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Algebra of Hecke operators on $M_k(\mathrm{SL}_2\mathbb{Z})$ is an integral domain?

You mean the (commutative, normal for the Petersson inner product thus diagonalizable) complex algebra $\Bbb{T(C)}$ of endomorphisms of the complex vector space $M_k(SL_2(Z))$ ($k$ even) generated by …
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