Eta Products and Models for Modular Curves

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Although we will only use the theorem to pull back forms of level 1 (in particular ∆), the theorem does tell us explicitly how to obtain the q-expansions of πl ∗ f at any cusp, given the q-expansions at the image cusp. (It’s just a substitution, since q is just a number here!)
Although we will only use the theorem to pull back forms of level 1 (in particular ∆), the theorem does tell us explicitly how to obtain the q-expansions of πl ∗ f at any cusp, given the q-expansions at the image cusp. (It’s just a substitution, since q is just a number here!) Corollary 1.1: Suppose f is a form for Γ 0 (1) with q-expansion f (q). Then the expansion at (C ∗ p/q d , 〈ζq〉) of πl ∗ f is given by f (ζ bNg/d q lg2 /d ) ( lg d ) k .
Page 1 and 2: Eta Products and Models for Modular
Page 3 and 4: Cusps, as Families of Tate Curves D
Page 5 and 6: Cusps, as Families of Tate Curves D
Page 7 and 8: Lemma: (C ∗ p/q d , 〈ζq〉)
Page 9 and 10: The Tate Curve C ∗ p/q d with Som
Page 11 and 12: Definition of Modular Forms Definit
Page 13 and 14: Pullbacks by Level-Lowering Maps Su
Page 15 and 16: Pullbacks by Level-Lowering Maps Su
Page 17 and 18: Theorem 1: Suppose r, d, M, and l a
Page 19: Theorem 1: Suppose r, d, M, and l a
Page 23 and 24: Ligozat’s Criteria Definition: Le
Page 25 and 26: q-expansions of ∆ pullbacks Theor
Page 27 and 28: Corollary 3.1: The leading term of
Page 29 and 30: Corollary 3.1: The leading term of
Page 31 and 32: Eta products on X 0 (18) Applying t
Page 33 and 34: Moreover, the values of f 24 at the
Page 39 and 40: What if there aren’t enough eta p
Page 41 and 42: A Nice Example Involving X 0 (11) D
Page 43 and 44: Remark: This reduces mod 11 to t 2
Page 45 and 46: Remark: This reduces mod 11 to t 2
Page 47 and 48: Conclusions: (1) It’s fairly stra
Page 49 and 50: Conclusions: (1) It’s fairly stra
Page 51 and 52: Eta Product Package Wish List Easy:
Page 53 and 54: Eta Product Package Wish List Easy:
Page 55 and 56: Basis Calculation for X 0 (18) Ligo
Page 57 and 58: Basis Calculation for X 0 (18) Ligo
Page 59 and 60: Using eta products to find an equat
Page 61 and 62: Using eta products to find an equat
Page 63 and 64: Since u = 13 at the cusp 0, we let
Page 65: Since u = 13 at the cusp 0, we let

Eta Products and Models for Modular Curves

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