For a translation invariant system of N bosons in the Gross-Pitaevskii regime, we establish a precise bound for the ground state energy E_N. While the leading, order N, contribution to E_N has been known since [30,28] and the second order corrections (of order one) have been first determined in [5], our estimate also resolves the next term in the asymptotic expansion of E_N, which is of the order (logN)/N.
