 33 30 14 56 25 29 19",
+        ])
+
+    def test_gamma0_2_dimensions(self):
+        """
+        The old Gamma0_2 dimension table M_{k,2}(Gamma_0(2)): the new
+        smf_newspaces dimensions agree with the classical generating
+        function exactly (e.g. dim S_{14,2}(Gamma_0(2)) = 16)
+        """
+        self.need_spaces("2.S.2.14.2.a")
+        self.check("2/S/2/14.2/a/", [
+            "S_{14,2}(\\Gamma_0(2))",
+            "Cusp forms 16 0 16",
+        ])
