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@article{agashe,
  author="Agash\'{e}, A.",
  title="On invisible elements of the \protect{Tate-Shafarevich} group",
  year=1999,
  pages={369--374},
  journal="Th\'{e}orie des nombres",
  volume={328}
}

@book {antwerpiv,
    TITLE = {Modular functions of one variable. \protect{IV}},
BOOKTITLE = {Proceedings of the International Summer School on Modular
             Functions of One Variable and Arithmetical Applications, RUCA,
             University of Antwerp, Antwerp, July 17--August 3, 1972},
   EDITOR = {Birch, B. J. and Kuyk, W.},
     NOTE = {Lecture Notes in Mathematics, Vol. 476},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1975},
    PAGES = {iv+151},
}

@incollection{birch:bsd,
   AUTHOR = {Birch, B.J.},
    TITLE = {Elliptic curves over \protect{${\mathbf{Q}}$: {A}} progress report},
BOOKTITLE = {1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol.
             XX, State Univ. New York, Stony Brook, N.Y., 1969)},
    PAGES = {396--400},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, R.I.},
     YEAR = {1971}
}

@article {boston-lenstra-ribet,
   AUTHOR = {Boston, N. and Lenstra, H.W., Jr. and Ribet, K.A.},
    TITLE = {Quotients of group rings arising from two-dimensional
             representations},
  JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.},
 FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
             Math\'ematique},
   VOLUME = {312},
     YEAR = {1991},
   NUMBER = {4},
    PAGES = {323--328},
     ISSN = {0764-4442},
    CODEN = {CASMEI},
}

@book{buhler-thesis,
   AUTHOR = {Buhler, Joe P.},
    TITLE = {Icosahedral \protect{G}alois representations},
     NOTE = {Lecture Notes in Mathematics, Vol. 654},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1978},
    PAGES = {ii+143},
     ISBN = {3-540-08844-X},
}

@article{atkin-lehner,
   AUTHOR = {Atkin, A. O. L. and Lehner, J.},
    TITLE = {Hecke operators on \protect{$\Gamma \sb{0}(m)$}},
  JOURNAL = {Math. Ann.},
   VOLUME = {185},
     YEAR = {1970},
    PAGES = {134--160},
}



@article{brueggeman:nonexistence,
   author = {Brueggeman, S.},
   title  = {The non-existence of certain \protect{Galois} extensions 
      unramified outside 5},
   journal = {Journal of Number Theory},
   volume = {75},
   date   = {1999},
   pages  = {47--52}
}

@article{brumer:rank,
   AUTHOR = {Brumer, A.},
    TITLE = {The rank of \protect{${J}\sb 0({N})$}},
     NOTE = {Columbia University Number Theory Seminar (New York, 1992)},
  JOURNAL = {Ast\'erisque},
 FJOURNAL = {Ast\'erisque},
   NUMBER = {228},
     YEAR = {1995},
    PAGES = {3, 41--68},
     ISSN = {0303-1179},
}

@incollection {cassels:global,
   AUTHOR = {Cassels, J. W. S.},
    TITLE = {Global fields},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965)},
    PAGES = {42--84},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}

@article{CAREARLY,
   author="Carayol, H.",
   title={Sur les \protect{repr\'esentations}
    \protect{$\ell$-adiques} \protect{associ\'ees}
     aux formes modulaires de \protect{Hilbert}},
   journal={Ann. scient. \protect{\'Ec.} Norm. Sup., 
            \protect{$4^{\rm eb}$ s\'erie}},
   volume={19},
   year={1986},
   pages={409--468}
}

@article{CAR,
   author={Carayol, H.},
   title={Sur les \protect{repr\'esentations} galoisiennes
  modulo \protect{$\ell$ attach\'ees} aux formes modulaires},
  journal={Duke Math. J.},
   volume={59},
   year ={1989},
   pages ={785--801}
}

@article{coleman:monodromy,
   author = {Coleman, R.},
   title = {The monodromy pairing},
    journal = {Asian Math. Journal},
   year = {1999}
}

@book {cremona:algs,
   AUTHOR = {Cremona, J.E.},
    TITLE = {Algorithms for modular elliptic curves},
  EDITION = {Second},
PUBLISHER = {Cambridge University Press},
  ADDRESS = {Cambridge},
     YEAR = {1997},
    PAGES = {vi+376},
     ISBN = {0-521-59820-6},
}


@article{cremona:gammaone,
   AUTHOR = {Cremona, J.E.},
    TITLE = {Modular symbols for \protect{$\Gamma\sb 1({N})$} 
and elliptic curves with
             everywhere good reduction},
  JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
 FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
             Society},
   VOLUME = {111},
     YEAR = {1992},
   NUMBER = {2},
    PAGES = {199--218},
     ISSN = {0305-0041},
    CODEN = {MPCPCO},
}


@article{cremona-mazur,
   author="J.E. Cremona and B. Mazur",
   title="Visualizing elements in the \protect{Shafarevich-Tate} Group",
   journal="Proceedings of the Arizona Winter School",
   year=1998,
}



