Contributions from conjugacy classes of regular elliptic elements in 𝑆𝑝(𝑛,𝑍) to the dimension formula

Abstract

The dimension of the space of cusp forms on the degree n n Siegel upper half-space can be obtained from the Selberg trace formula; in this paper we compute the contribution from the conjugacy classes of regular elliptic elements in Sp ⁡ ( n , Z ) \operatorname {Sp}(n,{\mathbf {Z}}) using Weyl’s character formula for representations of GL ( n , C ) {\text {GL}}(n,{\mathbf {C}}) .