Abstract by Eric Moss
Congruences for coefficients of level 2 modular functions with poles at 0
Let M_k^\\flat(N) be the space of weakly holomorphic modular forms in level N that are holomorphic away from 0. We prove congruences modulo powers of 2 of the Fourier coefficients for weight 0 forms in the space where N = 2. The congruences involve a modulus that depends on the binary expansion of the modular form's order of vanishing at infinity. We also present conjectured congruences for forms in M_0^\\flat(N) with N = 3, 5, and 7, and for forms in a similar space with N = 4 and 6.