We would like to know if certain sums of modular symbols span the
space. For a simple example, let
sage: M=ModularSymbols(11,2);M
Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with
sign 0 over Rational Field
sage: M.basis()
((1,0), (1,8), (1,9))
Now, say we have three sums of symbols expressed in terms of the basis
as follows
s1 = 2*(1,8) - (1,9)
s2 = -(1,0) + (1,9)
s3 = -(1,0) + (1,8)
How can we show, in Sage, that these three sums span the space? Or if
not, give the dimension of the subspace?
I realize that this would be a simple linear algebra problem if I
could get the coefficients involved into some kind of matrix format.
Best Wishes
Jack Fearnley
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