Siegel modular forms of degree two and level five

Haowu Wang; Brandon Williams

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arXiv · 2110.07241

Siegel modular forms of degree two and level five

Haowu Wang·Brandon Williams

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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.

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Haowu Wang, Brandon Williams. 2021-10-14. Siegel modular forms of degree two and level five. https://arxiv.org/abs/2110.07241

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