Some evidence for the Coleman–Oort conjecture

The Coleman–Oort conjecture says that for large g there are no positive-dimensional Shimura subvarieties of $${\mathsf {A}}_g$$ generically contained in the Jacobian locus. Counterexamples known $$g\le 7$$ . They can all be constructed using families Galois coverings curves satisfying a numerical condition. These already classified cases where: (a) group is cyclic, (b) it abelian and family 1-dimensional, or c) 9$$ By means carefully designed computations theoretical arguments excluding number we able to prove 100$$ other than those known.