#18061: Implement (correct) action of Atkin-Lehner operators on newforms
-------------------------------------+-------------------------------------
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 pbruin):
The following still fails:
{{{
sage: f = Newforms(Gamma1(15), 3, names='a')[2]
sage: f.atkin_lehner_eigenvalue(5)
Traceback (most recent call last):
...
ValueError: q + a2*q^2 + (-a2 - 2)*q^3 - q^4 - a2*q^5 + O(q^6) is not an
eigenform for W_5
}}}
This is wrong because `f` ''is'' an eigenform for `W_5`:
{{{
sage: f
q + a2*q^2 + (-a2 - 2)*q^3 - q^4 - a2*q^5 + O(q^6)
sage: _, g = f.atkin_lehner_action(5); g
q + a2*q^2 + (-a2 - 2)*q^3 - q^4 - a2*q^5 + O(q^6)
}}}
The reason is probably that the parents of `f` and `g` are different:
{{{
sage: parent(f)
Cuspidal subspace of dimension 8 of Modular Forms space of dimension 24
for Congruence Subgroup Gamma1(15) of weight 3 over Number Field in a2
with defining polynomial x^2 + 5
sage: parent(g)
Cuspidal subspace of dimension 2 of Modular Forms space of dimension 6,
character [-1, 1] and weight 3 over Number Field in a2 with defining
polynomial x^2 + 5
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/18061#comment:15>
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