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We present the results of first-principles cluster calculations of the electronic structure of La_2CuO_4. Several clusters containing up to nine copper atoms embedded in a background potential were investigated. Spin-polarized calculations were performed both at the Hartree-Fock level and with density functional methods with generalized gradient corrections to the local density approximation. The distinct results for the electronic structure obtained with these two methods are discussed. The dependence of the electric-field gradients at the Cu and the O sites on the cluster size is studied and the results are compared to experiments. The magnetic hyperfine coupling parameters are carefully examined. Special attention is given to a quantitative determination of on-site and transferred hyperfine fields. We provide a detailed analysis that compares the hyperfine fields obtained for various cluster sizes with results from additional calculations of spin states with different multiplicities. From this we conclude that hyperfine couplings are mainly transferred from nearest neighbor Cu^{2+} ions and that contributions from further distant neighbors are marginal. The mechanisms giving rise to transfer of spin density are worked out. Assuming conventional values for the spin-orbit coupling, the total calculated hyperfine interaction parameters are compared to informations from experiments., Comment: 23 pages, 9 figures