Assuming you do not have a roommate or a south/west facing window that gets beaten by the sun, a 5,000 BTU unit should be enough. You definitely need to find a unit that is specifically designed for casement windows.

5000 or 6000 btu casement or low profile will do it. Even a Walmart type room ac is pretty narrow. You will have to measure.

IF it a casement window, then it is highly recommended that you get a casement window air conditioner.

My room gets incredibly hot during the spring/summer, so I have decided to buy myself an air conditioner, the only problem is that I don't know which kind I should buy. The dimensions of my room are 11' x 11', with 8' ceilings. I only have one window in my room, tucked away in the corner of my room, and it's a casement window. So what power should I be looking to get, along with what type of air conditioner considering my window width is smaller than most normal sizes?