As far as I know this functionality currently does not exist in sage. In fact if one does for example:
sage: G=Gamma1(17) sage: M=ModularSymbols(G) sage: S=M.cuspidal_subspace() sage: A=S.abelian_variety() sage: A.dual? Warning: This is currently only implemented when self is an abelian > subvariety of the ambient Jacobian product, and the complement of self in > the ambient product Jacobian share no common factors. A more general > implementation will require implementing computation of the intersection > pairing on integral homology and the resulting Weil pairing on torsion. Now the intersection pairing on integral homology is i guess exactly the pairing that you are looking for but this is not implemented yet as this warning message shows. Depending on what you want there might be a workaround however. I.e. modular symbols that are in different irreducible submodules for the hecke algebra will often be orthogonal to each other (this will be the case for example when at least one of the two irreducible submodules is a submodule for S.new_subspace()). Le vendredi 28 février 2014 16:10:59 UTC+1, William stein a écrit : > > Forwarding to the sage-nt mailing list... > > > ---------- Forwarded message ---------- > From: Jungbae Nam <[email protected] <javascript:>> > Date: Fri, Feb 28, 2014 at 3:34 AM > Subject: Question on the modular symbols > To: [email protected] <javascript:> > > > Dear Dr. W. Stein, > > Hi, my name is Jungbae Nam and I was a Hershy Kisilevsky's master student. > > Currently I am trying to prove a non-vanishings of families of > critical L-values for a cubic twisted L-function over elliptic curve > using modular symbols. > I know that the space of cusp forms is dual to the space of > corresponding modular symbols. > Furthermore, I know that by Mazur, Tate and Teitelbaum, the modular > symbols can represent the critical L-values. > > Now, I want to find the orthogonality of two modular symbols similar > to the petersson's inner product. > I looked for the function on Sage for the orthogonality of two modular > symbols, but could not find it. > > Dr. Stein, is there any function on Sage for the orthogonality of > modular symbols? > I am sorry if I bother you by this way for question. I tried to used > ask.sagemath.org for the sage question, but the site looks down. > > Thank you for reading my question. > > Best regards, > > Jungbae Nam > (514) 482-9768 > [email protected] <javascript:> > > > > -- > William Stein > Professor of Mathematics > University of Washington > http://wstein.org > -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at http://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/groups/opt_out.
