Reference : On the generation of the coefficient field of a newform by a single Hecke eigenvalue
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/11540
On the generation of the coefficient field of a newform by a single Hecke eigenvalue
English
Koo, Koopa Tak-Lun [> >]
Stein, William [> >]
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2008
Journal de Théorie des Nombres de Bordeaux
20
2
373--384
Yes (verified by ORBilu)
International
1246-7405
[en] #

Let f be a non-CM newform of weight k>1 without nontrivial inner twists. In this article we study the set of primes p such that the eigenvalue a_p(f) of the Hecke operator T_p acting on f generates the field of coefficients of f. We show that this set has density 1, and prove a natural analogue for newforms having inner twists. We also present some new data on reducibility of Hecke polynomials, which suggest questions for further investigation.
http://hdl.handle.net/10993/11540
http://jtnb.cedram.org/item?id=JTNB_2008__20_2_373_0
2477510 (2010d:11047)

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