Siegel modular forms of degree $g$ transform under the action of a discrete subgroup $\Gamma$ of $\mathrm{Sp}_{2g}(\Q)$. We focus on certain discrete subgroups $\Gamma_F(N)$ belonging to a **family** $F$, indexed by $N \in \Z_{\geq 0}$, as follows:

**Siegel (parabolic) subgroup**: the subgroup of $\mathrm{Sp}_{2g}(\Z)$ whose lower $g \times g$ block is zero modulo $N$.**principal congruence subgroup**: the kernel of $\mathrm{Sp}_{2g}(\Z) \to \mathrm{Sp}_{2g}(\Z/N\Z)$.**paramodular subgroup**: corresponds to $(1,\dots,1,N)$-polarized abelian $g$-folds.

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- Review status: beta
- Last edited by Eran Assaf on 2023-06-24 19:58:55

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**History:**(expand/hide all)

- 2023-06-24 19:58:55 by Eran Assaf
- 2023-06-24 19:58:49 by Eran Assaf
- 2023-06-24 19:58:19 by Eran Assaf
- 2022-08-25 17:50:30 by John Voight
- 2022-08-25 17:49:46 by John Voight
- 2022-08-25 17:48:02 by John Voight
- 2022-08-25 17:31:55 by John Voight
- 2022-08-25 17:31:48 by John Voight
- 2022-08-25 17:26:12 by John Voight

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