  We study extra time-frequency shift invariance properties of Gabor spaces.
For a Gabor space generated by an integer lattice, we state and prove several
characterizations for its time-frequency shift invariance with respect to a
finer integer lattice. The extreme cases of full translation invariance, full
modulation invariance, and full time-frequency shift invariance are also
considered. The results show a close analogy with the extra translation
invariance of shift-invariant spaces.
