#5262: L-series attached to modular forms has a major bug in how it computes the
sign of the functional equation
---------------------------+------------------------------------------------
Reporter: was | Owner: craigcitro
Type: defect | Status: new
Priority: major | Milestone: sage-3.4
Component: modular forms | Keywords:
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This is wrong:
{{{
The following computation should produce identical values in the last
line:
E=EllipticCurve('37b2')
h=E.modular_form()
Lh = h.cuspform_lseries()
LE=E.lseries()
h.elliptic_curve()==E, Lh(1), LE(1)
The output is:
(True, 0, 0.725681061936153)
}}}
This is because the Atkin-Lehner sign is computed wrong in
sage/modular/modform/element.py. In fact, there one finds the code:
{{{
m = ModularSymbols(N,l,sign=1)
n = m.cuspidal_subspace().new_subspace()
e = (-1)**(l/2)*n.atkin_lehner_operator().matrix()[0,0]
}}}
Notice that m has absolutely nothing to do with the modular form!
The right fix is to implement an atkin_lehner_eigenvalue(...) function for
modularforms, and that should in turn be implemented correctly, and should
be called from the cuspform_lseries command.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5262>
Sage <http://sagemath.org/>
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