  Lehner's 1949 results on the $j$-invariant showed high divisibility of the
function's coefficients by the primes $p\in\{2,3,5,7\}$. Expanding his results,
we examine a canonical basis for the space of level $p$ modular functions
holomorphic at the cusp 0. We show that the Fourier coefficients of these
functions are often highly divisible by these same primes.
