Fast bases for half-integral weight modular forms

In this joint work with Ilker Inam, we exploit classical results of Kohnen and Cohen to give explicit bases of the spaces of half-integral weight modular forms of level Gamma_0(4) in any weight, which can be compared to the Miller bases for integral weight modular forms of level 1. They are very simple and can be computed quickly by performing power series multiplications. In further work with Inam et al., we apply them to a computational study of the distribution of signs of such modular forms.