On vector valued Siegel modular forms of degree 2 with small levels

Abstract

In this paper, we show that the space of vector valued Siegel modular forms of $\Gamma_{0} (N) \subset \mathrm{Sp}(2, \mathbb{Z})$ with respect to the symmetric tensor of degree $2$ has a simple unified structure for $N=2,3,4$. Each structure is similar to the structure of the full modular group.