  We give congruences modulo powers of $p \in \{3, 5,7\}$ for the Fourier
coefficients of certain modular functions in level $p$ with poles only at 0,
answering a question posed by Andersen and the first author and continuing work
done by the authors and Moss. The congruences involve a modulus that depends on
the base $p$ expansion of the modular form's order of vanishing at $\infty$.
