  Given a finite group $G$ and an abelian variety $A$ acted on by $G$, to any
subgroup $H$ of $G$, we associate an abelian subvariety $A_H$ on which the
associated Hecke algebra $\mathcal{H}_H$ for $H$ in $G$ acts. Any irreducible
rational representation $\widetilde W$ of $\mathcal{H}_H$ induces an abelian
subvariety of $A_H$ in a natural way. In this paper we give equations for this
abelian subvariety. In a special case these equations become much easier. We
work out some examples.
