On Deligne’s conjecture for symmetric fifth L-functions of modular forms

Abstract We prove Deligne’s conjecture for symmetric fifth L -functions of elliptic newforms of weight greater than 5. As a consequence, we establish period relations between motivic periods associated to an elliptic newform and the Betti–Whittaker periods of its symmetric cube functorial lift to GL 4 {\operatorname{GL}_{4}} .