On vector valued Siegel modular forms of degree 2 with small levels
Let \(\Gamma=\Gamma_0(N) \subseteq \text{Sp}_2(\mathbb{Z})\) (genus \(2\)) for \(N=2,3\) or \(4\), and consider the space \[ A_{*,2}(\Gamma) = \oplus_{k\in\mathbb{Z}} A_{k,2}(\Gamma), \] where \(A_{k,2}(\Gamma)\) is the space of Siegel modular forms of weight \(\rho = \text{Sym}^2 \otimes \det^k\). The main result of this paper is that \(A_{*,2}(\Gamma)\) is generated by ten specific modular forms, and that these generators can be constructed by differential operators.
scientific article; zbMATH DE number 6110919