 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
Epilogue
Epilogue
 Chapter:
 (p.399) Epilogue
 Source:
 Computational Aspects of Modular Forms and Galois Representations
 Author(s):
 Bas Edixhoven, JeanMarc Couveignes
 Publisher:
 Princeton University Press
This epilogue describes some work on generalizations and applications, as well as a direction of further research outside the context of modular forms. Theorems 14.1.1 and 15.2.1 will certainly be generalized to spaces of cusp forms of arbitrarily varying level and weight. This has already been done for the probabilistic variant of Theorem 14.1.1, in the case of squarefree levels (and of level two times a squarefree number). Some details and some applications of Bruin's work, as well as a perspective on point counting outside the context of modular forms are described. Deterministic generalizations of the two theorems mentioned above will lead to deterministic applications.
Keywords: modular forms, cusp forms, squarefree levels, Peter Bruin
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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