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arXiv · 0811.2259

Modular Forms of weight 8 for $Γ_g(1,2)$

M. Oura·C. Poor·R. Salvati Manni·D. Yuen
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Abstract

We complete the program indicated by the Ansatz of D'Hoker and Phong in genus ~4 by proving the uniqueness of the restriction to Jacobians of the weight 8 Siegel cusp forms satisfying the Anstaz. We prove $\dim [Γ_4(1,2),8]_0=2$ and $\dim [Γ_4(1,2),8]=7$. In each genus, we classify the linear relations among the self-dual lattices of rank {16}. We extend the program to genus ~5 by constructing the unique linear combination of theta series that satisfies the Ansatz.

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M. Oura, C. Poor, R. Salvati Manni, D. Yuen. 2009-07-22. Modular Forms of weight 8 for $Γ_g(1,2)$. https://arxiv.org/abs/0811.2259

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