Sage Days 17 Project
Rational Cuspidal Subgroups
See http://wstein.org/home/wstein/db/days17/cuspidal_torsion/ for some data.
Dimensions of Modular Forms Spaces for Gamma(N)
Pre-Sage Days Stuff
See projects. There are numerous ideas for projects there.
Implement the Hijikata Trace Formula
There are PARI and Magma implementations here along with some scans:
Do a Sage implementation. Then do some interesting computations say of the trace of T_2 on some high weight spaces...