We have obtained a moderate resolution spectrum of the quasar PKS 0528-250 with the Red Channel Spectrograph on the Multiple Mirror Telescope ( MMT ) in order to study a damped Ly \alpha absorption line system at z = 2.8115 . We obtain a new upper limit for the CO column density for the z = 2.8108 velocity component in the z = 2.8115 damped Ly \alpha system . The ionization of different species in this component rules out a quasar spectral energy distribution ( SED ) as the ionization field , and implies an ultraviolet radiation field intensity a few times that of the Milky Way value . The estimated total number density is n ( H ) \sim 20 cm ^ { -3 } . The physical size for the z = 2.8108 component implied by these models is about 40 parsecs . The ionization of different species also suggests a structure with a hot intercloud medium associated with a H I cloud in this component , that is , most low ionized ions are from the cold medium where photoionization and photodissociation dominates . The highly ionized species may be from the intercloud medium where collisional ionization dominates . We also present newly identified Ni II absorption lines in the z = 2.1408 and z = 2.8115 damped Ly \alpha systems . The derived depletion of nickel by dust confirms previous results that the dust-to-gas ratio in these two damped Ly \alpha systems is about 10 % of the Milky Way ratio . Millimeter wavelength observations obtained at the NRAO 12 meter telescope provide new upper limits on CO ( 3-2 ) emission in the z = 2.8115 damped Ly \alpha system .