Two properties of symmetric cube transfers of modular forms

Abstract

In this article, we study two important properties of the symmetric cube transfer of the automorphic representation π associated to a modular form. We first show how the local epsilon factor at each prime changes by twisting in terms of the local Weil-Deligne representation. From this variation number, for each prime p, we classify the types of transfers of the local representations . We also compute the conductor of as it is involved in the variation number. For transfer, the most difficult prime is .