  We study families of Galois covers of curves of positive genus. It is known
that under a numerical condition these families yield Shimura subvarieties
generically contained in the Jacobian locus. We prove that there are only 6
families satisfying this condition, all of them in genus 2,3 or 4. We also show
that these families admit two fibrations in totally geodesic subvarieties,
generalizing a result of Grushevsky and M\"oller. Countably many of these
fibres are Shimura. Thus the Jacobian locus contains infinitely many Shimura
subvarieties of positive dimension of any $g \leq 4$.
