#18672: Twists of newforms can return wrong coefficient field
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Reporter: davidloeffler | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.8
Component: modular forms | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The method {{{hecke_eigenvalue_field}}} of Newform objects is supposed to
return the number field '''generated''' by the Hecke eigenvalues. If f is
a newform and chi a Dirichlet character, the Hecke eigenvalue field of the
twist f x chi is a subfield of the composite of the coefficient field of f
and the field of values of chi; it needn't be the whole composite field.
The current implementation of twisting by newforms (introduced at #18086)
does not check this; it computes some ambient field containing the Hecke
eigenvalues and returns this, even though it can be much too large:
{{{
sage: f = Newforms(11)[0]
sage: chi = DirichletGroup(5, QQbar).0
sage: g = f.twist(chi)
sage: g
q - 2*I*q^2 + I*q^3 - 2*q^4 + O(q^6)
sage: g.hecke_eigenvalue_field()
Algebraic Field
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/18672>
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