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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Modular forms invariant under non-split Cartan subgroups


Authors: Pietro Mercuri and René Schoof
Journal: Math. Comp. 89 (2020), 1969-1991
MSC (2010): Primary 11F30, 14G35; Secondary 11Y40, 14Q05, 20C33
DOI: https://doi.org/10.1090/mcom/3503
Published electronically: February 3, 2020
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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.


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Additional Information

Pietro Mercuri
Affiliation: Dipartimento di Matematica, 2\textsuperscript{a} Università di Roma “Tor Vergata”, Roma, Italy 00133
Email: mercuri.ptr@gmail.com

René Schoof
Affiliation: Dipartimento di Matematica, 2\textsuperscript{a} Università di Roma “Tor Vergata”, Roma, Italy 00133
Email: schoof.rene@gmail.com

DOI: https://doi.org/10.1090/mcom/3503
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
Article copyright: © Copyright 2020 American Mathematical Society