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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Existence of CM Newforms in Level p

If $p$ is a prime and $k \geq 2$ is an even integer, what can we say about the existence of CM forms in the space $S_k^\text{new}(\Gamma_0(p))$? If it helps at all, I'm specifically interested in the …
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