A remark on decomposing the canonical representation of the Drinfeld curve

Recently, by studying an explicit basis, K\"ock and Laurent give the decomposition of the $\overline{\mathbb{F}}_q[\mathrm{SL}_2(\mathbb{F}_q)]$-module of holomorphic forms on the Drinfeld curve. We present a crystalline cohomological proof of this decomposition, without specifying a basis.
Comment: 4 pages