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The Hecke algebra acts on $$S_k^{\mathrm{new}}(N, \chi)$$, breaking it up into irreducible pieces. Each piece is spanned by a set of conjugate eigenforms with Fourier coefficients in a number field of degree equal to the dimension of the subspace. We refer to an irreducible orbit as a newform.

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• Review status: reviewed
• Last edited by David Roe on 2018-10-12 19:32:26
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