  Let $U(p)$ denote the Atkin operator of prime index $p$. Honda and Kaneko
proved infinite families of congruences of the form $f|U(p) \equiv 0 \pmod{p}$
for weakly holomorphic modular forms of low weight and level and primes $p$ in
certain residue classes, and conjectured the existence of similar congruences
modulo higher powers of $p$. 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 $\Gamma^*(N)$ for $N=1,2,3,4$
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.
