Somnath Jha (IIT Kanpur): $p^r$-Selmer companion modular forms

Given two elliptic curves $E_1$ and $E_2$ over a number field $K$, Mazur and Rubin have defined them to be $n$-Selmer companion if for every quadratic twist $\chi$ of $K$, the $n$-Selmer group of $E_1^\chi$ and $E_2^\chi$ over $K$ are isomorphic. We will discuss an analogue of this for modular forms.

This talk is based on a joint work with Sudhanshu Shekhar and Dipramit Majumdar.