  We analyze the finite size corrections to entanglement in quantum critical
systems. By using conformal symmetry and density functional theory, we discuss
the structure of the finite size contributions to a general measure of ground
state entanglement, which are ruled by the central charge of the underlying
conformal field theory. More generally, we show that all conformal towers
formed by an infinite number of excited states (as the size of the system $L
\to \infty$) exhibit a unique pattern of entanglement, which differ only at
leading order $(1/L)^2$. In this case, entanglement is also shown to obey a
universal structure, given by the anomalous dimensions of the primary operators
of the theory. As an illustration, we discuss the behavior of pairwise
entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary
length $L$ for both periodic and twisted boundary conditions.
