Siegel modular forms of level (4,8) and weight two

2025/04/01 by Freitag, Eberhard, Manni, Riccardo Salvati
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.00653

Abstract

We consider the space of Siegel modular forms of genus g of weight two relative to the main congruence subgroup of level 2 and to Igusa's group Γ_g(4, 8) and Γ_g(2,4).One of the main results of this paper is that in the case g≥ 8 the space [Γ_g[4,8],2] is generated by the products of 4 theta nullwerte. Thus this note can be considered as a completion of the example at the end of [Fr].

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