Theses and Dissertations Collection

This dissertation presents fundamental results on the structure of paramodular Hecke algebras for Siegel paramodular forms of prime level. We exhibit four double coset generators for the Hecke ring as well as explicit formulas for computing the coefficients and good coset representatives that appear in the multiplication of two elements of this ring. In addition, we show that there is a correspondence between the value of the coefficients appearing in a product of these Hecke operators and the number of sub-lattices of a paramodular lattice over a non-archimedean local field.