  Given a family of Galois coverings of the projective line we give a simple
sufficient condition ensuring that the closure of the image of the family via
the period mapping is a special (or Shimura) subvariety in A_g. By a computer
program we get the list of all families in genus up to 8 satisfying our
condition. There is no family in genus 8, all of them are in genus at most 7.
These examples are related to a conjecture of Oort. Among them we get the
cyclic examples constructed by various authors (Shimura, Mostow, De Jong-Noot,
Rohde, Moonen and others) and the abelian non-cyclic examples found by
Moonen-Oort. We get 7 new non-abelian examples.
