Multiple CO transitions, C-I, and HCN from the Cloverleaf quasar

New millimeter-wavelength emission lines are reported for the Cloverleaf (H1413+117), a gravitationally lensed quasar at redshift 2.56. High signal-to-noise ratio (S/N) spectra of four lines in CO (3 --> 2, 4 --> 3, 5 --> 4, and 7 --> 6) have been obtained and are modeled with an escape probability formalism. The line brightness temperatures are flat or rising between CO (3 --> 2) and CO (4 --> 3) and then drop to the CO (5 --> 4) and CO (7 --> 6) lines; this falloff suggests that the optical depths in the CO lines are modest (tau(4-3) less than or similar to 3) and that the gas is relatively warm (T greater than or similar to 100 K) and dense (n(H2) greater than or similar to 3 x 10(3) cm(-3)). The neutral carbon fine-structure line C I (P-3(1) --> P-3(0)) was detected with moderate S/N on two separate occasions and appears secure. The HCN (4 --> 3) line is somewhat more tentative, as it was observed only once and detected with moderate S/N. However, its brightness ratio relative to the CO (4 --> 3) line, L'(HCN)/L'(CO) approximate to 0.25, is very similar to the ratio seen in luminous infrared galaxies. This probably reflects the gas fraction maintained at high densities by radiation pressure from the active nucleus; alternatively, the HCN transition may be excited through absorption of infrared radiation at 14 mu m. The detectability of the Cloverleaf in molecular and neutral atomic transitions is largely due to high emissivity of the gas and magnification from gravitational lensing rather than an extremely large mass of gas.