Dimensions Of Spaces Of Siegel Cusp Forms Of Degree Two And Three (memoirs Of The American Mathematical Society)

The Selberg trace formula reduces the problem of calculating the dimension of cusp forms of Siegal upper-half space, when the fundamental domain is not compact but has finite volume, to the evaluation of certain integrals combining with special values of certain zeta functions. In this paper, all types of these integrals are evaluated and hence explicit formulas in term of polynomial of the weight can be obtained once the conjugacy classes of Sp(2, Z) and Sp(3, Z) are given explicitly. Indeed, we successfully obtain dimension formulas for the vector spaces of cusp forms of degree two with respect to Sp(2, Z) and its principal congruence subgroups