Modular forms invariant under non-split Cartan subgroups

Mercuri, Pietro; Schoof, René

doi:10.1090/mcom/3503

Modular forms invariant under non-split Cartan subgroups
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Math. Comp. 89 (2020), 1969-1991 Request permission

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 $\mathbb {Q}$ for the canonical embeddings of the associated modular curves.

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