Twist multiplicity (reviewed)

The multiplicity of a newform orbit $[g]$ as a twist of a newform orbit $[f]$ by a primitive character orbit $[\psi]$ is the number of distinct $\psi\in[\psi]$ for which $f\otimes\psi\in[g]$. This number is the same for every $f\in [f]$ and depends only on the Galois orbits $[g]$, $[f]$, and $[\psi]$.

When $g$ is an inner twist of $f$, this multiplicity is equal to the inner twist count of $f$.