#10177: Gamma0 equivalence function for number field cusps returns wrong
transformation matrix
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Reporter: mtaranes | Owner: craigcitro
Type: defect | Status: new
Priority: major | Milestone:
Component: modular forms | Keywords: number field cusps
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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The transformation matrix returned by 'is_Gamma0_equivalent' for number
field cusps is not in Gamma0(N). My fault (this is even wrong in the
example I wrote for the documentation, sorry...):
{{{
sage: k.<a> = NumberField(x^2 + 5)
sage: N = k.ideal(3)
sage: alpha = NFCusp(k, 3, a + 1)
sage: beta = NFCusp(k, 2, a - 3)
sage: alpha.is_Gamma0_equivalent(beta, N, Transformation=True)
(True, [2*a - 4, -3*a - 4, -5*a + 2, 3*a + 13])
}}}
The matrix is not in Gamma0(3)!
It's not difficult to compute the right matrix. I'll be happy to write a
patch in a few weeks (after I submit my thesis).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10177>
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