The possibility of non-square congruence subgroups for linear level polynomials

Let $\alpha$ and $\beta$ be such that $\alpha\neq 0$, and consider the congruence subgroups $\Gamma_1(\alpha T+\beta)$ and $\Gamma_0(\alpha T+\beta)$. A congruence subgroup is called non-square when it does not satisfy the paper's notion of being square.

Non-square congruence subgroup conjecture. Both $\Gamma_1(\alpha T+\beta)$ and $\Gamma_0(\alpha T+\beta)$ may be non-square congruence subgroups for any choice of $\alpha\neq 0$ and $\beta$.

The claim concerns the stabilizers of elliptic points and is used to determine the relevant geometric invariants of the associated Drinfeld modular curves. The supplied context does not state whether this possibility has been established or remains open.