cuspform_lseries() computing sign of functional equation incorrectly

[mabshoff]

Sal reports: 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)

I'm running Sage 3.3.alpha3 of sage.math.

The problem seems to be the sign of the functional equation -- it looks like the cuspform_lseries() incorrectly computes it to be -1, forcing the value at s=1 to be 0. In sage/modular/modform/element.py the sign of the functional equation fed into the Dokchister is computed by

e = (-1)**(l/2)*n.atkin_lehner_operator().matrix()[0,0]

which Gonzalo and Mark tell me is not correct.

[mabshoff]

This is a dupe of #5262. William did open the other ticket later, but since #5262 has the better description I am closing this ticket.

Cheers,

Michael