Tutorial: Computing With Modular Forms Using SAGE

Contents, General, Modular Forms, Modular Symbols, Future

The Future

The following general direction for the future of modular forms in SAGE.

  1. 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.
  2. Add computation of q-expansions of half-integral weight forms using the algorithm in Basmaji's thesis. This is a 1-page program.
  3. Include Kevin Buzzard's table of weight 1 forms.
  4. Greatly extend what is implemented for computing directly with modular forms without users having to know about modular symbols.
  5. Much more functionality for computing with the method of graphs.
  6. p-adic Modular symbols ala Pollack-Stevens (Robert Pollack has discussed with me implementing this or "guiding a student" to implement this).
  7. Quaternion algebras
  8. Hilbert Modular Forms, Siegel modular forms, etc.