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We present \ci\,(2--1) and multi-transition $^{12}$CO observations of a dustystar-forming galaxy, ACT\,J2029+0120, which we spectroscopically confirm to lieat $z$\,=\,2.64. We detect CO(3--2), CO(5--4), CO(7--6), CO(8--7), and\ci\,(2--1) at high significance, tentatively detect HCO$^{+}$(4--3), and placestrong upper limits on the integrated strength of dense gas tracers (HCN(4--3)and CS(7--6)). Multi-transition CO observations and dense gas tracers canprovide valuable constraints on the molecular gas content and excitationconditions in high-redshift galaxies. We therefore use this unique data set toconstruct a CO spectral line energy distribution (SLED) of the source, which ismost consistent with that of a ULIRG/Seyfert or QSO host object in the taxonomyof the \textit{Herschel} Comprehensive ULIRG Emission Survey. We employ RADEXmodels to fit the peak of the CO SLED, inferring a temperature of T$\sim$117 Kand $n_{\text{H}_2}\sim10^5$ cm$^{-3}$, most consistent with a ULIRG/QSO objectand the presence of high density tracers. We also find that the velocity widthof the \ci\ line is potentially larger than seen in all CO transitions for thisobject, and that the $L'_{\rm C\,I(2-1)}/L'_{\rm CO(3-2)}$ ratio is also largerthan seen in other lensed and unlensed submillimeter galaxies and QSO hosts; ifconfirmed, this anomaly could be an effect of differential lensing of a shockedmolecular outflow.

Multiwavelength characterisation of an ACT-selected, lensed dusty star-forming galaxy at z=2.64