ZEROS OF WEAKLY HOLOMORPHIC MODULAR FORMS OF LEVEL 4

Abstract

Let [Formula: see text] be the space of weakly holomorphic modular forms of weight k and level 4 that are holomorphic away from the cusp at ∞. We define a canonical basis for this space and show that for almost all of the basis elements, the majority of their zeros in a fundamental domain for Γ0(4) lie on the lower boundary of the fundamental domain. Additionally, we show that the Fourier coefficients of the basis elements satisfy an interesting duality property.