On 13 June 2012 15:25, Sam Chow <[email protected]> wrote: > I want to consider eigenspaces of S1 = > CuspForms(Gamma0(N),k).new_subspace(), but only for repeated > eigenvalues.
Dear Sam, One possibility you might like to try is to "work solely over QQ" by doing the following. Rather than working with eigenvalues as such, you can look for repeated irreducible factors over QQ of the characteristic polynomial of the Hecke operator. Then you can ask for ker(m(T)) where m is the repeated factor, etc. So this is just like what you were trying to do, but done simultaneously for all eigenvalues in some Galois orbit. Another possibility is to use the method "free_module" of modular forms spaces, which forgets the additional structure of modular forms spaces and returns everything in terms of spaces of row vectors and their subspaces, which gives you a bit more flexibility; e.g. sage: S = CuspForms(115).new_submodule() sage: S.hecke_polynomial(3).factor() x * (x + 1)^2 * (x^2 + x - 4)^2 sage: D = S.hecke_matrix(3).base_extend(QQbar).decomposition()[-1][0] # this picks out a non-rational repeated eigenspace sage: S.hecke_matrix(3).base_extend(QQbar).restrict(D) [-2.561552812808830? 0] [ 0 -2.561552812808830?] sage: S.hecke_matrix(2).base_extend(QQbar).restrict(D) [ 0 4.561552812808830?] [ 1 1] sage: S.hecke_matrix(5).base_extend(QQbar).restrict(D) [1 0] [0 1] sage: S.hecke_matrix(7).base_extend(QQbar).restrict(D) [ -1.561552812808831? -2] [-0.4384471871911698? -2] sage: > What's going on with the NotImplementedError? It means what it says: nobody's got around to implementing the feature you want yet. I'd say this definitely qualifies as a bug. David -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
