Abstract
We prove that for any Hecke eigenform f of level 1 (i.e., an eigenform on the complex upper-half plane with respect to SL2(Z)) and arbitrary weight there is a self-dual cuspidal automorphic form π of GL6(AQ) corresponding to Symm5(f), i.e., such that the system of Galois representations attached to π agrees with the 5-th symmetric power of the one attached to f.We also improve the base change result that we obtained in a previous work: for any newform f, and any totally real number field F (no extra assumptions on f or F), we prove the existence of base change relative to the extension F/Q.Finally, we combine the previous results to deduce that base change also holds for Symm5(f): for any Hecke eigenform f of level 1 and any totally real number field F, the automorphic form corresponding to Symm5(f) can be base changed to F.
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