#13198: old_submodule on modular symbols gives wrong answer
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Reporter: mderickx | Owner: craigcitro
Type: defect | Status: new
Priority: major | Milestone: sage-5.11
Component: modular forms | Resolution:
Keywords: sd51 | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies:
Stopgaps: |
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Changes (by davidloeffler):
* keywords: => sd51
Comment:
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:
{{{
#!python
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.
--
Ticket URL: <http://trac.sagemath.org/ticket/13198#comment:2>
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