Modular forms of half-integral weights on SL(2, ℤ)

Abstract

AbstractIn this paper, we prove that, for an integer r with (r, 6) = 1 and 0 < r < 24 and a nonnegative even integer s, the setis isomorphic toas Hecke modules under the Shimura correspondence. Here Ms(1) denotes the space of modular forms of weight is the space of newforms of weight 2k on Γ0 (6) that are eigenfunctions with eigenvalues €2 and €3 for Atkin-Lehner involutions W2 and W3, respectively, and the notation ⊕(12/.) means the twist by the quadratic character (12/-). There is also an analogous result for the cases (r, 6) = 3.