DETERMINING MULTIPLICITIES OF HALF-INTEGRAL WEIGHT NEWFORMS
DETERMINING MULTIPLICITIES OF HALF-INTEGRAL WEIGHT NEWFORMS
复制标题
确定半积分重新形式的重数
DOI：
10.2140/pjm.1995.167.345
复制
发表时间：
1995
影响因子：
0.6
通讯作者：
L. Walling
中科院分区：
文献类型：
--
作者：
T. Shemanske;L. Walling
我们将半整权的新形式空间分解为重数为1或2的整权的新形式空间的直和。这不仅证明了在一个精确的方式失败的一个多重性的结果举行半整数重量新形式，但此外表明，空间发生与一个给定的多重性。重数为2的空间与Kohnen子空间的集合一一对应。结果表明，在志村对应下，半整权的新形式的水平不取决于它所对应的整权的新形式的水平.由于Hecke特征值的知识是不足以charectesize半整数的重量新形式的标量，我们开发的平方自由系数的充分条件，增加的信息的特征值，允许这样的特征。在最后一节中，这些后来的结果结转到休伯特模设置。
We decompose the space of newforms of half-integral weight into a direct sum of spaces of newforms of integral weight which occur with multiplicity one or two. This not only demonstrates in a precise way the failure of a multiplicity-one result to hold for half-integral weight newforms, but moreover indicates which spaces occur with a given multiplicity. The spaces occuring with multiplicity two are shown to be in one-to-one correspondence with a collection of Kohnen subspaces. As a consequence, it is shown that under the Shimura correspondence, the level a newform of half-integral weight is not determined by the level of the integral weight newform to which it corresponds. Since a knowledge of the Hecke eigenvalues is insuffi-cient to charectesize half-integral weight newforms up to a scalar, we develop sufficient conditions on the squarefree coefficients, augmenting the information on the eigenvalues, which allow such a characterization. In the last section, these later results are carried over to the Hubert modular setting.