Computing overconvergent forms for small primes

Abstract

We construct explicit bases for spaces of overconvergent $p$-adic modular forms when $p=2,3$ and study their interaction with the Atkin operator. This results in an extension of Lauder’s algorithms for overconvergent modular forms. We illustrate these algorithms with computations of slope sequences of some $2$-adic eigencurves and the construction of Chow–Heegner points on elliptic curves via special values of Rankin triple product L-functions.