  We compute the spectral form factor of the modular Hamiltonian $K=-\ln\rho_A$
associated to the reduced density matrix of a Haar random state. A ramp is
demonstrated and we find an analytic expression for its slope. Our method
involves an application of the replica trick, where we first calculate the
correlator $<\text{tr}\rho_A^n\;\text{tr}\rho_A^m>$ at large bond dimension and
then analytically continue the indices $n,m$ from integers to arbitrary complex
numbers. We use steepest descent methods at large modular times to extract the
ramp. The large bond dimension limit of the replicated partition function is
dominated by a sum over \emph{annular non-crossing permutations}. We explored
the similarity between our results and calculations of the spectral form factor
in low dimensional gravitational theories where the ramp is determined by the
double trumpet geometry. We find there is an underlying resemblance in the two
calculations, when we interpret the annular non-crossing permutations as
representing a discretized version of the double trumpet. Similar results are
found for an equilibrated pure state in place of the Haar random state.
