FAST COMPUTATION OF HALF-INTEGRAL WEIGHT MODULAR FORMS

Abstract

To study statistical properties of modular forms, including for instance Sato-Tate like problems, it is essential to be able to compute a large number of Fourier coefficients. We show that this can be achieved in level 4 for a large range of half-integral weights by making use of one of three explicit bases, the elements of which can be calculated via fast power series operations.