Hi Kilian, I am forwarding this to the sage-nt mailing list as well since you might get a larger audience.
Best, Alex On Sun, 3 Jan 2010 13:51:19 -0800 (PST), Kilian <kkil...@googlemail.com> wrote: > Hello, > > i have a problem with sage and modular symbols for Gamma1(4) and odd > weight k, where the cusp 1/2 is irregular. > > According to Merel, there is (for k>2) an exact sequence: > > 0-> S_k -> M_k -> B_k -> 0 > > Here B_k is the boundary space and S_k is the cuspidal subspace. > > Let the weight k be 7. > > If I compute the appropriate dimensions with SAGE, I get 4,6 and 3 > which can't be. Furthermore, computing the boundary map, gives a > matrix which is definitely _not_ surjective. > > On the other hand, Merel explicitely states that the dimension of B_k > is the number of cusps, i.e. 3, so the failure must already be in > Merel's paper, or am I missing something? > > I assume that 4 and 6 are correct, as a comparison with the usual > dimension tables for modular forms suggest. > > What is even more confusing is that Merel states that the isomorphism > between the boundary space and the space B_k(Gamma) is an > _isomorphism_, whereas in the SAGE sourcecode and in William Stein's > book it is only stated that it's injective. > > Thanks in advance, > Kilian. > -- Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne -- Australia -- http://www.ms.unimelb.edu.au/~aghitza/ -- 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
