Let Mk♯(N) be the space of weight k, level N weakly holomorphic
modular forms with poles only at the cusp at ∞. We explicitly construct
a canonical basis for Mk♯(N) for N∈{8,9,16,25}, and show that
many of the Fourier coefficients of the basis elements in M0♯(N) are
divisible by high powers of the prime dividing the level N. Additionally, we
show that these basis elements satisfy a Zagier duality property, and extend
Griffin's results on congruences in level 1 to levels 2, 3, 4, 5, 7, 8, 9, 16,
and 25