Document Type

Article

Publication Date

8-2018

Embargo Period

8-2019

Publication Title

Ramanujan Journal

Abstract

We consider the set of classical newforms with rational coefficients and no complex multiplication. We study the distribution of quadratic twist-classes of these forms with respect to weight k and minimal level N. We conjecture that for each weight k ≥ 6, there are only finitely many classes. In large weights, we make this conjecture effective: in weights 18 ≤ k ≤ 24, all classes have N ≤ 30; in weights 26 ≤ k ≤ 50, all classes have N ∈ {2,6}; and in weights k ≥ 52, there are no classes at all. We study some of the newforms appearing on our conjecturally complete list in more detail, especially in the cases N = 2, 3, 4, 6, and 8, where formulas can be kept nearly as simple as those for the classical case N = 1.

Volume

46

Issue

3

First Page

835

Last Page

862

DOI

https://doi.org/10.1007/s11139-017-9914-5

ISSN

1382-4090

Comments

This is a pre-print of an article published in The Ramanujan Journal. The final authenticated version is available online at: https://doi.org/10.1007/s11139-017-9914-5

Rights

© Springer Science+Business Media New York 2018

Available for download on Thursday, August 01, 2019

Included in

Mathematics Commons

Share

COinS