  We construct an infinite class of eigenmodes with integer eigenvalues for the
Vacuum Modular Hamiltonian of a single interval $N$ in 2d CFT and study some of
its interesting properties, which includes its action on OPE blocks as well as
its bulk duals. Our analysis suggests that these eigenmodes, like the OPE
blocks have a natural description on the so called kinematic space of CFT$_2$
and in particular realize the Virasoro algebra of the theory on this kinematic
space. Taken together, our results hints at the possibility of an effective
description of the CFT$_2$ in the kinematic space language.
