  Warped conformal field theories (WCFTs) are a novel class of non-relativistic
theories. A simple, yet non-trivial, example of such theory is a massive Weyl
fermion in $(1+1)$-dimensions, which we study in detail. We derive general
properties of the spectrum and modular properties of partition functions of
WCFTs. The periodic (Ramond) sector of this fermionic system is non-trivial,
and we build two novel partition functions for this sector which have no
counterpart in a CFT$_2$. The thermodynamical properties of WCFTs are revisited
in the canonical and micro-canonical ensemble.
