Modular automorphisms of the Drinfeld modular curves \(X_ 0 ({\mathfrak n})\) (Q1924836)

Let \({\mathfrak n}\in \mathbb{F}_q [T]\). The group of modular automorphisms of the Drinfeld modular curve \(X_0 ({\mathfrak n})\) or, equivalently, the normalizer of the Hecke group \(\Gamma_0 ({\mathfrak n})\) in \(GL_2 (\mathbb{F}_q ((T^{-1})))\) is determined. It turns out that for \(q>2\) the partial Atkin-Lehner involutions are the only modular automorphisms, but for \(q=2\) there do exist further ones (depending on \({\mathfrak n}\)). Furthermore, a complete list of all strong Weil curves \(E\) over \(\mathbb{F}_2 (T)\) with conductor \(\infty \cdot {\mathfrak n}\), where \(\text{deg} ({\mathfrak n})\leq 4\), is given, and it is shown that most of these curves may be written as \(E= G\setminus X_0 ({\mathfrak n})\) where \(G\) is a subgroup of the group of modular automorphisms.