Fourier coefficients of noncongruence cuspforms

Wen Ching Winnie Li; Ling Long

doi:10.1112/blms/bdr122

Fourier coefficients of noncongruence cuspforms

Wen Ching Winnie Li, Ling Long

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Given a finite index subgroup of SL₂(ℤ) with modular curve defined over ℚ, under the assumption that the space of weight k (≥2) cuspforms is one-dimensional, we show that a form in this space with Fourier coefficients in ℚ has bounded denominators if and only if it is a congruence modular form.

Original language	English (US)
Pages (from-to)	591-598
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	44
Issue number	3
DOIs	https://doi.org/10.1112/blms/bdr122
State	Published - Jun 2012

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/blms/bdr122

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title = "Fourier coefficients of noncongruence cuspforms",

abstract = "Given a finite index subgroup of SL2(ℤ) with modular curve defined over ℚ, under the assumption that the space of weight k (≥2) cuspforms is one-dimensional, we show that a form in this space with Fourier coefficients in ℚ has bounded denominators if and only if it is a congruence modular form.",

author = "Li, {Wen Ching Winnie} and Ling Long",

note = "Funding Information: The research of the first author is partially supported by the NSF grants DMS-0801096 and DMS-1101368, and the second author by the NSF grant DMS-1001332.",

year = "2012",

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AU - Li, Wen Ching Winnie

AU - Long, Ling

N1 - Funding Information: The research of the first author is partially supported by the NSF grants DMS-0801096 and DMS-1101368, and the second author by the NSF grant DMS-1001332.

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Y1 - 2012/6

N2 - Given a finite index subgroup of SL2(ℤ) with modular curve defined over ℚ, under the assumption that the space of weight k (≥2) cuspforms is one-dimensional, we show that a form in this space with Fourier coefficients in ℚ has bounded denominators if and only if it is a congruence modular form.

AB - Given a finite index subgroup of SL2(ℤ) with modular curve defined over ℚ, under the assumption that the space of weight k (≥2) cuspforms is one-dimensional, we show that a form in this space with Fourier coefficients in ℚ has bounded denominators if and only if it is a congruence modular form.

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Fourier coefficients of noncongruence cuspforms

Abstract

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