We present new detections of the CO(5-4), CO(7-6), [CI](
3P
1 -
3P
0) and [CI](
3P
2 -
3P
1) molecular and atomic line transitions towards the unlensed, obscured quasar AMS12 (
z= 2.7672), observed with the Institut de Radioastronomie Millimétrique (IRAM) Plateau de Bure Interferometer (PdBI). This is the first unlensed, high-redshift source to have both atomic carbon ([CI]) transitions detected. Continuum measurements between 70 µm and 3 mm are used to constrain the far-infrared (FIR) spectral energy distribution (SED), and we find a best-fitting FIR luminosity of log
10[
LFIR/L
☉] = 13.5±0.1, dust temperature
TD= 88±8 K and emissivity index β= 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 models. The gas kinetic temperature
TG, density
n(H
2) 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
TG= 90 ±8 K,
n(H
2) = 10^3.9 ±0.1^/cm3 and
r0= 0.8±0.04 kpc. The ratio of the [CI] lines gives a [CI] excitation temperature of 43±10 K, indicating that the [CI] and the high-excitation CO are not in thermal equilibrium. The [CI] excitation temperature is below that of the dust temperature and the gas kinetic temperature 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) line. Using the [CI](
3P
1 -
3P
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 per cent) of the molecular gas is missed from the high-excitation line analysis, giving a gas mass higher than that inferred from the assumption that the high-excitation gas is a good tracer of the low-excitation gas. The stellar mass was estimated from the mid-/near-infrared SED to be
M*∼ 3 {x} 10
11 M
☉. The Eddington-limited black hole mass is found from the bolometric luminosity to be
M• ≳ 1.5 {x} 10
9 M
☉. These give a black hole–bulge mass ratio of
M•/
M* ≳ 0.005. This is in agreement with studies on the evolution of the
M•/
M*relationship at high redshifts, which find a departure from the local value of ∼0.002. We discuss the implications for the evolution of the black hole in AMS12 and its host galaxy.
Based on observations carried out with the IRAM Plateau de Bure Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).