CM newforms with rational coefficients
arXiv:math/0511228
Abstract
We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce tables for weights 3 and 4, where finiteness holds unconditionally.
17 pages, 3 tables; final version: Rem 7.2, Thm 9.2 added, references updated, minor changes