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Hoffman, Ling Long","submitted_at":"2010-03-19T15:10:21Z","abstract_excerpt":"This paper is concerned with a compatible family of 4-dimensional \\ell-adic representations \\rho_{\\ell} of G_\\Q:=\\Gal(\\bar \\Q/\\Q) attached to the space of weight 3 cuspforms S_3 (\\Gamma) on a noncongruence subgroup \\Gamma \\subset \\SL. For this representation we prove that: 1.)It is automorphic: the L-function L(s, \\rho_{\\ell}^{\\vee}) agrees with the L-function for an automorphic form for \\text{GL}_4(\\mathbb A_{\\Q}), where \\rho_{\\ell}^{\\vee} is the dual of \\rho_{\\ell}. 2.) 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