Depends on the distance the object will be from the camera and the resolution your rendering at. If you're rendering an object that is very close to camera and you render resolution is 4k then you're going to need a texture that is at least 4k.
if your resolution is say a more common 2k and your object will fill half the scene space then you'll need at least a 1k texture. If it's a tiny object thats taking up 2% of the final render then you can get away with smaller.
The above is not gospel by any means simply an aid to help you visualise
From a readers' Q and A column in TV GUIDE: "If we get involved in a nuclear war, would the electromagnetic pulses from exploding bombs damage my videotapes?"