Mathematics 257

Computing With Modular Forms

William Stein

References

Atkin-Lehner, Hecke Operators on Gamma₀(N) [PDF, 8.5MB]
Cohen, A Course in Computational Algebraic Number Theory (Amazon.com link)
Cohen and Oesterle, Dimensions des espaces de formes modulaires [PDF, 1MB], Lecture Notes in Math., Vol. 627
Cremona, Algorithms for modular elliptic curves [PDF, 3MB]
Diamond-Im, Modular forms and modular curves [PDF, 25MB]
Hijikata, Explicit formula of the trace of Hecke operators for Gamma₀(N), first three pages (PDF)
Kohel, Hecke module structure of quaternions [PDF]
MAGMA Documentation
Manin, Parabolic points and zeta functions of modular curves [PDF]
Merel, Intersections sur des courbes modulaires [PDF]
Merel, Universal Fourier Expansions of Modular Forms [PDF], [DVI].
Mestre, The Method of Graphs (see the bottom of this page)
Ribet, On modular representations of GalQ arising from modular forms, [PDF, 5MB]
Ribet-Stein, Lectures on Serre's Conjecture [PDF]
Serre, A Course in Arithmetic, chapter 7 [PDF, 16MB]
Serre, Sur les representations modulaires deg degre 2 de GalQ [PDF]
Shimura's chapter on dimension formulas from Introduction to the arithmetic theory of automorphic functions (chapters 1 and 2) [PDF, 19MB]
Stein, The Modular Forms Database
Stein, Math 252: Modular Abelian Varieties
Stein, Explicit Approaches to Modular Abelian Varieties (Ph.D. Thesis)
Sturm, On the congruence of modular forms [PDF], Lecture Notes in Math., 1240
Winnie-Li, Newforms and Functional Equations [TIF, 1.8MB, use a fax viewer]