We present JVLA observations of the cold (CO (1-0)) molecular gas in IRAS F10214+4724, a lensed ULIRG at z=2.3 with an obscured active nucleus. The galaxy is spatially and spectrally well-resolved in the CO (1-0) emission line. A CO (1-0) counter-image is detected at the 3-sigma level. Five of the 42 km/s channels (with >5-sigma detections) are mapped back into the source plane and their total magnification posterior PDFs sampled. This reveals a roughly linear arrangement, tentatively a rotating disk. We derive a molecular gas mass of M_gas = 1.2 +- 0.2 x 10^10 M_sun, assuming a ULIRG L_{CO}-to-M_{gas} conversion ratio of alpha = 0.8 M_sun / (K km/s pc^2) that agrees well with the derived range of alpha = 0.3 - 1.3 for separate dynamical mass estimates at assumed inclinations of i = 90 - 30 degrees. Based on the AGN and CO (1-0) peak emission positions and the lens model, we predict a distortion of the CO Spectral Line Energy Distribution (SLED) where higher order J lines that may be partially excited by AGN heating will be preferentially lensed owing to their smaller solid angles and closer proximity to the AGN and therefore the cusp of the caustic. Comparison with other lensing inversion results shows that the narrow line region and AGN radio core in IRAS F10214+4724 are preferentially lensed by a factor >~ 3 and 11 respectively, relative to the molecular gas emission. This distorts the global continuum emission Spectral Energy Distribution (SED) and suggests caution in unsophisticated uses of IRAS F10214+4724 as an archetype high-redshift ULIRG. We explore two Large Velocity Gradient (LVG) models, incorporating spatial CO (1-0) and (3-2) information and present tentative evidence for an extended, low excitation cold gas component that implies that the total molecular gas mass in IRAS F10214+4724 is a factor >~2 greater than that calculated using spatially unresolved CO observations.
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