  We introduce a new cluster character with coefficients for a cluster category
$\mathcal{C}$ and rather than using a Frobenius $2$-Calabi-Yau realization to
incorporate coefficients into the representation-theoretic model for a cluster
algebra, as done by Fu and Keller, we exploit intrinsic properties of
$\mathcal{C}$. For this purpose, we define an ice quiver associated to each
cluster tilting object in $\mathcal{C}$. In Dynkin case $\mathbb{A}_n$, we also
prove that the mutation class of the ice quiver associated to the cluster
tilting object given by the direct sum of all projective objects is in
bijection with set of ice quivers of cluster tilting objects in $\mathcal{C}$.
