Fixed points and conjugacy classes of regular elliptic elements in 𝑆𝑝(3,𝑍)

Abstract

In this paper, we obtain 13 13 isolated fixed points (up to a Sp ⁡ ( 3 , Z ) \operatorname {Sp}(3,{\mathbf {Z}}) -equivalence) and 86 86 conjugacy classes of regular elliptic elements in Sp ⁡ ( 3 , Z ) \operatorname {Sp}(3,{\mathbf {Z}}) . Hence the contributions from regular elliptic conjugacy classes in Sp ⁡ ( 3 , Z ) \operatorname {Sp}(3,{\mathbf {Z}}) to the dimension formula computed via the Selberg trace formula can be computed explictly by the main theorem of [ 4 {\mathbf {4}} or 5 {\mathbf {5}} ].