Abandoned Nest?

There is a cavity nest in a field across our road. It is a hole nest in a dying tree. The tree is small and still has some leaves, but most of the top is cut off and it is starting to rot. The entrance hole is 3 1/2 cm wide and 4 cm tall leading to a cavity more than 10 cm deep. Their is a small grass nest with four completely white eggs. Each egg is about an inch tall. I have visited the nest site several times, each time seeing no birds in the nest. I see Savannah Sparrows singing very near the nest, but they nest on the ground and don't have white eggs. So I assume it is abandoned, I can't touch the eggs to see if they're warm because they are too deep in the cavity. It might have been a woodpecker nest before but now it looks abandoned.