Iharas lemma and level rising in higher dimension

A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the classical Iharas lemma which is used to rise the modularity property between some congruent galoisian representations. In their work on Sato-Tate, Clozel-Harris-Taylor proposed a generalization of the Iharas lemma in higher dimension for some similitude groups. The main aim of this paper is then to prove some new instances of this generalized Iharas lemma by considering some particular non pseudo Eisenstein maximal ideals of unramified Hecke algebras. As a consequence, we prove a level rising statement.