Medium- and high-spin states of 132La have been studied based on the data obtained from 100Mo(36S,p3n) and 116Cd(23Na,α3n) fusion-evaporation reactions using the EUROBALL and Gammasphere detector arrays, respectively. Triple-γ coincidence relations, angular correlations, and linear polarizations of the observed γ transitions have been deduced. The level scheme of 132La has been considerably extended, and unambiguous spin and parity values have been assigned to most of the excited states. The configuration of one of the bands is πg7/2(h112)2νh11/2 instead of the previously thought πh11/2νh11/2; thus its previously suggested magnetic rotational character cannot be upheld. The observed similarities between the level structures of 132La and 134Pr suggest the possible existence of a third πh11/2νh 11/2 band in 132La that may show chiral features.