模形式空间在Hecke算子作用下不变的显式证明

Explicit proof of modular forms being invariant under Hecke operation

基于对模形式的研究,得到模形式空间及尖点形式子空间在Hecke算子作用下不变的1个显式证明,并得到模形式在Hecke算子作用前后的傅里叶系数关系的显式表达.

Based on the research of modular form theory, it is explicitly proved that modular form space and its cusp form subspace are invariant under Hecke operations. The explicit formula of the changes of Fourier coefficient between the modular form and the new form obtained by Hecke operation is also gotten.