#18061: Implement (correct) action of Atkin-Lehner operators on newforms
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Reporter: pbruin | Owner:
Type: defect | Status: needs_work
Priority: major | Milestone: sage-6.6
Component: modular forms | Resolution:
Keywords: newform Atkin- | Merged in:
Lehner operator | Reviewers:
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | 48e5d2d924072cdbbaf4051c549e268e8e39e589
u/pbruin/18061-atkin_lehner_action | Stopgaps:
Dependencies: #18068, #18072, |
#18086 |
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Comment (by davidloeffler):
Here's another gripe. The following is waaay too slow:
{{{
sage: F = Newforms(299,names='a')[0]
sage: time F.atkin_lehner_eigenvalue(299)
CPU times: user 4.99 s, sys: 18.9 ms, total: 5.01 s
Wall time: 5 s
1
}}}
What on earth can be taking the time here? According to the profiler, the
total time is 5.028 seconds, of which 5.026 is spent in four calls to the
"twist" routine. Ultimately, most of that is actually spent creating
Dirichlet character groups over number fields, which requires factoring
some fairly large polynomials over those number fields. Why on earth is
this necessary, or even relevant? Evaluating an Atkin--Lehner eigenvalue
can't possibly require factorising 82 polynomials over number fields!
--
Ticket URL: <http://trac.sagemath.org/ticket/18061#comment:16>
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