grow space

Is 15" x 15" x 40" big enough for 1 mother plant

Kinda tight.
I have a 3'X2' closet and all three touch the walls.

Yes if you grow it bonsai. Search for bonsai mother in the major forums and you will get plenty of info. Here is a pic of a bonsai mother from a thread at icmag, I kept it because I thought it was really cool.