The fibres of the Prym map of \'etale cyclic coverings of degree 7

We study the Prym varieties arising from 'etale cyclic coverings of degree 7 over a curve of genus 2. These Prym varieties are products of Jacobians JY x JY of genus 3 curves Y with polarization type D=(1,1,1,1,1,7). We describe the fibers of the Prym map between the moduli space of such coverings and the moduli space of abelian sixfolds with polarization type D, admitting an automorphism of order 7.