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For each prime dividing the level $$N$$, the Atkin-Lehner operator scales each newform by either $$1$$ or $$-1$$. Let $$j$$ be the number of primes dividing $$N$$. Ordering the $$2^j$$ vectors of $$\pm 1$$ lexicographically (with $$1$$ before $$-1$$), we show the dimensions of the subspaces of $$S_k^{\mathrm{new}}(\Gamma_0(N),\chi)$$ with prescribed Atkin-Lehner eigenvalues.

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• Review status: reviewed
• Last edited by David Farmer on 2019-04-29 10:21:23
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