@book {curtis-reiner,
   AUTHOR = {Curtis, C.W. and Reiner, I.},
    TITLE = {Representation theory of finite groups and associative
             algebras},
     NOTE = {Pure and Applied Mathematics, Vol. XI},
PUBLISHER = {Interscience Publishers, a division of John Wiley \& Sons, New
             York-London},
     YEAR = {1962},
    PAGES = {xiv+685},
}

@incollection{ddt,
   AUTHOR = {Darmon, H. and Diamond, F. and Taylor, R.},
    TITLE = {Fermat's last theorem},
BOOKTITLE = {Current developments in mathematics, 1995 (Cambridge, MA)},
    PAGES = {1--154},
PUBLISHER = {Internat. Press},
  ADDRESS = {Cambridge, MA},
     YEAR = {1994},
}



@inproceedings {deligne-rapoport,
   AUTHOR = {Deligne, P. and Rapoport, M.},
    TITLE = {Les sch\'emas de modules de courbes elliptiques},
BOOKTITLE = {Modular functions of one variable, II (Proc. Internat. Summer
             School, Univ. Antwerp, Antwerp, 1972)},
    PAGES = {143--316. Lecture Notes in Math., Vol. 349},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
}

@article {diamond-kramer,
   AUTHOR = {Diamond, F. and Kramer, K.},
    TITLE = {Modularity of a family of elliptic curves},
  JOURNAL = {Math. Res. Lett.},
 FJOURNAL = {Mathematical Research Letters},
   VOLUME = {2},
     YEAR = {1995},
   NUMBER = {3},
    PAGES = {299--304},
     ISSN = {1073-2780},
}

@article{hijikata:trace,
   author={Hijikata, H.},
   title={Explicit formula of the traces    
      of \protect{H}ecke operators for
      \protect{$\Gamma_0(N)$}}, 
   volume={26},
   year={1974},
   pages={56--82}
}

@book {katzmazur,
   AUTHOR = {Katz, N.M. and Mazur, B.},
    TITLE = {Arithmetic moduli of elliptic curves},
PUBLISHER = {Princeton University Press},
  ADDRESS = {Princeton, N.J.},
     YEAR = {1985},
    PAGES = {xiv+514},
     ISBN = {0-691-08349-5, 0-691-08352-5},
}


@incollection {lenstra-smit:explicit,
   AUTHOR = {de Smit, B. and Lenstra, H.W.,Jr.},
    TITLE = {Explicit construction of universal deformation rings},
BOOKTITLE = {Modular forms and Fermat's last theorem (Boston, MA, 1995)},
    PAGES = {313--326},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1997},
}

@incollection {mazur:deforming,
   AUTHOR = {Mazur, B.},
    TITLE = {Deforming \protect{G}alois representations},
BOOKTITLE = {Galois groups over \protect{${\bf Q}$} (Berkeley, CA, 1987)},
    PAGES = {385--437},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1989},
}

@article {mazur-ribet,
   AUTHOR = {Mazur, B. and Ribet, K.A.},
    TITLE = {Two-dimensional representations in the arithmetic of modular
             curves},
     NOTE = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)},
  JOURNAL = {Ast\'erisque},
 FJOURNAL = {Ast\'erisque},
   NUMBER = {196-197},
     YEAR = {1991},
    PAGES = {6, 215--255 (1992)},
     ISSN = {0303-1179},
}

@book {MR89b:14029,
    TITLE = {Arithmetic geometry},
   EDITOR = {Cornell, G. and Silverman, J.H.},
     NOTE = {Papers from the conference held at the University of
             Connecticut, Storrs, Conn., July 30--August 10, 1984},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1986},
    PAGES = {xvi+353},
     ISBN = {0-387-96311-1},
}

@book{milne:duality,
   author = {Milne, J.S.},
   TITLE = {Arithmetic duality theorems},
PUBLISHER = {Academic Press Inc.},
  ADDRESS = {Boston, Mass.},
     YEAR = {1986},
    PAGES = {x+421},
     ISBN = {0-12-498040-6},
}

@incollection {milne:abvars,
   AUTHOR = {Milne, J.S.},
    TITLE = {Abelian varieties},
BOOKTITLE = {Arithmetic geometry (Storrs, Conn., 1984)},
    PAGES = {103--150},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1986},
}

@incollection {rosen:abvars,
   AUTHOR = {Rosen, M.},
    TITLE = {Abelian varieties over \protect{${\bf {C}}$}},
BOOKTITLE = {Arithmetic geometry (Storrs, Conn., 1984)},
    PAGES = {79--101},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1986},
}

@article{SAITO,
 author={T. Saito},
 title={\protect{Modular forms and $p$-adic Hodge theory}},
 journal={Invent. Math.},
 volume={129},
 year={1997},
 pages={607--620}}

@book {shimura:intro,
   AUTHOR = {Shimura, G.},
    TITLE = {Introduction to the arithmetic theory of automorphic functions},
     NOTE = {\protect{Kan\^o} Memorial Lectures, No. 1},
PUBLISHER = {Publications of the Mathematical Society of Japan, No. 11.
             Iwanami Shoten, Publishers, Tokyo},
     YEAR = {1971},
    PAGES = {xiv+267},
}

