标题： 在特征$p$中定义新形式 显示英文标题

标题： Defining newforms in characteristic $p$

摘要： 新形式理论由Atkin和Lehner提出，为分解模形式空间提供了一种有效的方法。 然而，当尝试将此理论推广到特征$p$时，会出现许多问题。 最近，Deo和Medvedovsky通过使用纯粹的代数概念来定义新形式，提出了绕过这些问题的方法。 在本论文中，我们详细描述了Deo和Medvedovsky的方法，并尽可能地推广了他们的结果。 显示英文摘要

摘要： The theory of newforms, due to Atkin and Lehner, provides a powerful method for decomposing spaces of modular forms. However, many problems occur when trying to generalise this theory to characteristic $p$. Recently, Deo and Medvedovsky have suggested a way around these problems by using purely algebraic notions to define newforms. In this thesis, we describe the methods of Deo and Medvedovsky in detail and generalise their results where possible.