Multiplicities in the trace cocharacter sequence of two $4\times 4$   matrices
  We find explicitly the generating functions of the multiplicities in the pure and mixed trace cocharacter sequences of two $4\times 4$ matrices over a field of characteristic 0. We determine the asymptotic behavior of the multiplicities and show that they behave as polynomials of 14th degree. 
Vesselin Drensky and Georgi K. Genov