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A mature galaxy cluster at z=1.58 around the radio galaxy 7C1753+6311

We report on the discovery of a z=1.58 mature cluster around the high-redshift radio galaxy 7C1753+6311, first identified in the Clusters Around Radio-Loud AGN survey. Two-thirds of the excess galaxies within the central 1Mpc lie on a red sequence with a colour that is consistent with an average formation redshift of zf~3. We show that 80+/-6% of the red sequence galaxies in the cluster core are quiescent, while the remaining 20% are red due to dusty star formation. We demonstrate that the cluster has an enhanced quiescent galaxy fraction that is three times that of the control field. We also show that this enhancement is mass dependent: 91+/-9% of the M* >10^{10.5}Msun cluster galaxies are quiescent, compared to only 36+/-2% of field galaxies, whereas the fraction of quiescent galaxies with lower masses is the same in the cluster and field environments. The presence of a dense core and a well-formed, quiescent red sequence suggest that this is a mature cluster. This means that distant radio galaxies do not solely reside in young, uncollapsed protoclusters, rather they can be found in clusters in a wide range of evolutionary states.