Smooth quotients of principally polarized abelian varieties

We give an explicit characterization of all principally polarized abelian varieties $(A,\Theta)$ such that there is a finite subgroup $G\subseteq\mathrm{Aut}(A,\Theta)$ such that the quotient variety $A/G$ is smooth. We also give a complete classification of smooth quotients of Jacobians of curves.