Abstract :

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 $_X$ of $K$, the $n$-Selmer group of $E_1^X$ and $E_2^X$ 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