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We compute the second Hochschild cohomology space $HH^2(\mathcal{H}_1)$ ofConnes-Moscovici's Hopf algebra $\mathcal{H}_1$, giving the infinitesimaldeformations (up to equivalence) of the associative structure.  $HH^2(\mathcal{H}_1)$ is shown to be one dimensional, and thusConnes-Moscovici's formal deformation of $\mathcal{H}_1$ using Rankin-Cohenbrackets is unique up to equivalence.

Associative algebra deformations of the Connes-Moscovici's Hopf algebra $\mathcal{H}_1$