  In this article we give an explicit construction of the moduli space of
trigonal superelliptic curves with level 3 structure. The construction is given
in terms of point sets on the projective line and leads to a closed formula for
the number of connected (and irreducible) components of the moduli space. The
results of the article generalise the description of the moduli space of
hyperelliptic curves with level 2 structure, due to Dolgachev and Ortland,
Runge and Tsuyumine.
