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Author: William A. Stein
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MATH 583: Computing With Modular Forms, Spring 2006, UW.
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Lecture Plan
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[x] (Fri Apr 7) Level 1 modular forms 3: Structure theorem, Victor Miller Basis
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[x] SAGE 1: Software for Algebra and Geoemtry Experiementation -- intro
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[x] Level 1 modular forms 4: Hecke Operators; Maeda, Edixhoven
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[x] Special Topic: Fast computation of Bernoulli numbers
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[x] Modular symbols 1: basic definitions
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[x] Modular symbols 2: modular symbols
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[x] Modular symbols 3: Hecke operators
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[x] Modular symbols 4: computing modular forms using modular symbols
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[x] Dirichlet characters: intro and algorithm
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[x] (April 28) C. Doran -- elliptic modular surfaces
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[x] Dirichlet characters: more
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[x] Movie -- "The Proof"
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[x] Eisenstein series: computing an explicit basis
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[x] Dimension formulas: statement and how to compute
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[x] Linear algebra 1: computing echelon forms
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[x] Linear algebra 2: decomposition algorithms
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[x] Higher Weight Modular Symbols 1: basic definitions; how to compute:
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Sections 8.1 -- 8.2
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[x] Higher Weight Modular Symbols 2: Hecke operators on them
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Sections 8.3
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[x] Higher Weight Modular Symbols 3: the integration pairing
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Sections 8.5
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[x] Newforms 1: Atkin-Lehner-Li theory
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Sections 9.1 -- 9.3
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[x] Newforms 2: Computing (and storing!) systems of eigenvalues
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Section 9.4
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[] Special Values of L-functions using modular symbols
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Sections 10.1-10.4
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[] (may 29 -- memorial day holiday)
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[] Enumeration of all elliptic curves of given conductor (Cremona's program):
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Sections 10.6-10.7
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[] Sturm's bound: Congruences between modular forms; gen. Hecke algebras
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Chapter 11
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