It’s not strictly the dimensions of the image that are important but rather the file size. Of course, in general, images that are larger in size tend to be larger in file size so there is some correlation.
Also the file type (png, jpg) can affect the file size.
Remember if your backgroud image has be served to the viewer and the larger it is the longer your page will take to load.
For a seamless texture, I wouldn’t go with more than 100px square but it depends on the effect you are trying to achieve.