The spaces of new forms for harmonic weak Maalss forms and their level raising properties modulo ℓ

Dohoon Choi; Subong Lim

doi:10.1007/s11139-014-9557-8

The spaces of new forms for harmonic weak Maalss forms and their level raising properties modulo ℓ

Dohoon Choi, Subong Lim

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Bringmann et al. (Math. Ann., 355(3):1085–1121, 2013) and Guerzhoy (Proc. Am. Math. Soc., 136:3051–3059, 2008) studied the multiplicity two Hecke theory for weakly holomorphic modular forms on the full modular group. In this note, we consider a generalization of these results to congruence subgroups $$\Gamma _1(N)$$Γ1(N) with a new form theory. Using this, we define new forms for harmonic weak Maass forms and study a level raising property modulo $$\ell $$ℓ for them.

Original language	English
Pages (from-to)	65-77
Number of pages	13
Journal	Ramanujan Journal
Volume	37
Issue number	1
DOIs	https://doi.org/10.1007/s11139-014-9557-8
Publication status	Published - 2015 May 1
Externally published	Yes

Keywords

Harmonic weak Maass forms
Hecke operator

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s11139-014-9557-8

Cite this

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abstract = "Bringmann et al. (Math. Ann., 355(3):1085–1121, 2013) and Guerzhoy (Proc. Am. Math. Soc., 136:3051–3059, 2008) studied the multiplicity two Hecke theory for weakly holomorphic modular forms on the full modular group. In this note, we consider a generalization of these results to congruence subgroups $$\Gamma _1(N)$$Γ1(N) with a new form theory. Using this, we define new forms for harmonic weak Maass forms and study a level raising property modulo $$\ell $$ℓ for them.",

keywords = "Harmonic weak Maass forms, Hecke operator",

author = "Dohoon Choi and Subong Lim",

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AU - Lim, Subong

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N2 - Bringmann et al. (Math. Ann., 355(3):1085–1121, 2013) and Guerzhoy (Proc. Am. Math. Soc., 136:3051–3059, 2008) studied the multiplicity two Hecke theory for weakly holomorphic modular forms on the full modular group. In this note, we consider a generalization of these results to congruence subgroups $$\Gamma _1(N)$$Γ1(N) with a new form theory. Using this, we define new forms for harmonic weak Maass forms and study a level raising property modulo $$\ell $$ℓ for them.

AB - Bringmann et al. (Math. Ann., 355(3):1085–1121, 2013) and Guerzhoy (Proc. Am. Math. Soc., 136:3051–3059, 2008) studied the multiplicity two Hecke theory for weakly holomorphic modular forms on the full modular group. In this note, we consider a generalization of these results to congruence subgroups $$\Gamma _1(N)$$Γ1(N) with a new form theory. Using this, we define new forms for harmonic weak Maass forms and study a level raising property modulo $$\ell $$ℓ for them.

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The spaces of new forms for harmonic weak Maalss forms and their level raising properties modulo ℓ

Abstract

Keywords

ASJC Scopus subject areas

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