Here we report the first three-dimensional spatial spectrum of the low frequency magnetic turbulence obtained from the four Cluster spacecraft in the terrestrial magnetosheath close to the magnetopause. We show that the turbulence is compressible and dominated by mirror structures, its energy is injected at a large scale kρ∼0.3 (l∼2000 km) via a mirror instability well predicted by linear theory, and cascades nonlinearly and unexpectedly up to kρ∼3.5 (l∼150 km), revealing a new power law in the inertial range not predicted by any turbulence theory, and its strong anisotropy is controlled by the static magnetic field and the magnetopause normal.