34 research outputs found
Hecke grids and congruences for weakly holomorphic modular forms
Let denote the Atkin operator of prime index . Honda and Kaneko
proved infinite families of congruences of the form
for weakly holomorphic modular forms of low weight and level and primes in
certain residue classes, and conjectured the existence of similar congruences
modulo higher powers of . Partial results on some of these conjectures were
proved recently by Guerzhoy. We construct infinite families of weakly
holomorphic modular forms on the Fricke groups for
and describe explicitly the action of the Hecke algebra on these forms. As a
corollary, we obtain strengthened versions of all of the congruences
conjectured by Honda and Kaneko