#6071: [with patch, needs work] Weight 1 Eisenstein series
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Reporter: davidloeffler | Owner: davidloeffler
Type: defect | Status: assigned
Priority: major | Milestone: sage-4.1
Component: modular forms | Keywords: eisenstein series
Reviewer: | Author:
Merged: |
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Comment(by davidloeffler):
Fair point; I will add some more examples.
For your second point: if you install the patch and try it out, you'll see
that (for instance) ModularForms(Gamma1(23), 1) will raise a
NotImplementedError, as it should, but EisensteinForms(Gamma1(23),1) will
work. The thing that you describe as "very very wrong" is forced by the
general design we have for modular forms spaces, which insists that
Eisenstein forms are always a subspace of an ambient ModularForms space
spanned by the *last* few basis vectors. The point of the workaround above
is that when we can't find the dimension of the wt 1 cusp forms, we
pretend that there aren't any for the purposes of working with Eisenstein
series, but intercept any attempt to create the whole modular forms space
(or its cuspidal part) by raising an error.
Even once we have proper code for calculating weight 1 cusp forms this
will still be an issue, since for large N calculating dim S_1(Gamma_1(N))
is a serious and time-consuming calculation that we don't want to be
forced to do solely in order to know how many zeros to stick at the front
of the Eisenstein series.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6071#comment:5>
Sage <http://sagemath.org/>
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