Two properties of symmetric cube transfers of modular forms

Authors

• Debargha Banerjee, Indian Institute of Science Education and Research Pune
• Tathagata Mandal, Indian Statistical Institute, Kolkata
• Sudipa Mondal, HRI

Article Type

Research Article

Publication Title

Journal of Number Theory

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 sym³ transfers of the local representations πp. We also compute the conductor of sym³(π) as it is involved in the variation number. For sym³ transfer, the most difficult prime is p=3.

First Page

160

Last Page

195

DOI

10.1016/j.jnt.2024.12.013

Publication Date

10-1-2025

Recommended Citation

Banerjee, Debargha; Mandal, Tathagata; and Mondal, Sudipa, "Two properties of symmetric cube transfers of modular forms" (2025). Journal Articles. 5638.
https://digitalcommons.isical.ac.in/journal-articles/5638