On mod p representations which are defined over F_p: II

2009/05/27 by L. J. P. Kilford, Kilford, L. J. P., Gabor Wiese +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.NT #msc:11F25 #msc:11F33 #msc:11R29

paper · pdf · doi:10.48550/arxiv.0905.4372

10 pages

arxiv created 2009/05/27 · arxiv updated 2009/12/01

Abstract

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,χ_l,k for all primes l, all weights k>1 and all characters χtaking 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.

Citations

• CM newforms with rational coefficients

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