  We investigate the effect of a global degeneracy in the distribution of
entanglement spectrum in conformal field theories in one spatial dimension. We
relate the recently found universal expression for the entanglement hamiltonian
to the distribution of the entanglement spectrum. The main tool to establish
this connection is the Cardy formula. It turns out that the Affleck-Ludwig
non-integer degeneracy, appearing because of the boundary conditions induced at
the entangling surface, can be directly read from the entanglement spectrum
distribution. We also clarify the effect of the non-integer degeneracy on the
spectrum of the partial transpose, which is the central object for quantifying
the entanglement in mixed states. We show that the exact knowledge of the
entanglement spectrum in some integrable spin-chains provides strong analytical
evidences corroborating our results.
