Iwahori-spherical representations of \bm{GSp(4)} \\ and Siegel modular forms of degree 2 with square-free level

Abstract

A theory of local old- and newforms for representations of GSp(4) over a p-adic field with Iwahori-invariant vectors is developed. The results are applied to Siegel modular forms of degree 2 with square-free level with respect to various congruence subgroups.