Published online by Cambridge University Press: 01 February 2010
In this paper we display an explicit polynomial having Galois group SL2(F16), 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.