Weight-dependent congruence properties of modular forms

D. Choi; Y. Choie

doi:10.1016/j.jnt.2006.05.008

Weight-dependent congruence properties of modular forms

D. Choi, Y. Choie

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

2 Citations (Scopus)

Abstract

In this paper, we study congruence properties of modular forms in various ways. By proving a weight-dependent congruence property of modular forms, we give some sufficient conditions, in terms of the weights of modular forms, for a modular form to be non-p-ordinary. As applications of our main theorem we derive a linear relation among coefficients of new forms. Furthermore, congruence relations among special values of Dedekind zeta functions of real quadratic fields are derived.

Original language	English
Pages (from-to)	301-313
Number of pages	13
Journal	Journal of Number Theory
Volume	122
Issue number	2
DOIs	https://doi.org/10.1016/j.jnt.2006.05.008
Publication status	Published - 2007 Feb
Externally published	Yes

Keywords

11F11
11F33
Congruences
Modular form
Newform
Non-p-ordinary

ASJC Scopus subject areas

Algebra and Number Theory

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title = "Weight-dependent congruence properties of modular forms",

abstract = "In this paper, we study congruence properties of modular forms in various ways. By proving a weight-dependent congruence property of modular forms, we give some sufficient conditions, in terms of the weights of modular forms, for a modular form to be non-p-ordinary. As applications of our main theorem we derive a linear relation among coefficients of new forms. Furthermore, congruence relations among special values of Dedekind zeta functions of real quadratic fields are derived.",

keywords = "11F11, 11F33, Congruences, Modular form, Newform, Non-p-ordinary",

author = "D. Choi and Y. Choie",

note = "Funding Information: This work was partially supported by KOSEF R01-2003-00011596-0 and ITRC. Corresponding author. E-mail addresses: choija@postech.ac.kr (D. Choi), yjc@postech.ac.kr (Y. Choie).",

year = "2007",

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T1 - Weight-dependent congruence properties of modular forms

AU - Choi, D.

AU - Choie, Y.

N1 - Funding Information: This work was partially supported by KOSEF R01-2003-00011596-0 and ITRC. Corresponding author. E-mail addresses: choija@postech.ac.kr (D. Choi), yjc@postech.ac.kr (Y. Choie).

PY - 2007/2

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N2 - In this paper, we study congruence properties of modular forms in various ways. By proving a weight-dependent congruence property of modular forms, we give some sufficient conditions, in terms of the weights of modular forms, for a modular form to be non-p-ordinary. As applications of our main theorem we derive a linear relation among coefficients of new forms. Furthermore, congruence relations among special values of Dedekind zeta functions of real quadratic fields are derived.

AB - In this paper, we study congruence properties of modular forms in various ways. By proving a weight-dependent congruence property of modular forms, we give some sufficient conditions, in terms of the weights of modular forms, for a modular form to be non-p-ordinary. As applications of our main theorem we derive a linear relation among coefficients of new forms. Furthermore, congruence relations among special values of Dedekind zeta functions of real quadratic fields are derived.

KW - 11F11

KW - 11F33

KW - Congruences

KW - Modular form

KW - Newform

KW - Non-p-ordinary

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DO - 10.1016/j.jnt.2006.05.008

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EP - 313

JO - Journal of Number Theory

JF - Journal of Number Theory

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