  We study a filtered Lie splitting scheme for the cubic nonlinear
Schr\"{o}dinger equation. We establish error estimates at low regularity by
using discrete Bourgain spaces. This allows us to handle data in $H^s$ with
$0<s<1$ overcoming the standard stability restriction to smooth Sobolev spaces
with index $s>1/2$ . More precisely, we prove convergence rates of order
$\tau^{s/2}$ in $L^2$ at this level of regularity.
