论文标题
一种证明模块化galois表示的方法
A method to prove that a modular Galois representation has large image
论文作者
论文摘要
令$ρ$为新形式$ f $的mod $ \ ell $ galois表示。显式方法有时能够确定$ρ$的图像，甚至可以确定$ \ ell $和$ f $的级别$ n $的$ρ$所切的数字字段；但是，这些方法不适合$ \ ell $或$ n $大的情况。简短说明的目的是为$ρ$的图像建立足够的条件，并且对于中等大的$ \ ell $和$ n $，它仍然易于测试。
Let $ρ$ be a mod $\ell$ Galois representation attached to a newform $f$. Explicit methods are sometimes able to determine the image of $ρ$, or even the number field cut out by $ρ$, provided that $\ell$ and the level $N$ of $f$ are small enough; however these methods are not amenable to the case where $\ell$ or $N$ are large. The purpose of this short note is to establish a sufficient condition for the image of $ρ$ to be large and which remains easy to test for moderately large $\ell$ and $N$.
