FORMAL SIEGEL MODULAR FORMS FOR ARITHMETIC SUBGROUPS

Journal article, 2024

The notion of formal Siegel modular forms for an arithmetic subgroup Γ of the symplectic group of genus n is a generalization of symmetric formal Fourier-Jacobi series. Assuming an upper bound on the affine covering number of the Siegel modular variety associated with Γ, we prove that all formal Siegel modular forms are given by Fourier-Jacobi expansions of classical holomorphic Siegel modular forms. We also show that the required upper bound is always met if 2 ≤ n ≤ 4. As an application we consider the case of the paramodular group of squarefree level and genus 2.