Modular representations of the symplectic group

Let G=Sp(2m,2) be a finite symplectic group acting on $F_2^{2m}$. This group G acts 2-transitively on $\Omega_{+}$ and on $\Omega_{-}$. Let $F$ be an algebraic closure of $F_2$. I am interested to know what are all $G$- invariant sub-spaces of $F^{\Omega_{+}}$ and ${F} ^{\Omega_{-}}$. Does anyone know good reference where this is calculated?

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I did a little editing but the question needs more editing as well as an explanation of all the symbols used. What is the field here? Is the question about a finite group, an algebraic group, or a Lie group? There is a lot of literature relevant to actions and representations of symplectic groups over various fields, but the question needs to be stated precisely. – Jim Humphreys Feb 7 '12 at 20:42
Here $G$ is a finite syplectic group acting on $F_2^{2m}$. – Klim Efremenko Feb 7 '12 at 21:28
As far I understand finite symplectic group acts two transitively only over $F_2$ and it have two sets on which it acts two transitively. – Klim Efremenko Feb 7 '12 at 21:36