We present an exact diagonalization study of the low-energy singlet and triplet states for both the one-dimensional (1D) and 2D t-J models. A scan of the parameter ratio J/t shows that for most low-energy states in both 1D and 2D the excitation energy takes the form E(t,J)=a . t+b . J. In 1D this is the natural conse quence of the factorization of the low-energy wave functions, i.e., spin-charge separation. Examination of the low-energy eigenstates in 2D shows that most of these are collective modes, which for larger J correspond to a periodic modulation of the hole density. The modulation is well reproduced by treating holes as hard-core bosons with an attractive interaction.