Abstract
We prove the existence of a cuspidal automorphic representation Ο \pi for GL 79 β‘ / Q \operatorname {GL}_{79}/\mathbf {Q} of level one and weight zero. We construct Ο \pi using symmetric power functoriality and a change of weight theorem, using Galois deformation theory. As a corollary, we construct the first known cuspidal cohomology classes in H β ( GL n β‘ ( Z ) , C ) H^*(\operatorname {GL}_{n}(\mathbf {Z}),\mathbf {C}) for any n > 1 n > 1 .
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