  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 are known for $g\leq 7$. They
can all be constructed using families of Galois coverings of curves satisfying
a numerical condition. These families are already classified in cases where: a)
the Galois group is cyclic, b) it is abelian and the family is 1-dimensional,
and c) $g\leq 9$. By means of carefully designed computations and theoretical
arguments excluding a large number of cases we are able to prove that for
$g\leq 100$ there are no other families than those already known.
