ON THE THETA OPERATOR FOR MODULAR FORMS MODULO PRIME POWERS

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ON THE THETA OPERATOR FOR MODULAR FORMS MODULO PRIME POWERS. / Chen, Imin; Kiming, Ian.

In: Mathematika, Vol. 62, No. 2, 2016, p. 321- 336.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Chen, I & Kiming, I 2016, 'ON THE THETA OPERATOR FOR MODULAR FORMS MODULO PRIME POWERS', Mathematika, vol. 62, no. 2, pp. 321- 336. https://doi.org/10.1112/S0025579315000212

APA

Chen, I., & Kiming, I. (2016). ON THE THETA OPERATOR FOR MODULAR FORMS MODULO PRIME POWERS. Mathematika, 62(2), 321- 336. https://doi.org/10.1112/S0025579315000212

Vancouver

Chen I, Kiming I. ON THE THETA OPERATOR FOR MODULAR FORMS MODULO PRIME POWERS. Mathematika. 2016;62(2):321- 336. https://doi.org/10.1112/S0025579315000212

Author

Chen, Imin ; Kiming, Ian. / ON THE THETA OPERATOR FOR MODULAR FORMS MODULO PRIME POWERS. In: Mathematika. 2016 ; Vol. 62, No. 2. pp. 321- 336.

Bibtex

@article{b0e8f124fc9d4793928466d2f1721c07,
title = "ON THE THETA OPERATOR FOR MODULAR FORMS MODULO PRIME POWERS",
abstract = "We consider the classical theta operator θ on modular forms modulo pm and level N prime to p, where p is a prime greater than three. Our main result is that θ mod pm will map forms of weight k to forms of weight k+2+2pm−1(p−1) and that this weight is optimal in certain cases when m is at least two. Thus, the natural expectation that θ mod pm should map to weight k+2+pm−1(p−1) is shown to be false. The primary motivation for this study is that application of the θ operator on eigenforms mod pm corresponds to twisting the attached Galois representations with the cyclotomic character. Our construction of the θ-operator mod pm gives an explicit weight bound on the twist of a modular mod pm Galois representation by the cyclotomic character.",
author = "Imin Chen and Ian Kiming",
year = "2016",
doi = "10.1112/S0025579315000212",
language = "English",
volume = "62",
pages = "321-- 336",
journal = "Mathematika",
issn = "0025-5793",
publisher = "London Mathematical Society",
number = "2",

}

RIS

TY - JOUR

T1 - ON THE THETA OPERATOR FOR MODULAR FORMS MODULO PRIME POWERS

AU - Chen, Imin

AU - Kiming, Ian

PY - 2016

Y1 - 2016

N2 - We consider the classical theta operator θ on modular forms modulo pm and level N prime to p, where p is a prime greater than three. Our main result is that θ mod pm will map forms of weight k to forms of weight k+2+2pm−1(p−1) and that this weight is optimal in certain cases when m is at least two. Thus, the natural expectation that θ mod pm should map to weight k+2+pm−1(p−1) is shown to be false. The primary motivation for this study is that application of the θ operator on eigenforms mod pm corresponds to twisting the attached Galois representations with the cyclotomic character. Our construction of the θ-operator mod pm gives an explicit weight bound on the twist of a modular mod pm Galois representation by the cyclotomic character.

AB - We consider the classical theta operator θ on modular forms modulo pm and level N prime to p, where p is a prime greater than three. Our main result is that θ mod pm will map forms of weight k to forms of weight k+2+2pm−1(p−1) and that this weight is optimal in certain cases when m is at least two. Thus, the natural expectation that θ mod pm should map to weight k+2+pm−1(p−1) is shown to be false. The primary motivation for this study is that application of the θ operator on eigenforms mod pm corresponds to twisting the attached Galois representations with the cyclotomic character. Our construction of the θ-operator mod pm gives an explicit weight bound on the twist of a modular mod pm Galois representation by the cyclotomic character.

U2 - 10.1112/S0025579315000212

DO - 10.1112/S0025579315000212

M3 - Journal article

VL - 62

SP - 321

EP - 336

JO - Mathematika

JF - Mathematika

SN - 0025-5793

IS - 2

ER -

ID: 154005878