The rescaling irreducibility conjecture for holomorphic eta quotients

Let $f$ be an irreducible holomorphic eta quotient, and for a positive integer $\nu$ let its rescaling be $f_\nu(z)=f(\nu z)$. Rescaling irreducibility conjecture. The rescalings of an irreducible holomorphic eta quotient by positive integers are irreducible. The source reports numerical evidence for this assertion and states that it is equivalent to the Atkin–Lehner formulation below; it is not resolved there.