The gravitational magnification provided by massive galaxy clusters makes it possible to probe the physical conditions in distant galaxies that are of lower luminosity than those in blank fields and likely more representative of the bulk of the high-redshift galaxy population. We aim to constrain the basic properties of molecular gas in a strongly magnified submm galaxy located behind the massive Bullet Cluster. This galaxy (SMM J0658) is split into three images, with a total magnification factor of almost 100. We used the Australia Telescope Compact Array (ATCA) to search for {12}CO(1--0) and {12}CO(3--2) line emission from SMM J0658. We also used the SABOCA bolometer camera on the Atacama Pathfinder EXperiment (APEX) telescope to measure the continuum emission at 350 micron. CO(1--0) and CO(3--2) are detected at 6.8 sigma and 7.5 sigma significance when the spectra toward the two brightest images of the galaxy are combined. From the CO(1-0) luminosity we derive a mass of cold molecular gas of (1.8 \pm 0.3) * 10^9 Msun, using the CO to H_2 conversion factor commonly used for luminous infrared galaxies. This is 45 \pm 25 % of the stellar mass. From the width of the CO lines we derive a dynamical mass within the CO-emitting region L of (1.3 \pm 0.4) * 10^10 (L/1 kpc) Msun. We refine the redshift determination of SMM J0658 to z=2.7793 \pm 0.0003. Continuum emission at 350 micron from SMM J0658 was detected with SABOCA at a signal-to-noise ratio of 3.6. We study the spectral energy distribution of SMM J0658 and derive a dust temperature of 33\pm 5 K and a dust mass of 1.1*10^7 Msun. SMM J0658 is one of the least massive submm galaxies discovered so far. As a likely representative of the bulk of the submm galaxy population, it is a prime target for future observations.