On Tue, Mar 18, 2014 at 12:31 PM, Kenneth A. Ribet <[email protected]> wrote: > Hi Everyone, > > I'm getting what I perceive to be an error when I compute some spaces of > modular symbols mod 3. (Probably the same phenomenon occurs mod 2.) > Specifically: > > sage: N=7*13 > sage: for l in primes(20): > ... > ModularSymbols(Gamma0(N),2,base_ring=GF(l)).cuspidal_submodule().dimension() > 14 > 17 > 14 > 14 > 14 > 14 > 14 > 14 > > The genus of X_0(91) is 7, so I expected to see a string of 14's. The 17 > stands out like a sore thumb. > > Actually, I get an analogous error if I remove "cuspidal_submodule": the 14's > become 17's and the 17 becomes a 20. The consistent increment of 3 has to do > with the fact that there are four cusps. > > Thanks in advance!
In Sage (and Magma) "Modular symbols modulo 3" isn't H_1(X_0(N),Z;cusps) tensor F_3, which is what you are assuming. Instead, it is what is got by taking a choice of presentation for H_1(X_0(N),Q;cusps) and just reducing that modulo 3. It's entirely built for efficiency, when you know a bit of theory (about torsion in that presentation) to be sure you're good. I think the only torsion is 2 or 3. I implemented things this way when Kevin Buzzard and I were verifying some A5 representations are modular, and we had to work modulo 5 for efficiency reasons. > Ken See you at the Berkeley number theory seminar tomorrow, if you're going to be there! -- William > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- William Stein Professor of Mathematics University of Washington http://wstein.org -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
