where G is the Galois group GaI ( I ) /Q) and F is a finite field of characteristic I > 3. Suppose that p is modular of level N, i.e., that it arises from a weight-2 newform of level dividing N and… Expand

Suppose that is a newform of weight k on Г 1 ( N ). Thus f is in particular a cusp form on Г 1 ( N ), satisfying for all n≥1. Associated with f is a Dirichlet character such that for all, .

Let C be an elliptic curve over Q. Let N be the conductor of C. The Taniyama conjecture asserts that there is a non-constant map of algebraic curves X 0 (N) — C which is defined over Q. Here, X o (N)… Expand