@article {wiles:fermat,
   AUTHOR = {Wiles, A.},
    TITLE = {Modular elliptic curves and \protect{F}ermat's last theorem},
  JOURNAL = {Ann. of Math. (2)},
 FJOURNAL = {Annals of Mathematics. Second Series},
   VOLUME = {141},
     YEAR = {1995},
   NUMBER = {3},
    PAGES = {443--551},
     ISSN = {0003-486X},
    CODEN = {ANMAAH},
}

@article{diamond:modularity,
   AUTHOR = {Conrad, B. and Diamond, F. and Taylor, R.},
    TITLE = {Modularity of certain potentially \protect{B}arsotti-\protect{T}ate {G}alois
             representations},
  JOURNAL = {J. Amer. Math. Soc.},
 FJOURNAL = {Journal of the American Mathematical Society},
   VOLUME = {12},
     YEAR = {1999},
   NUMBER = {2},
    PAGES = {521--567},
     ISSN = {0894-0347},
}

@inproceedings{merel:1585,
   AUTHOR = {Merel, L.},
    TITLE = {Universal \protect{F}ourier expansions of modular forms},
BOOKTITLE = {On \protect{A}rtin's conjecture for odd $2$-dimensional representations},
    PAGES = {59--94},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1994},
}

@article{buzzard-taylor,
   author={Taylor, R. and Buzzard, K.},
   title={Companion forms and weight 1 forms},
   year={1999},
}

@article{taylor-wiles:fermat,
   AUTHOR = {Taylor, R. and Wiles, A.},
    TITLE = {Ring-theoretic properties of certain \protect{H}ecke algebras},
  JOURNAL = {Ann. of Math. (2)},
 FJOURNAL = {Annals of Mathematics. Second Series},
   VOLUME = {141},
     YEAR = {1995},
   NUMBER = {3},
    PAGES = {553--572},
     ISSN = {0003-486X},
    CODEN = {ANMAAH},
}

@article{edixhoven:serre,
   author={Edixhoven, B.},
   title={NOT DONE. \protect{S}erre's conjectures in \protect{B}oston proceedings}
}


@article{edixhoven:eisen,
   AUTHOR = {Edixhoven, B.},
    TITLE = {L'action de l'alg\`ebre de \protect{H}ecke sur les groupes de
             composantes des jacobiennes des courbes modulaires est
             ``{E}isenstein''},
     NOTE = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)},
  JOURNAL = {Ast\'erisque},
 FJOURNAL = {Ast\'erisque},
   NUMBER = {196-197},
     YEAR = {1991},
    PAGES = {7--8, 159--170 (1992)},
     ISSN = {0303-1179},
}


@article {edixhoven:weight,
   AUTHOR = {Edixhoven, B.},
    TITLE = {The weight in \protect{S}erre's conjectures on modular forms},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {109},
     YEAR = {1992},
   NUMBER = {3},
    PAGES = {563--594},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}

@article {edixcole,
   AUTHOR = {Coleman, R.F. and Edixhoven, B.},
    TITLE = {On the semi-simplicity of the ${U}\sb p$-operator on modular
             forms},
  JOURNAL = {Math. Ann.},
 FJOURNAL = {Mathematische Annalen},
   VOLUME = {310},
     YEAR = {1998},
   NUMBER = {1},
    PAGES = {119--127},
     ISSN = {0025-5831},
    CODEN = {MAANA},
}


@article {coleman-voloch,
   AUTHOR = {Coleman, R.F. and Voloch, J.F.},
    TITLE = {Companion forms and \protect{K}odaira-\protect{S}pencer theory},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {110},
     YEAR = {1992},
   NUMBER = {2},
    PAGES = {263--281},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}

@article{empiracalbsd,
   AUTHOR = {Flynn, E. V. and Lepr\'{e}vost F. and Schaeffer, E. F.
             and Stoll, M. and Wetherell J. L.},
    TITLE = {Empirical Evidence for the Birch and Swinnerton-Dyer
             Conjectures for Modular Jacobians of Genus 2 Curves},
     YEAR = {1999},
    JOURNAL = {Preprint}
}

@inproceedings{frey:boston,
   AUTHOR = {Frey, G.},
    TITLE = {On ternary equations of \protect{F}ermat type and relations with
             elliptic curves},
BOOKTITLE = {Modular forms and Fermat's last theorem (Boston, MA, 1995)},
    PAGES = {527--548},
PUBLISHER = {Springer},
  ADDRESS = {New York},
     YEAR = {1997},
  crossref="boston"
}

@incollection{frey-muller,
   AUTHOR = {Frey, G. and M{\"u}ller, M.},
    TITLE = {Arithmetic of modular curves and applications},
BOOKTITLE = {Algorithmic algebra and number theory (Heidelberg, 1997)},
    PAGES = {11--48},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1999}
}

@incollection {frohlich:local,
   AUTHOR = {Fr{\"o}hlich, A.},
    TITLE = {Local fields},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965) },
    PAGES = {1--41},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}


