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I came across the following statement several times while looking through literature on Eisenstein series and Hecke operators (like Iwaniec's books, articles by Cogdell, etc). I am looking for a reference that includes a proof.

The Eisenstein series for $\Gamma_0(N)$ (at any cusp) are eigenfunctions for the Hecke operators $T_n$ with $(n,N)=1$.

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See these Zagier's notes for instance :

http://people.mpim-bonn.mpg.de/zagier/files/scanned/IntroductionToModularForms/fulltext.pdf

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