Hecke structures of weakly holomorphic modular forms and their algebraic properties

Dohoon Choi, Subong Lim

Research output: Contribution to journalArticle

Abstract

Let Sk !1(N)) be the space of weakly holomorphic cusp forms of weight k on Γ1(N) with an even integer k>2 and Mk !1(N)) be the space of weakly holomorphic modular forms of weight k on Γ1(N). Further, let z denote a complex variable and D:=[Formula presented][Formula presented]. In this paper, we construct a basis of the space Sk !1(N))/Dk−1(M2−k !1(N))) consisting of Hecke eigenforms by using the Eichler–Shimura cohomology theory. Further, we study algebraicity of CM values of weakly holomorphic modular forms in the basis. This applies to an analogue of the Chowla–Selberg formula for a mock modular form whose shadow is the Ramanujan delta function.

Original languageEnglish
Pages (from-to)428-450
Number of pages23
JournalJournal of Number Theory
Volume184
DOIs
Publication statusPublished - 2018 Mar 1
Externally publishedYes

Fingerprint

Modular Forms
Cusp Form
Delta Function
Complex Variables
Ramanujan
Cohomology
Denote
Analogue
Integer

Keywords

  • Eichler–Shimura cohomology
  • Hecke operator
  • Weakly holomorphic modular form

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Hecke structures of weakly holomorphic modular forms and their algebraic properties. / Choi, Dohoon; Lim, Subong.

In: Journal of Number Theory, Vol. 184, 01.03.2018, p. 428-450.

Research output: Contribution to journalArticle

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