@article {gross:tameness,
   AUTHOR = {Gross, Benedict H.},
    TITLE = {A tameness criterion for \protect{G}alois 
             representations associated to
             modular forms (mod \protect{$p$})},
  JOURNAL = {Duke Math. J.},
 FJOURNAL = {Duke Mathematical Journal},
   VOLUME = {61},
     YEAR = {1990},
   NUMBER = {2},
    PAGES = {445--517},
     ISSN = {0012-7094},
    CODEN = {DUMJAO},
}

@book {grothendieck:monodromie,
    author= {Grothendieck, A.},
    TITLE = {Groupes de monodromie en g\'eom\'etrie alg\'ebrique. {I}},
     NOTE = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie
             1967--1969 (SGA 7 I),
             Dirig\'e par A. Grothendieck. Avec la collaboration de M.
             Raynaud et D. S. Rim,
             Lecture Notes in Mathematics, Vol. 288},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1972},
    PAGES = {viii+523},
}


@book {hartshorne,
   AUTHOR = {Hartshorne, R.},
    TITLE = {Algebraic geometry},
     NOTE = {Graduate Texts in Mathematics, No. 52},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1977},
    PAGES = {xvi+496},
     ISBN = {0-387-90244-9},
}


@article {igusa:fibre,
   AUTHOR = {Igusa, J.},
    TITLE = {Fibre systems of \protect{J}acobian varieties},
  JOURNAL = {Amer. J. Math.},
   VOLUME = {78},
     YEAR = {1956},
    PAGES = {171--199},
}

@article {jochnowitz:local,
   AUTHOR = {Jochnowitz, N.},
    TITLE = {A study of the local components of the {H}ecke algebra mod $l$},
  JOURNAL = {Trans. Amer. Math. Soc.},
 FJOURNAL = {Transactions of the American Mathematical Society},
   VOLUME = {270},
     YEAR = {1982},
   NUMBER = {1},
    PAGES = {253--267},
     ISSN = {0002-9947},
    CODEN = {TAMTAM},
}

@article{kohel:hecke,
  author="Kohel, D.",
  title="Hecke Module Structure of Quaternions", 
  year=1998
}

@article{koike:conjtwist,
  author="Koike, M.",
  title="On certain abelian varieties obtained from new forms of 
         weight $2$ on \protect{$\Gamma_0(3^4)$ and $\Gamma_0(3^5)$}",
  journal={Nogoya Math. J.},
  volume={62},
  year={1976},
  pages={29--39}
}

@article{kolyvagin-logachev:totallyreal,
   author = "Kolyvagin, V.A. and Logachev, D.Y.",
   title = "Finiteness of \protect{$\Sha$} over totally real fields",
   journal={Math. USSR Izvestiya},
   volume ={39}, 
   year = {1992},
   number = {1},
   pages={829--853}
}

@article{kolyvagin-logachev:finiteness,
   AUTHOR = {Kolyvagin, V.A. and Logachev, D.Y.},
    TITLE = {Finiteness of the \protect{S}hafarevich-\protect{T}ate group and the group of
             rational points for some modular abelian varieties},
  JOURNAL = {Algebra i Analiz},
 FJOURNAL = {Algebra i Analiz},
   VOLUME = {1},
     YEAR = {1989},
   NUMBER = {5},
    PAGES = {171--196},
     ISSN = {0234-0852},
}

@book {lang:ant,
   AUTHOR = {Lang, S.},
    TITLE = {Algebraic number theory},
  EDITION = {Second},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1994},
    PAGES = {xiv+357},
     ISBN = {0-387-94225-4},
}

@book {miyake,
   author = {Miyake},
   title  = {Modular forms}
}

@book {lang:modular,
   AUTHOR = {Lang, S.},
    TITLE = {Introduction to modular forms},
     NOTE = {With appendixes by D. Zagier and Walter Feit,
             Corrected reprint of the 1976 original},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1995},
    PAGES = {x+261},
     ISBN = {3-540-07833-9},
}


@article {lorenzini:abvarred,
   AUTHOR = {Lorenzini, D.J.},
   title = "On the Jacobian of the Modular Curve \protect{$X_0(N)$}",
   journal = "Preprint"
}
@article {lorenzini:compgrp,
   AUTHOR = {Lorenzini, D.J.},
    TITLE = {On the group of components of a \protect{N}\'eron model},
  JOURNAL = {J. Reine Angew. Math.},
 FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
   VOLUME = {445},
     YEAR = {1993},
    PAGES = {109--160},
     ISSN = {0075-4102},
    CODEN = {JRMAA8},
}

@article{manin:cyclo,
   AUTHOR = {Manin, J.I.},
    TITLE = {Cyclotomic fields and modular curves},
  JOURNAL = {Russian Math. Surveys},
   VOLUME = {26},
     YEAR = {1971},
   NUMBER = {6},
    PAGES = {7--78},
}


@article{mazur:visthree,
   author="Mazur, B.",
   title="Visualizing elements of order three in the Shafarevich-Tate group.",
   year={1999}
}

