  We consider Abelian M5 brane on a six-manifold which we take as a circle
bundle over a five-manifold $M$. We compute the zero mode part of the M5 brane
partition function using Chern-Simons theory and Hamiltonian formulation
respectively and find an agreement. We also show that the D4 brane on $M$
shares exactly the same zero mode partition function again using the
Hamiltonian formulation. For the oscillator modes we find that KK modes
associated with the circle compactification are missing from the D4 brane. By
making an infinitesimal noncommutative deformation we have instanton threshold
bound states. We explicitly compute the instanton partition function up to
instanton charge three, and show a perfect match with a corresponding
contribution inside the M5 brane partition function, thus providing a very
strong supporting evidence that D4 brane is identical with M5 brane which
extends beyond the BPS sector. We comment on the modular properties of the M5
brane partition function when compactified on $T^2$ times a four-manifold. We
briefly discuss a case of a singular fibration.
