Evaluating Igusa functions

The moduli space of principally polarized abelian surfaces is parametrized by three Igusa functions. In this article we investigate a new way to evaluate these functions by using the Siegel Eisenstein series. We explain how to compute the Fourier coefficients of certain Siegel modular forms using classical modular forms of half-integral weight. One of the results in this paper is an explicit algorithm to evaluate the Igusa functions to a prescribed precision.