### Abstract

Let S_{k} ^{!}(Γ_{1}(N)) be the space of weakly holomorphic cusp forms of weight k on Γ_{1}(N) with an even integer k>2 and M_{k} ^{!}(Γ_{1}(N)) be the space of weakly holomorphic modular forms of weight k on Γ_{1}(N). Further, let z denote a complex variable and D:=[Formula presented][Formula presented]. In this paper, we construct a basis of the space S_{k} ^{!}(Γ_{1}(N))/D^{k−1}(M_{2−k} ^{!}(Γ_{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 language | English |
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Pages (from-to) | 428-450 |

Number of pages | 23 |

Journal | Journal of Number Theory |

Volume | 184 |

DOIs | |

Publication status | Published - 2018 Mar 1 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory