A symplectic 2-form on a $2n$ dimensional manifold has to be closed, nondegenerate and antisymmetric. My question is: Do these conditions imply how many degrees of freedom the symplectic form has?
I know that any antisymmetric matrix will have $\frac{\big(2n\big)^2-2n}{2}$ but how do I account for the fact that it also has to be closed and nondegenerate?