  We give a new class of equivalent norms for modulation spaces by replacing
the window of the short-time Fourier transform by a Hilbert-Schmidt operator.
The main result is applied to Cohen's class of time-frequency distributions,
Weyl operators and localization operators. In particular, any positive Cohen's
class distribution with Schwartz kernel can be used to give an equivalent norm
for modulation spaces. We also obtain a description of modulation spaces as
time-frequency Wiener amalgam spaces. The Hilbert-Schmidt operator must satisfy
a nuclearity condition for these results to hold, and we investigate this
condition in detail.
