  It is known that the moduli space of plane quartic curves is birational to an
arithmetic quotient of a 6-dimensional complex ball. In this paper, we shall
show that there exists a 15-dimensional space of meromorphic automorphic forms
on the complex ball which gives a birational embedding of the moduli space of
plane quartics with level 2 structure into 14-dimensional projective space.
This map coincides with the one given by Coble by using Gopel invariants.
