Some remarks related to Maeda's conjecture

Abstract

In this article we deal with the problem of counting the number of pairs of normalized eigenforms $(f,g)$ of weight $k$ and level $N$ such that $a_p(f)=a_p(g)$ where $a_p(f)$ denotes the $p-$th Fourier coefficient of $f$. Here $p$ is a fixed prime.

6 pages, to appear in PAMS