A modular construction of unramified

We show that for primes N , p ≥ 5 N, \geq 5 with identical-to negative 1 mod p"> ≡ 0 encoding="application/x-tex">\Gamma _0(N^2) whose alttext="script l"> ℓ<!-- ℓ encoding="application/x-tex">\ell th Fourier coefficient congruent to l plus 1"> + encoding="application/x-tex">\ell + 1 modulo prime above all use Galois representation such explicitly construct an unramified degree-<inline-formula extension