论文标题
Siegel模块化形式的尺寸公式$ 4 $
Dimension formulas for Siegel modular forms of level $4$
论文作者
论文摘要
我们证明了标量价值的Siegel模块化形式$ 2 $的几个维度公式相对于某些级别的$ 4 $ $ 2 $。如果是尖式形式，所有模块化表格都认为是源自$ \ mathrm {gsp}的cuspidal自动形态表示（4，\ mathbb {a}）$，其本地组件的$ p = 2 $ p = 2 $允许在prijectal Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Qualtor Queldence afteral Qualtal Queldence supper last Level Level级别$ 2 $ 2 $ 2 $ 2 $中。使用已知的尺寸公式与$ p = 2 $的局部表示中固定向量的空间的尺寸结合在一起，我们获得了相关汽车表示数量的公式。这些反过来又导致了新的维度公式，尤其是Siegel模块化形式相对于Klingen一致性子组的$ 4 $。
We prove several dimension formulas for spaces of scalar-valued Siegel modular forms of degree $2$ with respect to certain congruence subgroups of level $4$. In case of cusp forms, all modular forms considered originate from cuspidal automorphic representations of $\mathrm{GSp}(4,\mathbb{A})$ whose local component at $p=2$ admits non-zero fixed vectors under the principal congruence subgroup of level $2$. Using known dimension formulas combined with dimensions of spaces of fixed vectors in local representations at $p=2$, we obtain formulas for the number of relevant automorphic representations. These in turn lead to new dimension formulas, in particular for Siegel modular forms with respect to the Klingen congruence subgroup of level $4$.
