Cuspidal cohomology classes for GL_n(Z)

We prove the existence of a cuspidal automorphic representation $\pi$ for $G{L}_{79}\mathrm{/}\mathbf{Q}$ of level one and weight zero. We construct $\pi$ 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 $H^{\ast }(G{L}_n(\mathbf{Z}),\mathbf{C})$ for any $n>1$.