NEWFORMS MOD p IN SQUAREFREE LEVEL WITH APPLICATIONS TO MONSKY’S HECKE-STABLE FILTRATION

Abstract

We propose an algebraic definition of the space of L-new mod-p modular forms for Γ0(N L) in the case that L is prime to N, which naturally generalizes to a notion of newforms modulo p in squarefree level. We use this notion of newforms to interpret the Hecke algebras on the graded pieces of the space of mod-2 level-3 modular forms described by Paul Monsky. Along the way, we describe a renormalized version of the Atkin-Lehner involution: No longer an involution, it is an automorphism of the algebra of modular forms, even in characteristic p.