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arXiv · 1309.1766

Vector Valued Siegel Modular Forms for Γ_2[2,4] and Sym^2

Thomas Wieber
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Abstract

We develop two structure theorems for vector valued Siegel modular forms for Igusa's subgroup Γ_2[2,4], the multiplier system induced by the theta constants and the representation Sym^2. In the proof, we identify some of these modular forms with rational tensors with easily handleable poles on P^3\C. It follows that the observed modules of modular forms are generated by the Rankin-Cohen brackets of the four theta series of the second kind.

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Thomas Wieber. 2013-09-06. Vector Valued Siegel Modular Forms for Γ_2[2,4] and Sym^2. https://arxiv.org/abs/1309.1766

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