On reducible $\ell$-torsion representations of Picard curves

Let $C/\mathbb{Q}$ be a Picard curve and let $\ell\equiv1\pmod3$ be a prime such that the $λ$-torsion representation of the Jacobian of $C$ is reducible for a prime $λ$ of $\mathbb{Q}(ζ_3)$ above $\ell$. We describe the constraints imposed by complex conjugation on the $2$-dimensional subquotient $ρ