diff --git a/lmfdb/siegel_modular_forms/dimensions.py b/lmfdb/siegel_modular_forms/dimensions.py index 817022fe0c..460d474466 100644 --- a/lmfdb/siegel_modular_forms/dimensions.py +++ b/lmfdb/siegel_modular_forms/dimensions.py @@ -54,91 +54,76 @@ def parse_dim_args(dim_args, default_dim_args): def dimension_Gamma_2(wt_range, j): r""" - -

More precisely, The triple $[a,b,c]$ in -

+ First entry of the respective triple: The full space. + Second entry: The codimension of the subspace of cusp forms. + Third entry: The subspace of cusp forms. + More precisely, The triple $[a,b,c]$ in + + row All + and in the $k$th column shows the dimension of + the full space $M_{k,j}(\Gamma(2))$, + of the non cusp forms, and of the cusp forms. + + in row $p$, where $p$ is a partition of $6$, + and in the $k$th column shows the multiplicity of the + $\mathrm{Sp}(4,\Z)$-representation + associated to $p$ in the full $\mathrm{Sp}(4,\Z)$-module + $M_{k,j}(\Gamma(2))$, + in the submodule of non cusp forms and of cusp forms. + (See below for details.) """ return _dimension_Gamma_2(wt_range, j, group='Gamma(2)') def dimension_Gamma1_2(wt_range, j): r""" - -

More precisely, The triple $[a,b,c]$ in -

+ First entry of the respective triple: The full space. + Second entry: The codimension of the subspace of cusp forms. + Third entry: The subspace of cusp forms. + + More precisely, The triple $[a,b,c]$ in + + row All + and in the $k$th column shows the dimension of + the full space $M_{k,j}(\Gamma(2))$, + of the non cusp forms, and of the cusp forms. + + in row $p$, where $p$ is a partition of $3$, + and in the $k$th column shows the multiplicity of the + $\Gamma_1(2)$-representation + associated to $p$ in the full $\Gamma_1(2)$-module $M_{k,j}(\Gamma(2))$, + in the submodule of non cusp forms and of cusp forms. + (See below for details.) """ return _dimension_Gamma_2(wt_range, j, group='Gamma1(2)') def dimension_Gamma0_2(wt_range, j): """ - + Total: The full space. + Non cusp: The codimension of the subspace of cusp forms. + Cusp: The subspace of cusp forms. """ return _dimension_Gamma_2(wt_range, j, group='Gamma0(2)') def dimension_Sp4Z(wt_range): """ - + Total: The full space. + Eisenstein: The subspace of Siegel Eisenstein series. + Klingen: The subspace of Klingen Eisenstein series. + Maass: The subspace of Maass liftings. + Interesting: The subspace spanned by cuspidal eigenforms that are not Maass liftings. """ return _dimension_Sp4Z(wt_range) def dimension_Sp4Z_2(wt_range): """ - + Total: The full space. + Non cusp: The subspace of non cusp forms. + Cusp: The subspace of cusp forms. """ return _dimension_Gamma_2(wt_range, 2, group='Sp4(Z)') @@ -160,11 +145,9 @@ def dimension_table_Sp4Z_j(wt_range, j_range): def dimension_Sp4Z_j(wt_range, j): """ - + Total: The full space. + Non cusp: The subspace of non cusp forms. + Cusp: The subspace of cusp forms. """ return _dimension_Gamma_2(wt_range, j, group='Sp4(Z)') @@ -307,12 +290,10 @@ def _dimension_Gamma_2(wt_range, j, group='Gamma(2)'): def dimension_Sp6Z(wt_range): """ - + Total: The full space. + Miyawaki lifts I: The subspace of Miyawaki lifts of type I. + Miyawaki lifts II: The subspace of (conjectured) Miyawaki lifts of type II. + Other: The subspace of cusp forms which are not Miyawaki lifts of type I or II. """ return _dimension_Sp6Z(wt_range) @@ -365,12 +346,10 @@ def __dimension_Sp6Z(wt): def dimension_Sp8Z(wt_range): """ - + Total: The subspace of cusp forms. + Ikeda lifts: The subspace of Ikeda lifts. + Miyawaki lifts: The subspace of Miyawaki lifts. + Other: The subspace that are not Ikeda or Miyawaki lifts. """ headers = ['Total', 'Ikeda lifts', 'Miyawaki lifts', 'Other'] dct = {} @@ -429,11 +408,9 @@ def _dimension_Sp8Z(wt): def dimension_Gamma0_4_half(wt_range): """ - + Total: The full space. + Non cusp: The codimension of the subspace of cusp forms. + Cusp: The subspace of cusp forms. """ headers = ['Total', 'Non cusp', 'Cusp'] dct = {} @@ -449,14 +426,17 @@ def _dimension_Gamma0_4_half(k): of half integral weight k - 1/2. INPUT - The realweight is k-1/2 + + The realweight is k-1/2 OUTPUT - ('Total', 'Non cusp', 'Cusp') + + ('Total', 'Non cusp', 'Cusp') REMARK - Note that formula from Hayashida's and Ibukiyama's paper has formula - that coefficient of x^w is for weight (w+1/2). So here w=k-1. + + Note that formula from Hayashida's and Ibukiyama's paper has formula + that coefficient of x^w is for weight (w+1/2). So here w=k-1. """ if k < 1: raise ValueError("$k$ must be a positive integer") @@ -475,9 +455,7 @@ def _dimension_Gamma0_4_half(k): def dimension_Gamma0_3_psi_3(wt_range): """ - + Total: The full space. """ headers = ['Total'] dct = {} @@ -493,10 +471,12 @@ def _dimension_Gamma0_3_psi_3(wt): on $Gamma_0(3)$ with character $\psi_3$. OUTPUT - ("Total") + + ("Total") REMARK - Not completely implemented + + Not completely implemented """ R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',)) (x,) = R._first_ngens(1) @@ -515,10 +495,9 @@ def _dimension_Gamma0_3_psi_3(wt): def dimension_Gamma0_4_psi_4(wt_range): """ - -

