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.
I: Mathematika, Bind 62, Nr. 2, 2016, s. 321- 336.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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