@ARTICLE{mazur:eisenstein,
   AUTHOR = {Mazur, B.},
    TITLE = {Modular curves and the \protect{Eisenstein} ideal},
  JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
 FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications
             Math\'ematiques},
   NUMBER = {47},
     YEAR = {1977},
    PAGES = {33--186 (1978)},
     ISSN = {0073-8301},
    CODEN = {PMIHA6},
}

@article{mazur:tower,
   AUTHOR = {Mazur, B.},
    TITLE = {Rational points of abelian varieties with values in towers of
             number fields},
  JOURNAL = {Invent. Math.},
   VOLUME = {18},
     YEAR = {1972},
    PAGES = {183--266},
}

@article{mazur:rational,
   AUTHOR = {Mazur, B.},
    TITLE = {Rational isogenies of prime degree (with an appendix by {D}.
             {G}oldfeld)},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {44},
     YEAR = {1978},
   NUMBER = {2},
    PAGES = {129--162},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}



@article{mazur:arizona, 
   author="Mazur, B.",
   title ="Three lectures about the arithmetic 
           of elliptic curves.",
   journal="To appear in the proceedings from the Arizona Southwest Geometry Winter School",
   year=1998
}
 
@article{mazur:visord3,
   author="Mazur, B.",
   title="Visualizing elements of order three 
          in the Shafarevich-Tate group.",
   journal="preprint", 
   year=1998
}

@article{mestre:graphs,
   AUTHOR = {Mestre, J.-F.},
    TITLE = {La m\'ethode des graphes. \protect{Exemples} et applications},
JOURNAL = {Proceedings of the international conference on class numbers
             and fundamental units of algebraic number fields (Katata)},
    PAGES = {217--242},
PUBLISHER = {Nagoya Univ.},
  ADDRESS = {Nagoya},
     YEAR = {1986},
}

@book {mumford:abvars,
   AUTHOR = {Mumford, D.},
    TITLE = {Abelian varieties},
     NOTE = {Tata Institute of Fundamental Research Studies in Mathematics,
             No. 5 },
PUBLISHER = {Published for the Tata Institute of Fundamental Research,
             Bombay},
     YEAR = {1970},
    PAGES = {viii+242},
}

@incollection {sturm:cong,
   AUTHOR = {Sturm, J.},
    TITLE = {On the congruence of modular forms},
BOOKTITLE = {Number theory (New York, 1984--1985)},
    PAGES = {275--280},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1987},
}

@proceedings {MR87m:11004,
    TITLE = {Number theory},
BOOKTITLE = {Proceedings of the seminar held at the City University of New
             York, New York, 1984--1985},
   EDITOR = {Chudnovsky, D. V. and Chudnovsky, G. V. and Cohn, H. and
             Nathanson, M. B.},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1987},
    PAGES = {vi+324},
     ISBN = {3-540-17669-1},
}


@book {mumford:geometric,
   AUTHOR = {Mumford, D. and Fogarty, J. and Kirwan, F.},
    TITLE = {Geometric invariant theory},
  EDITION = {Third},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1994},
    PAGES = {xiv+292},
     ISBN = {3-540-56963-4},
}

@inproceedings {queen,
   AUTHOR = {Queen, C.},
    TITLE = {The existence of \protect{$p$}-adic \protect{A}belian 
              \protect{${L}$}-functions},
BOOKTITLE = {Number theory and algebra},
    PAGES = {263--288},
PUBLISHER = {Academic Press},
  ADDRESS = {New York},
     YEAR = {1977},
}

@book {MR56:11675,
    TITLE = {Number theory and algebra},
   EDITOR = {Zassenhaus, H.},
     NOTE = {Collected papers dedicated to Henry B. Mann, Arnold E. Ross,
             and Olga Taussky-Todd},
PUBLISHER = {Academic Press [Harcourt Brace Jovanovich Publishers]},
  ADDRESS = {New York},
     YEAR = {1977},
    PAGES = {x1vi+393},
     ISBN = {0-12-776350-3.},
}
@inproceedings {ribet:galoisattached,
   AUTHOR = {Ribet, K.A.},
    TITLE = {Galois representations attached to eigenforms with
             \protect{N}ebentypus},
BOOKTITLE = {Modular functions of one variable, V (Proc. Second Internat.
             Conf., Univ. Bonn, Bonn, 1976)},
    PAGES = {17--51. Lecture Notes in Math., Vol. 601},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1977},
}

@inproceedings {katz:antwerp350,
   AUTHOR = {Katz, N.M.},
    TITLE = {$p$-adic properties of modular schemes and modular forms},
BOOKTITLE = {Modular functions of one variable, III (Proc. Internat. Summer
             School, Univ. Antwerp, Antwerp, 1972)},
    PAGES = {69--190. Lecture Notes in Mathematics, Vol. 350},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
}

@inproceedings {katz:antwerp601,
   AUTHOR = {Katz, N.M.},
    TITLE = {A result on modular forms in characteristic $p$},
BOOKTITLE = {Modular functions of one variable, V (Proc. Second Internat.
             Conf., Univ. Bonn, Bonn, 1976)},
    PAGES = {53--61. Lecture Notes in Math., Vol. 601},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1977}
}

