Siegel modular forms of degree two and level five

Abstract

We construct a ring of meromorphic Siegel modular forms of degree 2 and level 5, with singularities supported on an arrangement of Humbert surfaces, which is generated by four singular theta lifts of weights 1, 1, 2, 2 and their Jacobian. We use this to prove that the ring of holomorphic Siegel modular forms of degree 2 and level ${\Gamma }_0(5)$ is minimally generated by eighteen modular forms of weights 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 10, 11, 11, 11, 13, 13, 13, 15.

11 pages

References in corpus (1)

• Congruence Subgroups and Orthogonal Groups