We use ab initio simulations to investigate the properties of a sodium borosilicate glass of composition 3Na2 O-B2 O3 -6SiO2 . We find that the broadening of the first peak in the radial distribution functions gBO (r) and gBNa (r) is due to the presence of trigonal and tetrahedral boron units as well as to nonbridging oxygen atoms connected to BO3 units. In agreement with experimental results, we find that the [3] B units involve a significant number of nonbridging oxygens, whereas the vast majority of [4] B have only bridging oxygens. We determine the three-dimensional distribution of the Na atoms around the [3] B and [4] B units and use this information to explain why the sodium atoms associated with the latter share more oxygen atoms with the central boron atoms than the former units. From the distribution of the electrons we calculate the total electronic density of states, as well its decomposition into angular momentum contributions. The vibrational density of states shows at high frequencies a band that originates from the motion of the boron atoms. We find that the [3] B and [4] B units give rise to well-defined features in the spectrum, which thus can be used to estimate the concentration of these structural entities. The contribution of [3] B can be decomposed further into symmetric and asymmetric parts that can also be easily identified in the spectrum. Furthermore, it is found that certain features in the spectrum can be used to obtain information on the type of atom that is the second-nearest neighbor of a boron in the [4] B unit. We calculate the average Born charges on the bridging and nonbridging oxygen atoms and show that these depend linearly on the angle between the two bonds and the distance from the connected cation, respectively. Finally, we have determined the frequency dependence of the dielectric function, as well as the absorption spectra. The latter is in good quantitative agreement with the experimental data.