We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schrödinger equation. For initial datum (Formula presented) and s ∈ [−1, 0], we prove that there exists a conserved quantity which is equivalent to (Formula presented) norm of the solution. © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.