Abstract
We develop an operator C^Q) on the space Sk{λί, Φ) of Hubert cuspforms as an alternative to the Hecke operator Tq for primes q dividing λί. For f G Sk{λί, Φ) a newform, we have f | Cq(Φg) = f | Γq. We are able to decompose the space Sk(Λf, Φ) into a direct sum of common eigenspaces of {Γ p, Cq(Ψg) : p λί, q I ΛΓ}, each of dimension one. Each common eigenspace is spanned by an element with the property that its eigenvalue with respect to Tp (resp. Cq(ΦQ)) is its p th (resp qth) Fourier coefficient. We finish by deriving bounds for the eigenvalues of
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