TY - JOUR

T1 - CM newforms with rational coefficients

AU - Schütt, Matthias

N1 - Funding information: I am indepted to K. Hulek for his continuous interest and encouragement. Partial support by the DFG Schwerpunkt 1094 “Globale Methoden in der komplexen Geometrie” is gratefully acknowledged. My thanks go also to the referee for helpful comments. Part of the revising took place while I enjoyed the hospitality of the Dipartimento di Matematica “Frederico Enriques” of Milano University. Funding from the network Arithmetic Algebraic Geometry, a Marie Curie Research Training Network, is gratefully acknowledged. I particularly thank M. Bertolini and B. van Geemen. The final version was prepared while I was funded by DFG under grant Schu 2266/2-2.

PY - 2009/7

Y1 - 2009/7

N2 - 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.

AB - 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.

KW - Complex multiplication

KW - Hecke character

KW - Modular form

UR - http://www.scopus.com/inward/record.url?scp=67949089623&partnerID=8YFLogxK

UR - https://arxiv.org/abs/math/0511228

U2 - 10.1007/s11139-008-9147-8

DO - 10.1007/s11139-008-9147-8

M3 - Article

AN - SCOPUS:67949089623

VL - 19

SP - 187

EP - 205

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 2

ER -