Eta Products and Models for Modular Curves
Eta Products and Models for Modular Curves
Eta Products and Models for Modular Curves
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Theorem 1: Suppose r, d, M, <strong>and</strong> l are positive divisors of N, such<br />
that Ml ∣ ∣ N (so πl : X 0 (N) → X 0 (M)) <strong>and</strong> lcm(d, r) = N. Suppose ζ is<br />
a primitive r th root of unity. Suppose f is any weight k modular <strong>for</strong>m<br />
<strong>for</strong> Γ 0 (M).