---
title: "Bibliography"
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part: "Modular Arithmetic Geometry"
chapter: "Modular Symbols"
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  - {"title": "Modular Arithmetic Geometry", "source": "../index-modular-arithmetic-geometry.md"}
  - {"title": "Modular Symbols", "source": "index-modular-symbols.md"}
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---

# Bibliography

<a id="cite-agashe-stein-appendix"></a>
- **[AS02]** Amod Agashe and William A. Stein. Appendix to Joan-C. Lario and René Schoof: Some computations with Hecke rings and deformation rings. *submitted*, 2002.
<a id="cite-buzzardsteinicosahedral"></a>
- **[BS02]** Kevin Buzzard and William A. Stein. A mod five approach to modularity of icosahedral Galois representations. *Pacific J. Math.*, 203(2):265–282, 2002.
<a id="cite-cohen-oesterle-dimensions"></a>
- **[CO77]** Henri Cohen and J. Oesterlé. *Dimensions des espaces de formes modulaires*, pages 69–78. Volume 627 of Lecture Notes in Math. Springer, Berlin, 1977.
<a id="cite-cremona-gammaone"></a>
- **[Cre92]** J. E. Cremona. Modular symbols for ${\Gamma}_1({N})$ and elliptic curves with everywhere good reduction. *Math. Proc. Cambridge Philos. Soc.*, 111(2):199–218, 1992.
<a id="cite-cremona-algs"></a>
- **[Cre97]** J. E. Cremona. *Algorithms for modular elliptic curves*. Cambridge University Press, Cambridge, second edition, 1997. ISBN 0-521-59820-6.
<a id="cite-cremona-mazur"></a>
- **[CM00a]** J. E. Cremona and Barry Mazur. Visualizing elements in the Shafarevich-Tate group. *Experiment. Math.*, 9(1):13–28, 2000.
<a id="cite-diamond-im"></a>
- **[DI95]** Fred Diamond and Ju Im. Modular forms and modular curves. In *Seminar on Fermat's Last Theorem*, pages 39–133. Amer. Math. Soc., Providence, RI, 1995.
<a id="cite-empirical-evidence"></a>
- **[FLS+01]** E. V. Flynn, F. Leprévost, E. F. Schaefer, W. A. Stein, M. Stoll, and J. L. Wetherell. Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. *Math. of Comp.*, 70(236):1675–1697, 2001.
<a id="cite-frey-muller"></a>
- **[FM99]** Gerhard Frey and Michael Muller. Arithmetic of modular curves and applications. In *Algorithmic algebra and number theory (Heidelberg, 1997)*, pages 11–48. Springer, Berlin, 1999.
<a id="cite-kohel-stein-ants4"></a>
- **[KS00a]** David R. Kohel and William A. Stein. Component Groups of Quotients of $J_0(N)$. In *Proceedings of the 4th International Symposium (ANTS-IV), Leiden, Netherlands, July 2–7, 2000*. Berlin, 2000. Springer.
<a id="cite-mazur-eisenstein"></a>
- **[Maz77]** Barry Mazur. Modular curves and the Eisenstein ideal. *Inst. Hautes Études Sci. Publ. Math.*, 47:33–186 (1978), 1977.
<a id="cite-merel-intersections"></a>
- **[Mer93]** Loic Merel. Intersections sur des courbes modulaires. *Manuscripta Math.*, 80(3):283–289, 1993.
<a id="cite-merel1585"></a>
- **[Mer94]** Loic Merel. Universal Fourier expansions of modular forms. In *On Artin's conjecture for odd 2-dimensional representations*, 59–94. Springer, 1994.
<a id="cite-mestre-graphs"></a>
- **[Mes86b]** Jean-Francois Mestre. La méthode des graphes. Exemples et applications. *Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata)*, pages 217–242, 1986.
<a id="cite-poonen-stoll"></a>
- **[PS99]** Bjorn Poonen and Michael Stoll. The Cassels-Tate pairing on polarized abelian varieties. *Ann. of Math. (2)*, 150(3):1109–1149, 1999.
<a id="cite-stein-phd"></a>
- **[Ste00]** William A. Stein. Explicit approaches to modular abelian varieties. *Ph.D. thesis, University of California, Berkeley*, 2000.
<a id="cite-stein-compgroup"></a>
- **[Ste01]** William A. Stein. Component Groups of Purely Toric Quotients of Semistable Jacobians. *submitted*, 2001.
<a id="cite-stein-modsyms"></a>
- **[Ste08]** William A. Stein. An introduction to computing modular forms using modular symbols. In *Algorithmic number theory: lattices, number fields, curves and cryptography*, volume 44 of Math. Sci. Res. Inst. Publ., pages 641–652. Cambridge Univ. Press, Cambridge, 2008.
<a id="cite-sturm-congruence"></a>
- **[Stu87]** Jacob Sturm. On the congruence of modular forms. In *Number theory (New York, 1984–1985)*, pages 275–280. Springer, Berlin, 1987.