Computing Classical Modular Forms

Explicitly Computing Modular Forms

This is a textbook about algorithms for computing with modular forms. It is nontraditional in that the primary focus is not on underlying theory; instead, it answers the question “how do you explicitly compute spaces of modular forms?”

Classical and overconvergent modular forms

The purpose of this article is to use rigid analysis to clarify the relation between classical modular forms and Katz’s overconvergent forms. In particular, we prove a conjecture of F. Gouvêa [G, Conj. 3] which asserts that every overconvergent p-adic modular form of sufficiently small slope is classical. More precisely, let p > 3 be a prime, K a complete subfield of Cp, N be a positive integer...

Classical Modular forms and Galois representations

These notes are based on two lectures which were given by the author at the Workshop on Arithmetic Algebraic Geometry, I.I.T. Guwhati, India, fall 2008. They were intended to give a quick survey on classical complex modular forms and their l-adic Galois representations. Accordingly, the focus is rather on results and examples whereas proofs are mainly sketched or omitted. Nothing in these notes...

Algorithms For Computing With Modular Forms

An introduction to computing modular forms using modular symbols

We explain how weight-two modular forms on 0.N / are related to modular symbols, and how to use this to explicitly compute spaces of modular forms.