Modular Forms of Weight 4 / 5 for Γ ( 11
نویسندگان
چکیده
In this paper, we show how to construct some explicit modular forms of weight 4/5 for Γ(11). We first compute the group of all invariant line bundles on the modular curve of level p. We then show that many modular forms of certain fractional weights occur in nature, using work of Felix Klein and our computation of the invariant line bundles. Using Klein’s work, the Woods Hole Fixed Point Formula and previous work of the author in invariant theory, we derive a remarkable identity among theta functions and use it to compute the modular forms of weight 4/5. The methods used here appear likely to generalize to other levels and to have a number of applications which we will explore in subsequent papers. We release this short note now in order to expedite communication of this particular result. AMS Classification Numbers: 11F03, 11F11, 11F12, 14F05,14F10, 14F12, 14G35, 20C15, 20C20
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تاریخ انتشار 2007