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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 toGL  4{\operatorname{GL}_{4}}   .

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