> On Thu, Aug 4, 2011 at 1:17 AM, max flander <max.flan...@gmail.com> wrote: >> Hi John, >> >> I'm not sure if you remember me, I was at the Sage days in Leiden last year. >> >> I was hoping you could help me with a question. I need to compute Z bases of >> weight 2 cusp forms. I've noticed that the modular forms you get with >> CuspForms(N).basis() have integer coefficients.
This observation is in general incorrect. For example: sage: CuspForms(43).basis() [ q + 2*q^5 + O(q^6), q^2 - 1/2*q^4 + q^5 + O(q^6), q^3 - 1/2*q^4 + 2*q^5 + O(q^6) ] > > Do you know if this is a >> Z-basis for S_2(N, Z) , i.e. the submodule of S_2(N, C) containing all forms >> with q-expansion in Z[[]]? Or >> will it just span some sublattice? If you want that, use the integral_basis command, which gives a saturated basis for S_2(N,Z) in Hermite normal form (to the given precision). sage: C = CuspForms(43) sage: C.integral_basis() [ q + 2*q^5 + O(q^6), q^2 + q^3 - q^4 + 3*q^5 + O(q^6), 2*q^3 - q^4 + 4*q^5 + O(q^6) ] >> >> Cheers heaps, >> Max >> >> >> > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