@book {slnm601,
    TITLE = {Modular functions of one variable. {V}},
BOOKTITLE = {Proceedings of the Second International Conference, held at the
             University of Bonn, Bonn, July 2--14, 1976},
     NOTE = {Edited by J.-P. Serre and D. B. Zagier,
             Lecture Notes in Mathematics, Vol. 601},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1977},
    PAGES = {i+294},
}

@article{ribet:mestreletter,
   author = {Ribet, K.A.},
   title = {Letter to \protect{M}estre},
   year  = {November, 1987}
};

@article {ribet:modreps,
   AUTHOR = {Ribet, K.A.},
    TITLE = {On modular representations of \protect{${\rm {G}al}(\overline{\bf
             {Q}}/{\bf {Q}})$} arising from modular forms},
  JOURNAL = {Invent. Math.},
 FJOURNAL = {Inventiones Mathematicae},
   VOLUME = {100},
     YEAR = {1990},
   NUMBER = {2},
    PAGES = {431--476},
     ISSN = {0020-9910},
    CODEN = {INVMBH},
}


@incollection {ribet:report,
   AUTHOR = {Ribet, K.A.},
    TITLE = {Report on mod \protect{$l$} representations of 
         \protect{${\rm {G}al}(\overline{\bf{Q}}/{\bf {Q}})$}},
BOOKTITLE = {Motives (Seattle, WA, 1991)},
    PAGES = {639--676},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1994},
}

@book {schilling,
    TITLE = {Arithmetical algebraic geometry. (\protect{P}roceedings of a
             \protect{C}onference held at \protect{P}urdue 
             \protect{U}niversity, \protect{D}ecember 5--7,
             1963)},
   EDITOR = {Schilling, O. F. G.},
PUBLISHER = {Harper \& Row Publishers},
  ADDRESS = {New York},
     YEAR = {1965},
    PAGES = {vii+200},
}

@article{TOULOUSE,
  author={Toulouse},
  title={\protect{From the \Weil\ conjecture to Fermat's Last
         Theorem}},
  journal={\protect{Annales de la Facult\'e 
   des Sciences de l'Universit\'e de Toulouse}},
  volume={11},
  year={1990},
  pages={116--139},
}

@article{serre:congtau,
   author = {Serre, J.-P.},
   title  = {Une \protect{interpr\'etation} 
     des congruences relatives \protect{\`a}
     la fonction \protect{$\tau$} de Ramanujan},
   journal = {\protect{S\'eminaire Delange-Pisot-Poitou}},
   year    = {1967--68},
   volume  = {\protect{${\roman n}^{\roman o}$ 14}},
   note    = {English translation: 
    \protect{\tt http://www.rzuser.uni-heidelberg.de/uhb3/Trans.html}}
}
   
@book {serre:ladic,
   AUTHOR = {Serre, J.-P.},
    TITLE = {Abelian $l$-adic representations and elliptic curves},
     NOTE = {With the collaboration of Willem Kuyk and John Labute,
             Revised reprint of the 1968 original},
PUBLISHER = {A K Peters Ltd.},
  ADDRESS = {Wellesley, MA},
     YEAR = {1998},
    PAGES = {199},
     ISBN = {1-56881-077-6},
}


@book {serre:linear,
   AUTHOR = {Serre, Jean-Pierre},
    TITLE = {Linear representations of finite groups},
     NOTE = {Translated from the second French edition by Leonard L. Scott,
             Graduate Texts in Mathematics, Vol. 42},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1977},
    PAGES = {x+170},
     ISBN = {0-387-90190-6},
}

@article{NOMULT,
  author={Ribet, K.A.},
  title = {Lowering the levels of modular representations 
       without multiplicity one},
  journal={International Mathematics Research Notices},
  year={1991},
  pages={15--19}
}


@incollection {serre:local,
   AUTHOR = {Serre, J.-P.},
    TITLE = {Local class field theory},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965)},
    PAGES = {128--161},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}

@book {serre:alggroups,
   AUTHOR = {Serre, J.-P.},
    TITLE = {Algebraic groups and class fields},
     NOTE = {Translated from the French},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1988},
    PAGES = {x+207},
     ISBN = {0-387-96648-X},
}

@book {serre:arithmetic,
   AUTHOR = {Serre, J.-P.},
    TITLE = {A Course in Arithmetic},
     NOTE = {Translated from the French,
             Graduate Texts in Mathematics, No. 7},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1973},
    PAGES = {viii+115},
}


@book {serre:localfields,
   AUTHOR = {Serre, J.-P.},
    TITLE = {Local fields},
     NOTE = {Translated from the French by Marvin Jay Greenberg},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1979},
    PAGES = {viii+241},
     ISBN = {0-387-90424-7},
}

@article{serre:propgal, 
   author = {Serre, J.-P.},
   title = {\protect{Propri\'{e}t\'{e}s} galoisennes de
             points d'ordre fini des courbes elliptiques},
   journal = {Invent. Math.},
   volume = {15},
   year   = {1972},
   pages  = {259--331}
}

