  We prove the classical $l = p$ local-global compatibility conjecture for
certain regular algebraic cuspidal automorphic representations of weight 0 for
GL$_2$ over CM fields. Using an automorphy lifting theorem, we show that if the
automorphic side comes from a twist of Steinberg at $v | l$, then the Galois
side has nontrivial monodromy at $v$. Based on this observation, we will give a
definition of the Fontaine-Mazur $\mathcal{L}$-invariants attached to certain
automorphic representations.
