Invariant subspace shift operator $\psi H^2$

Question

$H^2$ - Hardy space analytics function on unit disk; $M_z:H^2 \to H^2$, $M_z f = zf(z)$. We know Beurling theorem: Every invariant subspace shift operator other than $\{0\}$ has the form $\phi H^2$, where $\phi$ is an inner function. Let $\psi = exp(\frac{z+1}{z-1})$, then $M = \psi H^2$ is invariant subspace of shift operator. QUESTION: Describe subspace $M$?