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# numberof modular formseigenforms with integerintegral coefficients [Maeda'sConjecture]

Are there infinitely many (linearly independent) cuspidal eigenforms for $\Gamma(1)$ with integer coefficients?

Someone told me that the Hecke algebra is conjectured to act irreducibly on the space of modular forms of level 1, so there would be no eigenforms if $\mathrm{dim} S_k > 1$, i.e. for $k \geq 12$.

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Are there infinitely many eigenforms for $\Gamma(1)$ with integer coefficients?

Someone told me that the Hecke algebra is conjectured to act irreducibly on the space of modular forms of level 1, so there would be no eigenforms if $\mathrm{dim} S_k > 1$, i.e. for $k \geq 12$.

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# number of modular forms with integer coefficients

Are there infinitely many eigenforms for $\Gamma(1)$ with integer coefficients?