Shimura varieties in the Torelli locus via Galois coverings of elliptic curves

We study Shimura subvarieties of obtained from families of Galois coverings where is a smooth complex projective curve of genus and . We give the complete list of all such families that satisfy a simple sufficient condition that ensures that the closure of the image of the family via the Torelli map yields a Shimura subvariety of for and for all and for and . In Frediani et al. Shimura varieties in the Torelli locus via Galois coverings, similar computations were done in the case . Here we find 6 families of Galois coverings, all with and and we show that these are the only families with satisfying this sufficient condition. We show that among these examples two families yield new Shimura subvarieties of , while the other examples arise from certain Shimura subvarieties of already obtained as families of Galois coverings of in Frediani et al. Shimura varieties in the Torelli locus via Galois coverings, . Finally we prove that if a family satisfies this sufficient condition with , then .