论文标题
显式小图像定理，用于残留模块化表示
Explicit Small Image Theorems for Residual Modular Representations
论文作者
论文摘要
令$ρ$ f，$λ$是其系数字段的整数环中附加到新形式F和Prime Ideal $λ$的剩余galois表示形式。在本文中，我们证明了Prime Ideals $λ$的残留特性的明确界限，因此$ρ$ f，$λ$是例外的，可降低的，可降低，是投影性二面图像或投影图像同构对A4，S4或A5的构图。我们还制定了明确的标准，以检查$ρ$ f，$λ$的降低性，从而导致了计算此类$λ$的精确集的算法。我们已经在Pari/GP中实现了该算法。一路上，我们以零角色构建了katz'Ulives的升降机，并且证明了一个新的sturm绑定定理。
Let $ρ$ f,$λ$ be the residual Galois representation attached to a newform f and a prime ideal $λ$ in the integer ring of its coefficient field. In this paper, we prove explicit bounds for the residue characteristic of the prime ideals $λ$ such that $ρ$ f,$λ$ is exceptional, that is reducible, of projective dihedral image, or of projective image isomorphic to A4, S4 or A5. We also develop explicit criteria to check the reducibility of $ρ$ f,$λ$ , leading to an algorithm that compute the exact set of such $λ$. We have implemented this algorithm in PARI/GP. Along the way, we construct lifts of Katz' $θ$ operator in character zero, and we prove a new Sturm bound theorem.
