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We analyzed 252 hours of High Energy Stereoscopic System (H.E.S.S.)observations towards the supernova remnant (SNR) LMC N132D that wereaccumulated between December 2004 and March 2016 during a deep survey of theLarge Magellanic Cloud, adding 104 hours of observations to the previouslypublished data set to ensure a > 5 sigma detection. To broaden the gamma-rayspectral coverage required for modeling the spectral energy distribution, ananalysis of Fermi-LAT Pass 8 data was also included. We unambiguously detectN132D at very high energies (VHE) with a significance of 5.7 sigma. We reportthe results of a detailed analysis of its spectrum and localization based onthe extended H.E.S.S. data set. The joint analysis of the extended H.E.S.S andFermi-LAT data results in a spectral energy distribution in the energy rangefrom 1.7 GeV to 14.8 TeV, which suggests a high luminosity of N132D at GeV andTeV energies. We set a lower limit on a gamma-ray cutoff energy of 8 TeV with aconfidence level of 95%. The new gamma-ray spectrum as well as multiwavelengthobservations of N132D when compared to physical models suggests a hadronicorigin of the VHE gamma-ray emission. SNR N132D is a VHE gamma-ray source thatshows a spectrum extending to the VHE domain without a spectral cutoff at a fewTeV, unlike the younger oxygen-rich SNR Cassiopeia A. The gamma-ray propertiesof N132D may be affected by an interaction with a nearby molecular cloud thatpartially lies inside the 95% confidence region of the source position.[Abridged]

LMC N132D: A mature supernova remnant with a power-law gamma-ray spectrum extending beyond 8 TeV