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

We study Shimura subvarieties of (Formula presented.) obtained from families of Galois coverings (Formula presented.) where (Formula presented.) is a smooth complex projective curve of genus (Formula presented.) and (Formula presented.). 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 (Formula presented.) for (Formula presented.) and for all (Formula presented.) and for (Formula presented.) and (Formula presented.). In Frediani et al. Shimura varieties in the Torelli locus via Galois coverings, arXiv:1402.0973 similar computations were done in the case (Formula presented.). Here we find 6 families of Galois coverings, all with (Formula presented.) and (Formula presented.) and we show that these are the only families with (Formula presented.) satisfying this sufficient condition. We show that among these examples two families yield new Shimura subvarieties of (Formula presented.) , while the other examples arise from certain Shimura subvarieties of (Formula presented.) already obtained as families of Galois coverings of (Formula presented.) in Frediani et al. Shimura varieties in the Torelli locus via Galois coverings, arXiv:1402.0973. Finally we prove that if a family satisfies this sufficient condition with (Formula presented.) , then (Formula presented.).