Band structures and dielectric functions are calculated using density-functional theory and local-density approximation for three β-cristobalite modifications of SiO₂ with space-group symmetries Fd3m, I4¯2d, and P213. Quasiparticle corrections for the Kohn-Sham eigenvalues are determined in a GW approach. The fundamental energy gaps, absorption onsets, and dielectric functions are discussed and compared in the light of experimental data and previous calculations.