  A (2+1)D topologically ordered phase may or may not have a gappable edge,
even if its chiral central charge $c_-$ is vanishing. Recently, it is
discovered that a quantity regarded as a "higher" version of chiral central
charge gives a further obstruction beyond $c_-$ to gapping out the edge. In
this Letter, we show that the higher central charges can be characterized by
the expectation value of the \textit{partial rotation} operator acting on the
wavefunction of the topologically ordered state. This allows us to extract the
higher central charge from a single wavefunction, which can be evaluated on a
quantum computer. Our characterization of the higher central charge is
analytically derived from the modular properties of edge conformal field
theory, as well as the numerical results with the $\nu=1/2$ bosonic Laughlin
state and the non-Abelian gapped phase of the Kitaev honeycomb model, which
corresponds to $\mathrm{U}(1)_2$ and Ising topological order respectively. The
letter establishes a numerical method to obtain a set of obstructions to the
gappable edge of (2+1)D bosonic topological order beyond $c_-$, which enables
us to completely determine if a (2+1)D bosonic Abelian topological order has a
gappable edge or not. We also point out that the expectation values of the
partial rotation on a single wavefunction put a constraint on the low-energy
spectrum of the bulk-boundary system of (2+1)D bosonic topological order,
reminiscent of the Lieb-Schultz-Mattis type theorems.
