 Title Pages
 Let $\tau :\mathbb{N}\to \mathbb{Z}$ 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 X_{1}(5l) 
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 V_{f} over the complex numbers 
Chapter Thirteen Computing V_{f} modulo p 
Chapter Fourteen Computing the residual Galois representations 
Chapter Fifteen Computing coefficients of modular forms  Epilogue
 Bibliography
 Index
Bounds for Arakelov invariants of modular curves
Bounds for Arakelov invariants of modular curves
 Chapter:
 (p.217) Chapter Eleven Bounds for Arakelov invariants of modular curves
 Source:
 Computational Aspects of Modular Forms and Galois Representations
 Author(s):
Bas Edixhoven
Robin de Jong
 Publisher:
 Princeton University Press
This chapter gives bounds for all quantities on the righthand side in the inequality in Theorems 9.1.1 and 9.2.5, in the context of the modular curves X₁(5l) with l > 5 prime, using the upper bounds for Green functions from Chapter 10. The final estimates are given in the last section of the chapter.
Keywords: modular forms, bounds, inequality, polynomials, Green functions, modular curves
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 Title Pages
 Let $\tau :\mathbb{N}\to \mathbb{Z}$ 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 X_{1}(5l) 
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 V_{f} over the complex numbers 
Chapter Thirteen Computing V_{f} modulo p 
Chapter Fourteen Computing the residual Galois representations 
Chapter Fifteen Computing coefficients of modular forms  Epilogue
 Bibliography
 Index