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Let $\mathcal{M}$ denote the moduli stack of smooth elliptic curves over $\mathbb{C}$. There is a local system, $\mathcal{H}$, on $\mathcal{M}$ with fibre $H^{1}(E,\mathbb{C})$ at the $\mathbb{C}$-...

I want to start by considering a familiar congruence subgroup of the integral symplectic group $\text{Sp}_{4}(\mathbb{Z})$. For a positive integer $N$, let $\Gamma _{0}^{(2)}(N) \subset \text{Sp} _{4}(...

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\...

Let $f\colon \mathbb{H}_g \to \mathbb{C}$ be a Siegel modular form of weight $k$ with respect to $\Gamma_g$. Then, $f$ admits a Fourier expansion $f(Z) = \sum_T a(T) \exp(i\pi \mathop{tr} TZ)$, where $...