2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159909Let A be a modular abelian variety over \Q of arbitrary even dimension. We establish criteria to prevent a given quaternion algebra over a totally real number field to be the endomorphism algebra of A over \bar\Q. We accomplish this by analyzing the representation of Gal(\bar\Q /\Q) on the points of N-torsion of A at primes N which ramify in B.Math. Res. letters 15 (2008), 251-263. Misprint on Theorem 1.2 (ii) correctedNumber TheoryAlgebraic Geometry11G18, 14G35text