Primitive Cusp Forms
نویسنده
چکیده
For example, let f11A denote the (unique) level 11 weight 2 cusp form, then both f11A(z) and f11A(2z) are level 22 cusp forms. Similarly, both f14A(z) and f14A(2z) are level 28 cusp forms, and both f15A(z) and f15A(2z) are level 30 cusp forms. None of these are “new” at N = 22, 28 or 30 since they arise from lower levels. Define S k (N) to be the vector space of weight k primitive cusp forms (or Hecke newforms) on Γ0(N) with trivial character. We restrict attention to the case k = 2 henceforth. The dimension δ 0 (N) of S # 2 (N) over C possesses the following formula [3, 4, 5]:
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