Geodesic
Raising the level for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\text {GL}_{{n}}$
Forum of Mathematics, Sigma, Tome 2 (2014)

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We prove a simple level-raising result for regular algebraic, conjugate self-dual automorphic forms on $\mathrm{GL}_n$ . This gives a systematic way to construct irreducible Galois representations whose residual representation is reducible. 
@article{10_1017_fms_2014_14,
     author = {JACK A. THORNE},
     title = {Raising the level for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\text {GL}_{{n}}$},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {2},
     year = {2014},
     doi = {10.1017/fms.2014.14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2014.14/}
}
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JACK A. THORNE. Raising the level for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\text {GL}_{{n}}$. Forum of Mathematics, Sigma, Tome 2 (2014). doi: 10.1017/fms.2014.14

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