Header requirements for basement egress window
There are a couple of issues: 1) is the window going to be an egress window in a sleeping area? , and 2) structural concerns. 

1) If the window is going to be used as an egress window, then the opening in the window must be 5.0 square feet and the width must be a minimum of 20” clear opening, the height must be a minimum 24” high and the opening must be a maximum of 44” off the floor. 

If you ever put a pullout couch or bed in that basement, you’d better have a window that meets those requirements or a door that opens directly to the exterior. 

If it needs to be a minimum of 20” wide, a slider will require a rough opening of about 48” wide. 

2) Structurally with two floors, roof and concrete wall resting on your new header, you’ll need at least 4 - 2x6 header on 1 - 2x6 trimmer at each end for a 4’ wide window, unless you have a point load above it (large post), refrigerator, or waterbeds. If you stay with your 3’ wide opening, you could use 3 - 2x6’s.