Odd weights are not yet implemented.

+ Total: The full space. + + Odd weights are not yet implemented. """ headers = ['Total'] dct = {} @@ -537,10 +516,12 @@ def _dimension_Gamma0_4_psi_4(wt): with character $\psi_4$. OUTPUT - ("Total") + + ("Total") REMARK - The formula for odd weights is unknown or not obvious from the paper. + + The formula for odd weights is unknown or not obvious from the paper. """ R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',)) (x,) = R._first_ngens(1) @@ -556,9 +537,7 @@ def _dimension_Gamma0_4_psi_4(wt): def dimension_Gamma0_4(wt_range): """ - + Total: The full space. """ headers = ['Total'] dct = {} @@ -573,10 +552,12 @@ def _dimension_Gamma0_4(wt): Return the dimensions of subspaces of Siegel modular forms on $Gamma0(4)$. OUTPUT - ("Total",) + + ("Total",) REMARK - Not completely implemented + + Not completely implemented """ R = PowerSeriesRing(ZZ, 'x') x = R.gen().O(wt + 1) @@ -590,9 +571,7 @@ def _dimension_Gamma0_4(wt): def dimension_Gamma0_3(wt_range): """ - + Total: The full space. """ headers = ['Total'] dct = {} @@ -607,10 +586,12 @@ def _dimension_Gamma0_3(wt): Return the dimensions of subspaces of Siegel modular forms on $Gamma0(3)$. OUTPUT - ("Total") + + ("Total") REMARK - Only total dimension implemented. + + Only total dimension implemented. """ R = PowerSeriesRing(ZZ, 'x') x = R.gen().O(wt + 1) @@ -624,11 +605,9 @@ def _dimension_Gamma0_3(wt): def dimension_Dummy_0(wt_range): """ - + Total: The subspace of cusp forms. + Yoda lifts: The subspace of Master Yoda lifts. + Hinkelstein series: The subspace of Hinkelstein series. """ headers = ['Total', 'Yoda lifts', 'Hinkelstein series'] dct = {}