#18061: Implement (correct) action of Atkin-Lehner operators on newforms
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Reporter: pbruin | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: modular forms | Resolution:
Keywords: newform Atkin- | Merged in:
Lehner operator | Reviewers:
Authors: Peter Bruin, | Work issues:
David Loeffler | Commit:
Report Upstream: N/A | 90f0b3b0e0050d686169f7dc53da62e667fd8f6e
Branch: | Stopgaps:
u/pbruin/18061-rebased |
Dependencies: #18068, #18072, |
#18086, #18478 |
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Comment (by pbruin):
Replying to [comment:21 davidloeffler]:
> I had another look at your implementation. When using the modular-
symbols algorithm, why do you take the conjugate of the (0,0) matrix
entry? This is going to be quite slow to compute (because Sage has to
verify from first principles that the coefficient fields are CM); and,
more importantly, isn't it clearly the wrong answer?
To be honest I ran into this through a doctest failure, and figured that
in all probability either the (0,0) entry or its conjugate would be the
correct value, with the conjugate being explained by some sesquilinear
pairing intervening somewhere...
> (Maybe Sage's conventions for Atkin--Lehner operators aren't the same as
Atkin and Li, and the conjugation is the difference between conventions;
but I think it would be very bad and confusing if Sage's conventions
weren't internally consistent!)
I didn't realise that the various conventions for the Atkin-Lehner
operator differ in other ways than by a power of ''Q''. We should
carefully document what convention we use and how it differs from others!
--
Ticket URL: <http://trac.sagemath.org/ticket/18061#comment:27>
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