Products of Eisenstein series and Fourier expansions of modular forms at cusps

JOURNAL OF NUMBER THEORY

卷:188

Article

Dickson, Martin¹  Neururer, Michael¹ 

[1] Tech Univ Darmstadt, Schlossgartenstr 7, D-64289 Darmstadt, Germany

关键词: Modular forms;    Modular symbols;    Fourier expansions;   

DOI  :  10.1016/j.jnt.2017.12.013

来源: Elsevier

【 摘 要 】

We show, for levels of the form N = p(a)q(b)N' with N' squarefree, that in weights k >= 4 every cusp form f is an element of S-k(N) is a linear combination of products of certain Eisenstein series of lower weight. In weight k = 2 we show that the forms f which can be obtained in this way are precisely those in the subspace generated by eigenforms g with L(g,1) not equal 0. As an application of such representations of modular forms we can calculate Fourier expansions of modular forms at arbitrary cusps and we give several examples of such expansions in the last section. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free