The first 2+ and 3- states of the doubly magic nucleus 132Sn are populated via safe Coulomb excitation employing the recently commissioned HIE-ISOLDE accelerator at CERN in conjunction with the highly efficient MINIBALL array. The 132Sn ions are accelerated to an energy of 5.49 MeV / nucleon and impinged on a 206Pb target. Deexciting γ rays from the low-lying excited states of the target and the projectile are recorded in coincidence with scattered particles. The reduced transition strengths are determined for the transitions 0g.s.+→21+, 0g.s.+→31-, and 21+→31- in 132Sn. The results on these states provide crucial information on cross-shell configurations which are determined within large-scale shell-model and Monte Carlo shell-model calculations as well as from random-phase approximation and relativistic random-phase approximation. The locally enhanced B(E2;0g.s.+→21+) strength is consistent with the microscopic description of the structure of the respective states within all theoretical approaches. The presented results of experiment and theory can be considered to be the first direct verification of the sphericity and double magicity of 132Sn.