CM newforms with rational coefficients

Mathematics – Number Theory

Scientific paper

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17 pages, 3 tables; final version: Rem 7.2, Thm 9.2 added, references updated, minor changes

Scientific paper

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.

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