Quantum representations are families of finite-dimensional representations of mapping class groups satisfying strong compatibility conditions. One of the most well-known (the so-called SO(3)-TQFT) depends on a parameter q which is a root of unity of order 2r (r odd). These representations preserve a Hermitian form: recently, with B. Deroin, we explained how to compute its signature (among other things). More recently, I observed that this computation is related to the trace field of the 2-bridge knot K(r,s) where q=exp(iπs/r). During the talk, I will explain this relation and the objects involved in it.