In this note, R is the algebra of 2 by 2 generic matrices over two generators, R' is the characteristic ring of R. In the first part, we compute a Molien formula for the invariant of R and R' under a finite subgroup of $GL_2$. In a second part we study the case of finite subgroup of $\SLm{2}{k}$. They are parametrized by the Coxeter diagram of type $A$, $D$ and $E$. We determine the Poincaré series of the invariants under groups of the $A$ and $E$.