The GTR parameters for nucleotides consist of an equilibrium base frequency vector, \vec{\pi} = (\pi_1, \pi_2, \pi_3, \pi_4), giving the frequency at which each base occurs at each site, and the rate matrix .
In general, to compute the number of parameters, you count the number of entries above the diagonal in the matrix, i.e. for n trait values per site {{n^2-n} \over 2} , and then add n-1 for the equilibrium frequencies, and subtract 1 because \mu is fixed.