I want to consider eigenspaces of S1 = CuspForms(Gamma0(N),k).new_subspace(), but only for repeated eigenvalues. So, given a Hecke eigenform T, and a repeated eigenvalue e, I'd like to take the kernel of T-e acting on S1. This doesn't work because elements of S1 must have rational coefficients, and e need not be rational, so e might not act on S1. I'd like to do CuspForms(Gamma0(N),k,base_ring = QQbar).new_subspace(), but there's a NotImplementedError. One solution is to use S1 to get the repeated eigenvalues, and then get an "upper bound" for the kernel I want by taking the kernel of T-e acting on S2. This is okay for small S2, but if N and k have a lot of factors then the dimension of S2 is high, and the matrices get very large. I've tried to shrink S2 artificially by checking coefficients of the basis elements to see if they're eigenforms, but I'm having difficulty putting certain basis elements together to get a subspace.
- What's going on with the NotImplementedError? - Is there a solution, perhaps not using newforms but instead using general eigenforms? - Could I somehow take S1 and change the base ring, either directly or manually (putting the basis vectors as a module over say QQbar)? - If I use numerical eigenforms, I can't seem to get the Hecke operators to work. Is there a way? - I encountered similar problems when I used L instead of QQbar, where the number field L is gotten by adjoining the eigenvalues. Has anybody done something like this before? - Any other ideas? Thanks. -- 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
