Abstract by Ryan Keck
Congruences for Coefficients of Modular Forms in Levels 3, 5, and 7 with Poles at 0
Let Mk♭(N) be the space of weakly holomorphic modular forms that are holomorphic away from the cusp at 0. We prove congruences modulo powers of 3, 5, and 7 for the Fourier coefficients of weight 0 forms in the spaces where N = 3, 5, 7 respectively. We conjecture that these congruences can be improved to a congruence involving counting the number of times certain digits appear in the base N expansion of the modular form's order of vanishing at infinity.