Classical and overconvergent modular forms of higher level

Abstract

We define the notion overconvergent modular forms on Γ1 (Npn) where p is a prime, N and n are positive integers and N is prime to p. We show that an overconvergent eigenform on Γ1 (Npn) of weight k whose Upeigenvalue has valuation strictly less than k-1 is classical.