@article{serre:propres,
   author={Serre, J.-P.},
   title={Valeurs propres des \protect{op\'{e}rateurs} de
          \protect{Hecke} modulo \protect{$\ell$}},
   journal = {\protect{Ast\'{e}risque}},
   volume = {24--25},
   year   = {1975},
   pages  = {109--117}
}

@article {serre:conjectures,
   AUTHOR = {Serre, J.-P.},
    TITLE = {Sur les repr\'esentations modulaires de degr\'e \protect{$2$} 
             de \protect{${\rm{G}al}(\overline{\bf {Q}}/{\bf {Q}})$}},
  JOURNAL = {Duke Math. J.},
 FJOURNAL = {Duke Mathematical Journal},
   VOLUME = {54},
     YEAR = {1987},
   NUMBER = {1},
    PAGES = {179--230},
     ISSN = {0012-7094},
    CODEN = {DUMJAO},
}


@article {serre-tate,
   AUTHOR = {Serre, J.-P. and Tate, J.},
    TITLE = {Good reduction of abelian varieties},
  JOURNAL = {Ann. of Math. (2)},
   VOLUME = {88},
     YEAR = {1968},
    PAGES = {492--517},
}

@article{shimura:factors,
    AUTHOR = {Shimura, G.},
    TITLE={On the factors of the jacobian variety of a modular function field},
    journal={J. Math. Soc. Japan},
    volume={25},
    number={3},
    year={1973},
    pages={523--544},
}

@article{shimura:onperiods,
    author={Shimura, G.},
    title={On the periods of modular forms},
    journal={Math. Ann.},
    volume={229},
    pages={211--221},
    year={1977}
}

@article {shimura:surles,
   AUTHOR = {Shimura, G.},
    TITLE = {Sur les int\'egrales attach\'ees aux formes automorphes},
  JOURNAL = {J. Math. Soc. Japan},
   VOLUME = {11},
     YEAR = {1959},
    PAGES = {291--311},
}

@book {silverman:aec2,
   AUTHOR = {Silverman, J.H.},
    TITLE = {Advanced topics in the arithmetic of elliptic curves},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1994},
    PAGES = {xiv+525},
     ISBN = {0-387-94328-5},
}

@book {silverman:aec,
   AUTHOR = {Silverman, J.H.},
    TITLE = {The arithmetic of elliptic curves},
     NOTE = {Corrected reprint of the 1986 original},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1992},
    PAGES = {xii+400},
     ISBN = {0-387-96203-4},
}

@article{stein:compgroup,
    author = "Stein, W.A.",
    title = {Component groups of optimal 
              quotients of Jacobians},
    journal = {Preprint},
    year = {1999}
}

@article{stein:congruence,
    author = "Stein, W.A.",
    title  = {Congruences between modular forms},
    journal = {Notes},
    year = {1999}
}

@article{generatinghecke,
    author = "Agashe, A. and Stein, W.A.",
    title  = {Generating the \protect{H}ecke algebra},
    journal = {Preprint},
    year = {1999}
}

@article{stein:hecke,
    author = "Stein, W.A.",
    title  = {\protect{{\tt HECKE}: The} modular forms calculator},
    journal = {Software (available online)},
    year = {1999}
}

@article{stein:vissha,
    author = "Stein, W.A.",
    title = {Some abelian varieties with visible 
             Shafarevich-Tate groups},
    journal = {Preprint},
    year = {1999}
}

@article{stein:periods,
    author = "Stein, W.A. and Verrill, H.",
    title = {Computing period lattices associated to newforms},
    journal = {Preprint},
    year = {1999}
}

@article{stein:phd,
    author="Stein, W.",
    title={Optimal quotients of \protect{$J_0(N)$}},
    journal={U.C. Berkeley Ph.D. thesis, in preparation},
    year={1999}
}

@article{tate:nonexistence,
    author={Tate, J.T.},
    title={The non-existence of certain \protect{Galois} extensions
    of \protect{$\Q$} unramified outside \protect{$2$}},
    journal={Contemporary Math.},
    volume={174},
    year={1994},
    pages={153--156}
}

@incollection {tate:global,
   AUTHOR = {Tate, J. T.},
    TITLE = {Global class field theory},
BOOKTITLE = {Algebraic Number Theory (Proc. Instructional Conf., Brighton,
             1965)},
    PAGES = {162--203},
PUBLISHER = {Thompson, Washington, D.C.},
     YEAR = {1967},
}


@Comment {should be V\'{e}lu but this causes problems.}
@inproceedings {velu:groupes,
   AUTHOR = {Velu, J.},     
    TITLE = {Groupes de \protect{G}alois 
             attach\'es aux points d'ordre fini des
             courbes elliptiques sur un corps de 
             nombres, d'apr\`es \protect{J}.
             \protect{P}. \protect{S}erre},
BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, 1971--1972 (Univ.
             Bordeaux I, Talence), Exp. No. 30},
    PAGES = {12},
PUBLISHER = {Lab. Th\'eorie des Nombres, Centre Nat. Recherche Sci.,
             Talence},
     YEAR = {1972},
}



