On a Theorem of Ono and Skinner Original Research Article

In a recent paper, Ono and Skinner [1998, Ann. of Math.147, 453–470] show that if a half integral weight eigenform g(z) is good, then g(z) has infinitely many coefficients prime to ℓ, for all but finitely many primes ℓ. Their paper ends with the conjecture that all half-integral weight eigenforms (with the exception of certain theta functions) are, in fact, good. We give a brief and elementary proof of the “good” conjecture.