#8622: Atkin-Lehner operators don't work for odd weight modular forms
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Reporter: davidloeffler | Owner: craigcitro
Type: defect | Status: new
Priority: major | Milestone:
Component: modular forms | Resolution:
Keywords: atkin-lehner | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by robharron):
Replying to [comment:6 davidloeffler]:
>
> Just to be clear: are you referring here to your very specific case of
odd weight CM forms with CM by their own nebentypus? Otherwise this
statement is false: you know the product of the pseudo-eigenvalues of f
and f*, but there is no reason why these two numbers should be equal.
Right. I'm only referring to that specific case. And while it does seem
like an extremely specific case, it is also true that the only newforms on
Γ,,1,, that are actual eigenvectors of Atkin-Lehner are those of trivial
character and those with CM by their own Nebentypus. Since the function in
question is atkin_lehner_eigenvalue, and it seems like we can deal with
all cases in which it makes sense to call this function, I think it makes
sense it implement it. For the pseudoeigenvalues, it might be better to
make a new function atkin_lehner_pseudoeigenvalue which can return the
eigenvalue in the above cases. Of course, if you think this student
working on pseudoeigenvalues will be done soon, then maybe it's not worth
the trouble.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8622#comment:7>
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