Klingen vectors of level 2 for GSp(4)

Abstract

The theory of Siegel modular forms generalizes classical elliptic modular forms which is, in fact, the degree one case. Dimension formulas for spaces of elliptic modular forms have been much studied, however, the situation for Siegel modular forms still needs a lot of work to do. In particular, the dimension formula for the space of Siegel cusp forms of degree 2 with respect to the congruence subgroup $\Gamma$ is related to the dimensional data of spaces of fixed vectors with respect to the congruence subgroup $\Gamma$ for the irreducible, admissible representations of GSp(4, F), where F is a $\mathfrak{p}$-adic field. In this thesis, we use a variety of methods to determine the dimensions of the spaces of invariant vectors under the Klingen congruence subgroup of level $\mathfrak{p}^2$ for all irreducible, admissible representations of the algebraic group GSp(4) over F.