Associated to each newform $f$ and primitive Dirichlet character $\psi$, there is a unique newform $g:=f\otimes\psi$, the twist of $f$ by $\psi$, that satisfies \[ a_n(g)=\psi(n)a_n(f) \] for all integers $n\ge 1$ coprime to $N$ and the conductor of $\psi$. If the newform $g$ is a Galois conjugate of $f$, it is said to be an inner twist.
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- Last edited by Andrew Sutherland on 2020-01-03 05:50:44
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