The Atkin–Lehner irreducibility conjecture for holomorphic eta quotients

Let $f$ be an irreducible holomorphic eta quotient, and let an Atkin–Lehner involution act on eta quotients in the usual way. Atkin–Lehner irreducibility conjecture. The images of an irreducible holomorphic eta quotient under the Atkin–Lehner involutions are irreducible. The source states that this is equivalent to the rescaling irreducibility conjecture and that it follows from the reducibility conjecture; however, the supplied parser status is unknown and the paper excerpt does not establish the reducibility conjecture.