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The space of newforms of weight $$k$$ on $$\Gamma_1(N)$$ decomposes as $S_k^{\mathrm{new}}(\Gamma_1(N)) \cong \bigoplus_{\chi \bmod N} S_k^{\mathrm{new}}(N, \chi),$ where the direct sum is over all Dirichlet characters modulo $$N$$. If $$\chi$$ and $$\chi'$$ are in the same Galois orbit, then $$S_k^{\mathrm{new}}(N, \chi)$$ and $$S_k^{\mathrm{new}}(N, \chi')$$ are Galois conjugate and we identify them since we define newforms as Galois orbits.

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• Review status: reviewed
• Last edited by David Roe on 2018-10-12 19:32:03
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