论文标题
临界形式的尺寸和紧凑的扭曲模块形式与相关
Dimensions of paramodular forms and compact twist modular forms with involutions
论文作者
论文摘要
We give an explicit dimension formula for paramodular forms of degree two of prime level with plus or minus sign of the Atkin--Lehner involution of weight $\det^k\operatorname{Sym}(j)$ with $k\geq 3$, as well as a dimension formula for algebraic modular forms of any weight associated with the binary quaternion hermitian maximal lattices in non-principal genus of prime具有固定迹象的判别。这两个公式本质上是相当于Dummigan，A。Pacetti的最新结果。 G. Rama和G.tornaría关于代数模块化形式和带有符号的偏形形式之间的对应关系。因此，我们通过计算后者来提供公式。当$ p $很奇怪时，我们的后者公式基于T. asai的某些Quinary Lattices的类号公式及其对以前作品中给出的Quaternion Hermitian形式的类型数量的解释。在偏尾形式上，我们还给出了Plus和减去特征空间之间的尺寸偏差，一些Palindromic Hilbert系列列表，小$ P $和$ K $的数值示例，以及Primes $ P $的完整列表，因此没有Paramodular cusp cusp cusp cusp cusp的级别级别的级别$ p $ p $ with plus afr sign with plus sign。最后一个结果具有$（1，p）$极化的Kummer表面模量的几何含义。
We give an explicit dimension formula for paramodular forms of degree two of prime level with plus or minus sign of the Atkin--Lehner involution of weight $\det^k\operatorname{Sym}(j)$ with $k\geq 3$, as well as a dimension formula for algebraic modular forms of any weight associated with the binary quaternion hermitian maximal lattices in non-principal genus of prime discriminant with fixed sign of the involution. These two formulas are essentially equivalent by a recent result of N. Dummigan, A. Pacetti. G. Rama and G. Tornaría on correspondence between algebraic modular forms and paramodular forms with signs. So we give the formula by calculating the latter. When $p$ is odd, our formula for the latter is based on a class number formula of some quinary lattices by T. Asai and its interpretation to the type number of quaternion hermitian forms given in our previous works. On paramodular forms, we also give a dimensional bias between plus and minus eigenspaces, some list of palindromic Hilbert series, numerical examples for small $p$ and $k$, and the complete list of primes $p$ such that there is no paramodular cusp form of level $p$ of weight 3 with plus sign. This last result has geometric meaning on moduli of Kummer surface with $(1,p)$ polarization.
