On “good” Half-integral Weight Modular Forms
نویسندگان
چکیده
If k is a positive integer, let Sk(N) denote the space of cusp forms of weight k on Γ1(N), and let S k (N) denote the subspace of Sk(N) spanned by those forms having complex multiplication (see [Ri]). For a non-negative integer k and any positive integer N ≡ 0 (mod 4), let Mk+ 2 (N) (resp. Sk+ 2 (N)) denote the space of modular forms (resp. cusp forms) of half-integral weight k + 12 on Γ1(N). Similarly, if k ∈ 1 2N, then let Mk(N,χ) (resp. Sk(N,χ)) denote the space of modular (resp. cusp) forms with respect to Γ0(N) and Nebentypus character χ. Throughout this note we shall refer to classical facts which may be found in [Ko, Mi, S-S, Sh]. If i = 0 or 1, 0 ≤ r < t, and a ≥ 1, then let θa,i,r,t(z) denote the Shimura theta function
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