[en] The behaviour of Hecke polynomials modulo p has been the subject of some study. In this note we show that, if p is a prime, the set of integers N such that the Hecke polynomials T^{N,\chi}_{l,k} for all primes l, all weights k>1 and all characters \chi taking values in {+1,-1} splits completely modulo p has density 0, unconditionally for p=2 and under the Cohen-Lenstra heuristics for odd p. The method of proof is based on the construction of suitable dihedral modular forms.
Disciplines :
Mathématiques
Auteur, co-auteur :
Kilford, L. J. P.
WIESE, Gabor ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Langue du document :
Anglais
Titre :
On mod $p$ representations which are defined over $\Bbb F_p$: II
