We present a detailed study of the large-scale anisotropies of cosmic rays with energies above 4 EeV measured using the Pierre Auger Observatory. For the energy bins [4,8] EeV and $E\geq 8$ EeV, the most significant signal is a dipolar modulation in right ascension at energies above 8 EeV, as previously reported. In this paper we further scrutinize the highest-energy bin by splitting it into three energy ranges. We find that the amplitude of the dipole increases with energy above 4 EeV. The growth can be fitted with a power law with index $\beta=0.79\pm 0.19$. The directions of the dipoles are consistent with an extragalactic origin of these anisotropies at all the energies considered. Additionally we have estimated the quadrupolar components of the anisotropy: they are not statistically significant. We discuss the results in the context of the predictions from different models for the distribution of ultrahigh-energy sources and cosmic magnetic fields.