Hello Jack,
typically you want
sage: E = EllipticCurve(11a1)
sage: m = 5
sage: ms = E.modular_symbol()
sage: chi = DirichletGroup(m).0
sage: chi
Dirichlet character modulo 5 of conductor 5 mapping 2 |-- zeta4
sage: sum( (chi^2)(a) * ms(a/m) for a in [1..(m-1)] )
5
The symbol ms is already
Doug has successfully cleared up my confusion off-list. I now have
working code.
Best wishes,
Jack Fearnley
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On Jul 31, 10:35 pm, D. S. McNeil dsm...@gmail.com wrote:
We would like to know if certain sums of modular symbols span the
space.
Is this the sort of thing you had in mind?
sage: M=ModularSymbols(11,2);M
Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with
sign 0 over
Thanks for this. There still seems to be a manual step in going from,
say,
s1 = 2*(1,8) - (1,9)
to
s1 = 2*b[1] - b[2]
I may be misunderstanding you. Are you saying you want to enter the line
s1 = 2*(1,8)-(1,9)
verbatim and have it work? That I don't think I can do (unless you're
.. I suppose you could even add a convenience function
def b(*x):
return m[x]
after which
sage: s = [2*b(1,8) - b(1,9),
: -b(1,0) + b(1,9),
: -b(1,0) + b(1,8)]
sage: s
[2*(1,8) - (1,9), -(1,0) + (1,9), -(1,0) + (1,8)]
would work.
Doug
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On Aug 1, 11:10 pm, D. S. McNeil dsm...@gmail.com wrote:
Thanks for this. There still seems to be a manual step in going from,
say,
s1 = 2*(1,8) - (1,9)
to
s1 = 2*b[1] - b[2]
I may be misunderstanding you. Are you saying you want to enter the line
s1 = 2*(1,8)-(1,9)
