Abstract

For any we study the group algebra decomposition of an -dimensional family of principally polarized abelian varieties of dimension with an action of the dihedral group of order . For any odd prime and we compute the induced polarization on the isotypical components of these varieties and some other distinguished subvarieties. In the case of the family contains a one-dimensional family of Jacobians. We use this to compute a period matrix for Klein's icosahedral curve of genus 5.