An explicit dimension formula for Siegel cusp forms with respect to the non-split symplectic groups

TL;DR

This paper derives an explicit formula for the dimension of vector valued Siegel cusp forms of degree two for certain non-split symplectic groups, extending previous results in the literature.

Contribution

It provides a new explicit dimension formula for Siegel cusp forms on non-split symplectic groups, generalizing earlier formulas.

Findings

Derived an explicit dimension formula for these cusp forms.

Extended previous formulas to non-split symplectic groups.

Utilized results from Hashimoto, Ibukiyama, and Wakatsuki.

Abstract

The purpose of this paper is to give an explicit dimension formula for the spaces of vector valued Siegel cusp forms of degree two with respect to a certain kind of arithmetic subgroups of the non-split Q-forms of Sp(2,R). We obtain our result by using Hashimoto and Ibukiyama's results in [HI80],[HI83] and Wakatsuki's formula in [Wak]. Our result is a generalization of formulae in [Has84,Theorem 4.1] and [Wak,Theorem 6.1].