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Questions about modular forms and related areas
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Question about Fourier coefficients of a newform at primes
For $q:=e^{2\pi i z},$ let $f(z)=\sum_{n\ge 1}\lambda(n)n^{(k-1)/2}q^n$ be a normalized newform of type $(k,\chi)$ and level $N$. For any prime $p,$ we have
$$\lambda(p)=2\cos(\theta_p)\;\;\;\text{f …