- Title Pages
- Let τ:ℕ→ℤ be defined by
- Contents
- Preface
- Acknowledgments
- Author information
- Dependencies between the chapters
- Chapter One Introduction, main results, context
- Chapter Two Modular curves, modular forms, lattices, Galois representations
- Chapter Three First description of the algorithms
- Chapter Four Short introduction to heights and Arakelov theory
- Chapter Five Computing complex zeros of polynomials and power series
- Chapter Six Computations with modular forms and Galois representations
- Chapter Seven Polynomials for projective representations of level one forms
- Chapter Eight Description of <i>X</i><sub>1</sub>(5<i>l</i>)
- Chapter Nine Applying Arakelov theory
- Chapter Ten An upper bound for Green functions on Riemann surfaces
- Chapter Eleven Bounds for Arakelov invariants of modular curves
- Chapter Twelve Approximating <i>V<sub>f</sub></i> over the complex numbers
- Chapter Thirteen Computing <i>V<sub>f</sub></i> modulo <i>p</i>
- Chapter Fourteen Computing the residual Galois representations
- Chapter Fifteen Computing coefficients of modular forms
- Epilogue
- Bibliography
- Index

# Computations with modular forms and Galois representations

# Computations with modular forms and Galois representations

- Chapter:
- (p.129) Chapter Six Computations with modular forms and Galois representations
- Source:
- Computational Aspects of Modular Forms and Galois Representations
- Author(s):
### Johan Bosman

- Publisher:
- Princeton University Press

This chapter discusses several aspects of the practical side of computing with modular forms and Galois representations. It starts by discussing computations with modular forms, and from there work towards the computation of polynomials that give the Galois representations associated with modular forms. Throughout, the chapter denotes the space of cusp forms of weight *k*, group Γ₁(*N*), and character ε by *S*ₖ(*N*, ε).

*Keywords:*
modular forms, Galois representations, modular symbols, polynomials, cusp forms

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- Title Pages
- Let τ:ℕ→ℤ be defined by
- Contents
- Preface
- Acknowledgments
- Author information
- Dependencies between the chapters
- Chapter One Introduction, main results, context
- Chapter Two Modular curves, modular forms, lattices, Galois representations
- Chapter Three First description of the algorithms
- Chapter Four Short introduction to heights and Arakelov theory
- Chapter Five Computing complex zeros of polynomials and power series
- Chapter Six Computations with modular forms and Galois representations
- Chapter Seven Polynomials for projective representations of level one forms
- Chapter Eight Description of <i>X</i><sub>1</sub>(5<i>l</i>)
- Chapter Nine Applying Arakelov theory
- Chapter Ten An upper bound for Green functions on Riemann surfaces
- Chapter Eleven Bounds for Arakelov invariants of modular curves
- Chapter Twelve Approximating <i>V<sub>f</sub></i> over the complex numbers
- Chapter Thirteen Computing <i>V<sub>f</sub></i> modulo <i>p</i>
- Chapter Fourteen Computing the residual Galois representations
- Chapter Fifteen Computing coefficients of modular forms
- Epilogue
- Bibliography
- Index