Computing overconvergent forms for small primes

Abstract

In this note, we construct explicit bases for spaces of overconvergent $p$-adic modular forms when $p=2,3$ and study their stability under the Atkin operator. The resulting extension of the algorithms of Lauder is illustrated 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.

Cited by in corpus (4)

• Slopes of modular forms and the ghost conjecture
• A control theorem for $p$-adic automorphic forms and Teitelbaum's $\mathcal{L}$-invariant
• Eisenstein series, $p$-adic modular functions, and overconvergence, II
• Newton Polygons of Hecke Operators