We report calculations on the surface tension of the water-air interface using ab initio molecular dynamics (AIMD) simulations. We investigate the influence of the cell size on surface tension of water from force field molecular dynamics simulations. We find that the calculated surface tension increases with increasing simulation cell size, thereby illustrating that a correction for finite size effects is essential for small systems that are customary in AIMD simulations. Moreover, AIMD simulations reveal that the use of a double-ζ basis set overestimates the experimentally measured surface tension due to the Pulay stress while more accurate triple and quadruple-ζ basis sets give converged results. We further demonstrate that van der Waals corrections critically affect the surface tension. AIMD simulations without the van der Waals correction substantially underestimate the surface tension while the van der Waals correction with the Grimme's D2 technique results in a value for the surface tension that is too high. The Grimme's D3 van der Waals correction provides a surface tension close to the experimental value. Whereas the specific choices for the van der Waals correction and basis sets critically affect the calculated surface tension, the surface tension is remarkably insensitive to the details of the exchange and correlation functionals, which highlights the impact of long-range interactions on the surface tension. Our simulated values provide important benchmarks, both for improving van der Waals corrections and AIMD simulations of aqueous interfaces.