Andrew Coursin

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 $\lambda$-torsion representation of the Jacobian of $C$ is reducible for a prime $\lambda$ of $\mathbb{Q}(\zeta_3)$ above $\ell$. We describe the constraints imposed by complex conjugation on the $2$-dimensional subquotient $\rho$...