We present new detections of the CO(5-4), CO(7-6), [CI](1-0) and [CI](2-1) molecular and atomic line transitions towards the unlensed, obscured quasar AMS12 (z=2.7672), observed with the IRAM PdBI. This is the first unlensed, high redshift source to have both [CI] transitions detected. Continuum measurements between 70 $mu$m and 3 mm are used to constrain the FIR SED, and we find a best fit FIR luminosity of log[Lfir/Lsol] = 13.5+/-0.1, dust temperature T_d = 88+/-8 K and emissivity index {beta} = 0.6+/-0.1. The highly-excited molecular gas probed by CO(3-2), (5-4) and (7-6), is modelled with large velocity gradient (LVG) models. The gas kinetic temperature T_g, density n(H2), and the characteristic size r0, are determined using the dust temperature from the FIR SED as a prior for the gas temperature. The best fitting parameters are T_g = 90+/-8 K, n(H2) = 10^(3.9+/-0.1) cm^(-3) and r0 = 0.8+/-0.04 kpc. The ratio of the [CI] lines gives a [CI] excitation temperature of 43+/-10 K, indicating the [CI] and the high-excitation CO are not in thermal equilibrium. The [CI] excitation temperature is below that of T_d and T_g of the high-excitation CO, perhaps because [CI] lies at a larger radius where there may also be a large reservoir of CO at a cooler temperature, perhaps detectable through the CO(1-0). Using the [CI](1-0) line we can estimate the strength of the CO(1-0) line and hence the gas mass. This suggests that a significant fraction (~30%) of the molecular gas is missed from the high-excitation line analysis. The Eddington limited black hole mass is found from the bolometric luminosity to be Mbh >~ 1.5x10^9 Msol. Along with the stellar mass of 3x10^11 Msol, these give a black hole - bulge mass ratio of Mbh/Mbulge >~ 0.005. This is in agreement with studies on the evolution of the Mbh/Mbulge relationship at high redshifts, which find a departure from the local value ~0.002.
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