Modular forms invariant under non-split Cartan subgroups

Abstract

In this paper we describe a method for computing a basis for the space of weight $2$ cusp forms invariant under a non-split Cartan subgroup of prime level $p$. As an application we compute, for certain small values of $p$, explicit equations over $\mathbf{Q}$ for the canonical embeddings of the associated modular curves.