Galois representations attached to Picard curves

Let J(C) be the Jacobian of a Picard curve C defined over a number field K containing Q(ζ3). We consider the family of l-adic representations defined by the natural action of the Galois group on the l-power torsion of J(C).We show that for a Picard curve C with endomorphism ring Z[ζ3] the images of these representations are full for all but finitely many primes l. We consider the reduction modulo l of the image of , that is, the action of on the l-torsion of the Jacobian. This gives a representation ρl into either GL3(Fl) or into a unitary group over Fl2, depending on the splitting behavior of l in Q(ζ3). It is sufficient to show that the image of ρl is full in order to show that the image of is full.