[with patch, with positive review] Membership testing for modular forms subspaces is hopeless

[davidloeffler]

This is pretty poor, IMHO:

sage: M = ModularForms(17, 4)
sage: S = M.cuspidal_submodule()
sage: M.0 == S.0
True
sage: M.0 in S
False

As far as I can tell at a glance this is happening because S.__call__(x) tests whether or not the parent of x has a canonical inclusion map to S; it should probably be testing whether the parent of x has a canonical inclusion map to the *ambient space* of S.

Once the above is fixed we should also have a method is_cuspidal() for modular forms objects, which would be secretly just self in self.parent().cuspidal_submodule(). A corresponding is_eisenstein() would be good, too.

[davidloeffler]

apply after #4357 and #5736

[davidloeffler]

Here's a patch, which adds is_cuspidal, is_eisenstein, is_new and is_old, and corrects a funny glitch whereby elliptic curve newforms consistently claimed not to be cuspidal :-) I wrote the patch and ran tests with this and everything else (including the not-yet-fully-refereed #5968) installed simultaneously, but it should at least apply as long as you have the patches at #4357 and #5736 installed.

[cremona]

Looks good to me. Patch applies fine to 4.0 and tests in sage/modular/{modform,hecke} pass.

[mhansen]

Merged in 4.0.1.alpha0.