Let $\mathcal{C}$ be a spherical tensor category. It is known that the Drinfeld center of $\mathcal{C}$ is modular (and therefore also spherical), see for example, Corollary 8.20.14 in [1]. Recall the notion of dimension in spherical tensor categories obtained by taking the quantum trace of the identity.

**Question:** For a given object $Z = (X,\gamma)$ in the Drinfeld center is there a simple way to express the dimension $d(Z)$ in terms of $X$ and $\gamma$?

[1] *Etingof, Pavel; Gelaki, Shlomo; Nikshych, Dmitri; Ostrik, Victor*, **Tensor categories**, Mathematical Surveys and Monographs 205. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2024-6/hbk). xvi, 343 p. (2015). ZBL1365.18001..