Arithmetic properties for the minus space of weakly holomorphic modular forms

JOURNAL OF NUMBER THEORY

卷:196

Article

Choi, So Young¹  Kim, Chang Heon²  Lee, Kyung Seung² 

[1] Gyeongsang Natl Univ, Dept Math Educ & RINS, 501 Jinjudae Ro, Jinju 660701, South Korea

[2] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

关键词: Hecke group;    Fricke involution;    Atkin-Lehner involution;    Weakly holomorphic modular form;   

DOI  :  10.1016/j.jnt.2018.09.006

来源: Elsevier

【 摘 要 】

Let M-k(!) (p) be the space of weakly holomorphic modular forms of weight k on Gamma(0) (p), and let M-k(!-) (p) be the minus space which is the subspace of M-k(!) (p) consisting of all eigenforms of the Fricke involution W-p with eigenvalue -1. We are interested in finding a canonical basis for the minus space M-k(!-) (p) for certain levels. Using this result, along with previous works of Choi and Kim [CK13], we find a canonical basis for the space M-k(!) (p), and investigate its arithmetic properties. We also give another generalization of [CK13] to the cases of square-free integer levels. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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