A Polynomial with Galois Groups SL₂(F₁₆)

Abstract

In this paper we display an explicit polynomial having Galois group SL 2 ( F 16 ), filling in a gap in the tables of Jürgen Klüners and Gunter Malle. Furthermore, the polynomial has small Galois root discriminant; this fact answers a question of John Jones and David Roberts. The computation of this polynomial uses modular forms and their Galois representations.