@book {MR52:8007,
    TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres. 1971--1972},
     NOTE = {Tenu \`a l'Universit\'e de Bordeaux I, Talence, ann\'ee
             universitaire 1971--1972},
PUBLISHER = {Laboratoire de Th\'eorie des Nombres, Centre National de
             Recherche Scientifique, Talence},
     YEAR = {1972},
    PAGES = {224 pp. (not consecutively paged)},
}

@article{diamond:refined,
    author={Diamond, F.},
    title={NOT DONE. The refined conjecture of Serre}
}

@article{diamond-im,
   AUTHOR = {Diamond, F. and Im, J.},
    TITLE = {Modular forms and modular curves},
BOOKTITLE = {Seminar on Fermat's Last Theorem (Toronto, ON, 1993--1994)},
    PAGES = {39--133},
PUBLISHER = {Amer. Math. Soc.},
  ADDRESS = {Providence, RI},
     YEAR = {1995},
}

@book {MR96f:11004,
    TITLE = {Seminar on \protect{F}ermat's \protect{L}ast \protect{T}heorem},
   EDITOR = {Murty, V. Kumar},
     NOTE = {Papers from the seminar held at the Fields Institute for
             Research in Mathematical Sciences, Toronto, Ontario,
             1993--1994},
PUBLISHER = {Published by the American Mathematical Society, Providence, RI},
     YEAR = {1995},
    PAGES = {x+265},
     ISBN = {0-8218-0313-1},
}



@proceedings{boston,
    TITLE = {Modular forms and \protect{F}ermat's last theorem},
   EDITOR = {Cornell, G. and Silverman, J.H. and Stevens, G.},
     NOTE = {Papers from the Instructional Conference on Number Theory and
             Arithmetic Geometry held at Boston University, Boston, MA,
             August 9--18, 1995},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {New York},
     YEAR = {1997},
    PAGES = {xx+582},
     ISBN = {0-387-94609-8},
}

@article{deligne:ladic,
   author = {Deligne, P.},
    title={Formes modulaires et \protect{repr\'{e}sentations $\ell$-adiques.}},
     NOTE = {Lecture Notes in Mathematics, Vol. 179},
PUBLISHER = {Springer-Verlag},
  booktitle = {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69},
  ADDRESS = {Berlin and New York},
  year = {1971},
  pages = {139--172}
}

@book {MR48:8389,
    TITLE = {Modular functions of one variable. {I}{I}},
BOOKTITLE = {Proceedings of the International Summer School, University of
             Antwerp, RUCA, July 17--August 3, 1972},
   EDITOR = {Deligne, Pierre and Kuyk, Willem},
     NOTE = {Lecture Notes in Mathematics, Vol. 349},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1973},
    PAGES = {iv+598},
}

@book {MR48:2080,
    TITLE = {Modular functions of one variable. {I}{I}{I}},
BOOKTITLE = {Proceedings of the International Summer School, University of
             Antwerp, RUCA, July 17--August 3, 1972},
   EDITOR = {Kuyk, Willem and Serre, J.-P.},
     NOTE = {Lecture Notes in Mathematics, Vol. 350},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1973},
    PAGES = {iv+350},
}

@article{ntl,
    title = {\protect{NTL: Number} theory library},
   author = {Shoup, V.},
}

@article{lidia,
    title = {\protect{LiDIA: C++} number theory library},
   author = {Buchmann, J. and others}
}

@article{cremona-luiz,
    title = {\protect{C++} matrix classes},
   author = {Cremona, J.E. and Luiz F.}
}

@book {freyetal,
    TITLE = {On {A}rtin's conjecture for odd 2-dimensional representations},
BOOKTITLE = {On \protect{A}rtin's conjecture for odd $2$-dimensional representations},
   EDITOR = {Frey, G.},
PUBLISHER = {Springer-Verlag},
  ADDRESS = {Berlin},
     YEAR = {1994},
    PAGES = {viii+148},
     ISBN = {3-540-58387-4},
}

@article{winnie,
   author = {Li, Winnie},
   title  = {Unfinished reference}
}

@article {casselman,
   AUTHOR = {Casselman, W.},
    TITLE = {On representations of 
   \protect{${\rm {G}{L}}\sb{2}$} and the arithmetic
             of modular curves},
BOOKTITLE = {Modular functions of one variable, II (Proc. Internat. Summer
             School, Univ. Antwerp, Antwerp, 1972)},
    PAGES = {107--141. Lecture Notes in Math., Vol. 349},
PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1973},
}


@proceedings {cassels-frohlich,
    TITLE = {Algebraic number theory},
BOOKTITLE = {Proceedings of the instructional conference held at the
             University of Sussex, Brighton, September 1--17, 1965},
   EDITOR = {Cassels, J. W. S. and Fr{\"o}hlich, A.},
     NOTE = {Reprint of the 1967 original},
PUBLISHER = {Academic Press Inc. [Harcourt Brace Jovanovich Publishers]},
  ADDRESS = {London},
     YEAR = {1986},
    PAGES = {xviii+366},
     ISBN = {0-12-163251-2},
}