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 .