The unbounded denominators conjecture for the noncongruence subgroups of index 7

We study modular forms for the minimal index noncongruence subgroups of the modular group. Our main theorem is a proof of the unbounded denominator conjecture for these groups, and we also provide a study of the Fourier coefficients of Eisenstein series for one of these minimal groups.

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Bibliographic Details
Published in:Journal of number theory 2022-11, Vol.240, p.611-640, Article 611
Main Authors: Fiori, Andrew, Franc, Cameron
Format: Article
Language:English
Subjects:
Eisenstein series
Noncongruence modular forms
Unbounded denominators conjecture
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Summary:We study modular forms for the minimal index noncongruence subgroups of the modular group. Our main theorem is a proof of the unbounded denominator conjecture for these groups, and we also provide a study of the Fourier coefficients of Eisenstein series for one of these minimal groups.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2021.11.014