Generalized Atkin polynomial congruence conjecture

Let $p\ge5$ be prime, and write

$$p-1=12m+4\delta+6\varepsilon,$$

where $m\in\mathbb{Z}_{\ge0}$ and $\delta,\varepsilon\in\{0,1\}$. Let $A_{u,a}^{(r)}(X)$ be the generalized Atkin polynomial associated with the normalized extremal quasimodular form of weight $12n+a$ and depth $r$, as defined by the source. Generalized Atkin polynomial congruence conjecture. For $r\ge2$,

$$A_{m+\delta+\varepsilon,2}^{(1)}(X)\equiv A_{m+\delta+\varepsilon,2r}^{(r)}(X)\pmod{p}.$$

This conjecture predicts that generalized Atkin polynomials in different depths satisfy the same reduction modulo primes $p\ge5$; existence of the relevant extremal forms and polynomials for depths $r\ge5$ remains open in the source.