Bounds for the coefficients of cusp forms for Γ0(3)

We give bounds of the coefficients of cusp forms f for Γ0(3) in terms of its first dk numbers of coefficients of f and f|kW3, where W3 is the Fricke involution of level 3, and dk is the dimension of the space Sk(Γ0(3)) of weight k cusp forms for Γ0(3). In particular, we find bounds of the coefficien...

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Bibliographic Details
Published inJournal of number theory Vol. 188; pp. 48 - 70
Main Authors Choi, SoYoung, Im, Bo-Hae
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2018
Subjects
Weakly holomorphic modular form
11F03
Weakly holomorphic modular form
11F11
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Summary:We give bounds of the coefficients of cusp forms f for Γ0(3) in terms of its first dk numbers of coefficients of f and f|kW3, where W3 is the Fricke involution of level 3, and dk is the dimension of the space Sk(Γ0(3)) of weight k cusp forms for Γ0(3). In particular, we find bounds of the coefficients of cusp forms for Γ0+(3).
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2018.01.008