Redshifted formaldehyde from the gravitational lens B0218+357

Context. Little is known about individual molecular clouds at high redshifts. The gravitational lens toward B0218+ 357 offers the unique possibility to study cool moderately dense gas with high sensitivity and angular resolution in a cloud that existed half a Hubble time ago. Aims. This non-CO molecular multi-level study of a significantly redshifted cloud aims at a better definition of the physical properties of molecular gas in a kind of interstellar environment that is rarely studied in the Galaxy or in the nearby extragalactic space. Methods. Observations of the radio continuum and six formaldehyde (H2CO) lines were carried out with the VLA, the Plateau de Bure interferometer and the Effelsberg 100-m telescope. Results. Three radio continuum maps indicate a flux density ratio between the two main images, A and B, of similar to 3.4 +/-0.2. Within the errors the ratio is the same at 8.6, 14.1, and 43 GHz. The 1(01)-0(00) line of para-H2CO is shown to absorb the continuum of image A. Large Velocity Gradient radiative transfer calculations are performed to reproduce the optical depths of the observed two cm-wave ''K-doublet" and four mm-wave rotational lines. These calculations also account for a likely frequency-dependent continuum cloud coverage. Confirming the diffuse nature of the cloud, an n(H-2) density of < 1000 cm(-3) is derived, with the best fit suggesting n(H-2) similar to 200 cm(-3). The H2CO column density of the main velocity component is similar to 5 x 10(13) cm(-2), to which about 7.5 x 10(12) cm(-2) has to be added to also account for a weaker feature on the blue side, 13 kms(-1) apart. N(H2CO)/N(NH3) similar to 0.6, which is four times less than the average ratio obtained from a small number of local diffuse (galactic) clouds seen in absorption. The ortho-to-para H2CO abundance ratio is 2.0 -3.0, which is consistent with the kinetic temperature of the molecular gas associated with the lens of B0218+ 357. With the gas kinetic temperature and density known, it is found that optically thin transitions of CS, HCN, HNC, HCO+, and N2H+ (but not CO) will provide excellent probes of the cosmic microwave background at redshift z = 0.68.