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. -- 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
