Tutorial: Computing With Modular Forms Using SAGE
The following general direction for the future of modular forms in SAGE.
- Speed up the linear algebra even more, especially over number
fields. SAGE now uses the highly optimized
IML and Linbox libraries; use even more of their functionality.
- Add computation of q-expansions of half-integral weight forms using
the algorithm in Basmaji's thesis. This is a 1-page program.
- Include Kevin Buzzard's table of weight 1 forms.
- Greatly extend what is implemented for computing directly
with modular forms without users having to know about modular symbols.
- Much more functionality for computing with the method of graphs.
- p-adic Modular symbols ala Pollack-Stevens (Robert Pollack has discussed
with me implementing this or "guiding a student" to implement this).
- Quaternion algebras
- Hilbert Modular Forms, Siegel modular forms, etc.