You can clone with
What is the max size in pixels for a texture?
I tried with different file sizes and that didn't matter but when I went up a certain size, the picture wasn't loaded.
This is GPU specific:
"Proper" discrete desktop GPUs will probably support 8,192 x 8,192 pixels (up to maximum of 16,384 x 16,384).
If you want to be safe, seems 2,048 x 2,048 is minimum supported across wide variety of systems (including integrated Intel GPUs and old discrete GPUs):
For mobile devices, from above stats it seems for iOS maximum is 2,048 x 2,048, for Android it's 4,096 x 4,096 pixels.