old_submodule on modular symbols gives wrong answer

[koffie]

The following is clearly wrong

sage: M=ModularSymbols(Gamma1(22),sign=1)
sage: S=M.cuspidal_submodule();S
Modular Symbols subspace of dimension 6 of Modular Symbols space of dimension 25 for Gamma_1(22) of weight 2 with sign 1 and over Rational Field
sage: S.new_submodule()
Modular Symbols subspace of dimension 4 of Modular Symbols space of dimension 25 for Gamma_1(22) of weight 2 with sign 1 and over Rational Field
sage: S.old_submodule()
Modular Symbols subspace of dimension 3 of Modular Symbols space of dimension 25 for Gamma_1(22) of weight 2 with sign 1 and over Rational Field

It's wrong because the new and the old subspace should be disjoint and together span the whole space.
Note that the answers are as expected when using modular forms:

sage: M=ModularForms(Gamma1(22))
sage: S=M.cuspidal_submodule();S
Cuspidal subspace of dimension 6 of Modular Forms space of dimension 25 for Congruence Subgroup Gamma1(22) of weight 2 over Rational Field
sage: S.new_submodule()
Modular Forms subspace of dimension 4 of Modular Forms space of dimension 25 for Congruence Subgroup Gamma1(22) of weight 2 over Rational Field
sage: S.old_submodule()
Modular Forms subspace of dimension 2 of Modular Forms space of dimension 25 for Congruence Subgroup Gamma1(22) of weight 2 over Rational Field

Ps. I tested this using sage 5.2.alpha0

Component: modular forms

Keywords: sd51

Author: David Loeffler

Reviewer: Alex Ghitza

Merged: sage-5.12.beta2

Issue created by migration from https://trac.sagemath.org/ticket/13198

[koffie]

comment:1

The cause of this bug and a way to fix it is mentioned in the google group discussion: https://groups.google.com/forum/?fromgroups#!topic/sage-nt/pCggjYWRdMg

I just post this here just in case someone stumbles upon this bug and fixes it before I have the time. Hopefully saving that person debugging time.

[loefflerd]

Changed keywords from none to sd51

[loefflerd]

comment:2

I am not sure I agree with your diagnosis on the sage-devel thread. The definition of the old submodule as the sum of the images of the degeneracy level-raising maps makes perfect sense in this setting; it won't be orthogonal to the kernel of the level-lowering maps, but it should still be Hecke-invariant and the space Sage is returning here just isn't:

sage: M22 = ModularSymbols(Gamma1(22), sign=1)                                                       
sage: M2 = ModularSymbols(Gamma1(2))                                                                 
sage: d1 = M2.degeneracy_map(M22,1)                                                                  
sage: d2 = M2.degeneracy_map(M22,11)                                                                 
sage: M22.hecke_matrix(17).restrict((d1.image() + d2.image()).free_module())                         
...
ArithmeticError: subspace is not invariant under matrix

The problem, I think, is this:

sage: M2                                                                                             
Modular Symbols space of dimension 1 for Gamma_0(2) of weight 2 with sign 0 over Rational Field

and thus M2 is trying to use code intended for passing between Gamma0 levels instead of Gamma1 levels.

I will fix this during SD51 if I have time.

[loefflerd]

Attachment: trac_13198.patch.gz

Patch against 5.11.beta3

[loefflerd]

Author: David Loeffler

[loefflerd]

comment:3

Here's a patch. The actual change is very small, but I cleaned up some ReST formatting and added a file to the ref manual at the same time.

[aghitza]

Reviewer: Alex Ghitza