Modular forms invariant under non-split Cartan subgroups
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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.References
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Additional Information
- Pietro Mercuri
- Affiliation: Dipartimento di Matematica, 2a Università di Roma “Tor Vergata”, Roma, Italy 00133
- MR Author ID: 1105728
- Email: mercuri.ptr@gmail.com
- René Schoof
- Affiliation: Dipartimento di Matematica, 2a Università di Roma “Tor Vergata”, Roma, Italy 00133
- Email: schoof.rene@gmail.com
- Received by editor(s): July 2, 2019
- Received by editor(s) in revised form: October 16, 2019, and November 1, 2019
- Published electronically: February 3, 2020
- © Copyright 2020 American Mathematical Society
- Journal: Math. Comp. 89 (2020), 1969-1991
- MSC (2010): Primary 11F30, 14G35; Secondary 11Y40, 14Q05, 20C33
- DOI: https://doi.org/10.1090/mcom/3503
- MathSciNet review: 4081925