I am wondering what subspaces of modular varieties defined as the zero locus of modular forms have been studied in the literature.

To be more clear let me explain the example I have in mind.

Let $N\ge 5$ be a natural number prime to a prime number $p$. Let $\mathfrak{X}$ be a smooth integral model over $\mathbb{Z}[1/N]$ of the modular curve of level $\Gamma_1(N)$. Then in the special fiber $X:=\mathfrak{X}\otimes_{\mathbb{Z}[1/N]}\mathbb{F}_p$ we can consider the supersingular locus $X^{ss}$ which is defined as the zero locus of the Hasse invariant $h\in H^0(X,\omega^{\otimes(p-1)})$ where $\omega^{\otimes(p-1)}$ is the sheaf of weight $p-1$ modular forms.

Do you know any other meaningful example as $X^{ss}$?


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