  The coefficient forms \( {}_{a} \ell_{k} \) and the para-Eisenstein series
\(\alpha_{k}\) are simplicial Drinfeld modular forms. We study the attached
simplicial complexes \(\mathcal{BT}^{r}( {}_{a} \ell_{k})\) and
\(\mathcal{BT}^{r}(\alpha_{k})\), which are full subcomplexes of the
Bruhat-Tits building \(\mathcal{BT}^{r}\) of \( \mathrm{PGL}(r, K_{\infty})\).
They are connected (if the rank \(r\) is larger than 2), strongly
equidimensional of codimension 1 in \(\mathcal{BT}^{r}\), boundaryless, and
satisfy a symmetry property under the non-trivial involution of the Dynkin
diagram \(A_{r-1}\).
