Personal tools
You are here: Home Publications On the generation of the coefficient field of a newform by a single Hecke eigenvalue

On the generation of the coefficient field of a newform by a single Hecke eigenvalue

Koopa Tak-Lun Koo, William Stein and Gabor Wiese

Number 17
Author Gabor Wiese
Project A09
Year 2008

Let f be a non-CM newform of weight k ≥ 2. Let L be a subfield of the coefficient field of f. We completely settle the question of the density of the set of primes p such that the p-th coefficient of f generates the field L. This density is determined by the inner twists of f. As a particular case, we obtain that in the absence of non-trivial inner twists, the density is 1 for L equal to the whole coefficient field. We also present some new data on reducibility of Hecke polynomials, which suggest questions for further investigation.

More information about this publication…

Document Actions
« July 2023 »
July
MoTuWeThFrSaSu
12
3456789
10111213141516
17181920212223
24252627282930
31