一次本征形式的素数幂同余
Prime-power congruences for level-one eigenforms
AI总结：
本文研究权重变化时一次本征形式的素数幂同余，通过构造Hecke等变转移映射将问题简化为有限计算，并对p=2,3,5,7分别获得模2^8、3^4、5^3和7^2的全权重分类。
AI中文摘要：
我们研究了当权重变化时，归一化的尖点一次本征形式的素数到p的Hecke本征系统的素数幂同余，并解决了对小素数幂分类此类系统的问题。我们通过乘以Dickson不变量的合适提升，构造了一次模符号模之间的Hecke等变转移映射；这些映射将问题简化为有限计算，并通过所有权重传播Hecke算子关系。对于p=2,3,5,7，我们分别获得了模2^8、3^4、5^3和7^2的全权重分类。
英文摘要：
We study prime-power congruences for the prime-to-\(p\) Hecke eigensystems of normalized cuspidal level-one eigenforms as the weight varies, and we address the problem of classifying such systems for small prime powers. We construct Hecke-equivariant transfer maps between level-one modular-symbol modules via multiplication by suitable lifts of Dickson invariants; these maps reduce the problem to finite computation and propagate Hecke operator relations through all weights. For \(p=2,3,5,7\), we obtain all-weight classifications modulo \(2^8\), \(3^4\), \(5^3\), and \(7^2\), respectively.
