Some remarks related to Maeda's conjecture

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.

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