The Stockwell transform and its modified version, a hybrid of the Gabor and the wavelet transform, using modulation, translation and dilation operations, fall into the class of square-integrable group representations. The resolution of the identity can then be used to introduce localization operators. First Schatten-von-Neumann classes and localization operators corresponding to square-integrable representations of locally compact and Hausdorff groups are recalled. The trace class norm inequalities for the trace class localization operators are studied and an explicit formula for the lower bound of the trace norm is given.