Siegel modular forms and finite symplectic groups

Abstract

The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this representation, for various (small) values of the genus and the level, into irreducible representations. As a consequence we obtain uniqueness results for certain modular forms related to the superstring measure, a better understanding of certain modular forms in genus three studied by D'Hoker and Phong as well as a new construction of Miyawaki's cusp form of weight twelve in genus three.

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References in corpus (7)

• Modular Forms and Three Loop Superstring Amplitudes
• Asyzygies, modular forms, and the superstring measure II
• Superstring scattering amplitudes in higher genus
• Remarks on Superstring amplitudes in higher genus
• Two loop superstring amplitudes and S_6 representations
• Miyawaki's $F_{12}$ Spinor L-function Conjecture
• On the image of code polynomials under theta map

Cited by in corpus (8)

• Modular Forms and Three Loop Superstring Amplitudes
• Superstring measure and non-renormalization of the three-point amplitude
• Getting superstring amplitudes by degenerating Riemann surfaces
• The vanishing of two-point functions for three-loop superstring scattering amplitudes
• The superstring cosmological constant and the Schottky form in genus 5
• Towards Functoriality Of Spinor L-functions
• Binary Forms and the Hyperelliptic Superstring Ansatz
• Construction of chiral superstring measure