  We use holography to study the large spin $J$ limit of the spectrum of low
energy states with charge $Q$ under a $U(1)$ conserved current in CFTs in $d>2$
dimensions, with a focus on $d=3$ and $d=4$. For $Q=2$, the spectrum of such
states is known to be universal and properly captured by the long-distance
limit of holographic theories, regardless of whether the CFT itself is
holographic. We study in detail the holographic description of such states at
$Q>2$, by considering the contribution to the energies of $Q$ scalar particles
coming from single photon and graviton exchange in the bulk of AdS; in some
cases, scalar exchange and bulk contact terms are also included. For a range of
finite values of $Q$ and $J$, we numerically diagonalize the Hamiltonian for
such states and examine the resulting spectrum and wavefunctions as a function
of the dimension $\Delta$ of the charge-one operator and the central charges
$c_{\mathcal{T}}, c_{\mathcal{J}}$ of the stress tensor and U(1) current,
finding multiple regions in parameter space with qualitatively different
behavior. We discuss the extension of these results to the regime of
parametrically large charge $Q$, as well as to what extent such results are
expected to hold universally, beyond the limit of holographic CFTs. We compare
our holographic computations to results from the conformal bootstrap for the
$3d$ O(2) model at $Q=3$ and $Q=4$ and find excellent agreement.
