On 20 June 2012 15:23, Sam Chow <[email protected]> wrote: > Thanks for the reply, David. Your suggestions work well, in that I seem to > end up with an exact result most of the time and a close result otherwise > (compared to some weight 2 data by Stein). > > I'll try to describe how the imprecision comes about. Say I get (x^2 + 1)^2. > Ideally, I'd like to separate the i-eigenspace and the (-i)-eigenspace (this > is for distinguishing Hecke eigenforms by looking at the first however many > Fourier coefficients), and then continue with each of those separately. > Combining those will give me an upper bound for how many primes I need to > check, but not always an exact result, for instance q + i*q^2 + ... and q - > i*q^2 + ... do not get distinguished by this particular Hecke operator > (using this procedure). > > I can continue with the current procedure and get some results, however I'd > still be very interested if you or anybody else knows a good way to separate > eigenspaces within a Galois orbit.
Dear Sam, Could you be more specific about exactly what you're trying to do here? Are you referring to the first approach I outlined (working over QQ) or the second approach (working over QQbar using explicit subspaces of free modules and the hecke_matrix() method)? Regards, 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
