Publication Date:
2014-03-28
Description:
Let $f$ be a (cuspidal) newform of weight $k\ge 2$ and level $\Gamma _0(N)$ with $N\ge 1$ . Ribet proved that, under the assumption that $f$ is non-CM, the residual representations $\bar {\rho }_{f,\lambda }$ attached to $f$ by Deligne have a large image, in a precise sense, for all but finitely many prime ideals $\lambda$ . In this paper, we make Ribet's theorem explicit by proving that the residue characteristics of these finitely many prime ideals for which the conclusion of Ribet's theorem fails to satisfy some divisibility relation, or are bounded from above by explicit constants, depending on $k$ and $N$ . The results split into different cases according to the possible types for the image, and each of them is illustrated by some numerical examples.
Print ISSN:
0024-6107
Electronic ISSN:
1469-7750
Topics:
Mathematics
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