Twists of newforms and pseudo-eigenvalues ofW-operators
Twists of newforms and pseudo-eigenvalues ofW-operators
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DOI：
10.1007/bf01390245
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发表时间：
1978-10
影响因子：
3.1
通讯作者：
A. Atkin;Wein-Ch'ing Winnie Li
中科院分区：
文献类型：
--
作者：
A. Atkin;Wein-Ch'ing Winnie Li
设F是权为k、水平为N、特征标为v的尖顶归一化新形式，且)~是某个导体M的本原特征标.如果M是N的相对素数，则F的Z的扭转Fx是一个新形式，并且可以用F的整体常数来表示Fx的整体常数(参见[Weil]，[Li]).如果M对N不是相对质数，情况并不总是如此，这就是我们在本文中研究的情况。设q是除N的素数，q是N的q-主因子，本文的另一个主要内容是研究算子wq在F(Cf)处的伪本征值2q(F)。W 1表示定义)，在表示理论语言中称为局部常量。乘积[I 2Q(F)给出(直到涉及的已知因数
Let F be a cuspidal normalized newform of weight k, level N and character v; and let)~ be a primitive character of some conductor M. If M is relatively prime to N, then the twist F x of F by Z is a newform, and one can express the global constant for FX in terms of that for F in this case (cf.[Weil],[Li]). The situation is not always so if M is not relatively prime to N. This is the case we investigate in the present paper. The special case when e is trivial and Z is quadratic was discussed in [ALl.Let q be a prime dividing N, and Q be the q-primary factor of N. Another main theme of this paper is to study the pseudo-eigenvalue 2q (F) of the operator WQ at F (cf. w 1 for definition), known as the local constant in the representationtheoretic language. The product [I 2q (F) gives (up to a known factor involving