Repr\'esentations galoisiennes di\'edrales et formes \`a multiplication complexe

Abstract

Pour une repr\'esentation galoisienne di\'edrale en caract\'eristique l on \'etablit (sous certaines hypoth\`eses) l'existence d'une newform \`a multiplication complexe, dont on contr\^ole le poids, le niveau et le caract\`ere, telle que la repr\'esentation l-adique associ\'ee est congrue modulo l \`a celle de d\'epart. Given a dihedral Galois representation in characteristic l, we establish (under some assumption) the existence of a CM newform, whose weight, level and Nebentypus we pin down, such that its l-adic representation is congruent modulo l to the one we started with.