  We provide a dual version of the Geck--Rouquier Theorem on the center of an
Iwahori--Hecke algebra, which also covers the complex case. For the eight
complex reflection groups of rank $2$, for which the symmetrising trace
conjecture is known to be true, we provide a new faithful matrix model for
their Hecke algebra $H$. These models enable concrete calculations inside $H$.
For each of the eight groups, we compute an explicit integral basis of the
center of $H$.
