I believe that it is 1178px x 250px (from
source).
The various background/color themes we have are custom styles, but they were all created before this banner feature existed, and I see no overrides for this part of our styles, so that dimension should be it.
In general, when you select an image to use, there is a clip box shown and you can use that to select the portion of the original image to use, so I'm not sure there is a need to create an image with those exact dimensions.