Hi, I have to find the number of subspaces of where is a finite field with elements.

I know there are the trivial subspaces.

I thought the subspaces may be the possible lines ( I mean the possible inclinations )

For example, would have the lines whose parallel vectors are (0,1) (0,2) ... (0,6) (1,0) (1,1) (1,2) (1,3) ... (1,6) (2,0) (2,1) (2,3) (2,5) etc.

Is it right?