What is the Dimension of Equilibrium Space in Longitudinal Space?
I never heard of the term "Equilibirum Space" in flight dynamics and I can't find references in a quick google search. 

However, I assume you are talking about describing the flight dynamics of an aircraft as a linear state-space model. When linearising, you can indeed separate the equations of motion in the plane symmetry (longitudinal) from the assymetric (lateral) motions.

$\dot{ \vec{x}}=\mathbf{A} \vec{x} + \mathbf{B} \vec{u} $

The dimension of the state vector $\vec{x}$ is usually 4 (velocity, flight path angle, pitch angle and pitch rate), in your case the dimension of the control vector  $\vec{u}$ is 2 (thrust and elevator deflection).

You linearise the equations of motion around an equilibrium point; the state and control vectors describe the deviation from that equilibrium point. The dimension of the equilibrium points is 6 (4 state variable, 2 control variables).

One could say that the equilibrium point is in the space spanned by the 6 independent state and control variables. If that is what you mean, then dimension of the equilibrium space is 6.