I think there isn't one optimal dimension for everyone, as it depends. I found a way to determine it yourself. Maybe not the most high-tech way, but it kinda works.

To start with, compare some of the contestants here. On their profile page they have written something about themselves (visible under their name). Some have 1 line of text, some 2 or 3. As you can probably see, this has an influence on the height of the cover image.

So, first write your 'about' info to determine the height of the cover image. After that printscreen your page, paste it in paint and use the select tool to select only the cover image part. Down in your screen you see the dimension!

For me that results in a dimension of 1899x269 when having 3 'about' lines (let's round that up to 1900x270). Haven't tried it, but any factor of these dimensions (3800x540, 5700x710, etc.) might work, as long as you keep the ratio. That is, if it will fit your uploaded cover image into the cover image field. Easy to check.

If someone has a easier/better way to do it, I would like to hear it!