Siegel modular forms of genus 2 and level 2

Abstract

We study vector-valued Siegel modular forms of genus 2 on the three level 2 groups Γ[2] ◁ Γ1[2] ◁ Γ0[2] ⊂ Sp(4, ℤ). We give generating functions for the dimension of spaces of vector-valued modular forms, construct various vector-valued modular forms by using theta functions and describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued Siegel modular forms.