- Amod Agashe, Kenneth A. Ribet, and William A. Stein. "The Modular Degree, Congruence Primes and Multiplicity One." Available online (http:// modular.math.washington.edu/papers/ars-congruence/), 2006. http:// modular.math.washington.edu/papers/ars-congruence/
- W. Bosma, J. Cannon, and C. Playoust. "The Magma Algebra System I: The User Language." J. Symb. Comp. 24:3–4 (1997) 235–265.
- Nigel Boston, Hendrik W. Lenstra, Jr., and Kenneth A. Ribet. "Quotients of Group Rings Arising from Two-Dimensional Representations." C. R. Acad. Sci. Paris Sér. I Math. 312:4 (1991), 323–328.
- David W. Boyd and H. Kisilevsky. "On the Exponent of the Ideal Class Groups of Complex Quadratic Fields." Proc. Amer. Math. Soc. 31 (1972), 433-436.
- K. Buzzard. "Appendix." In Arithmetic Algebraic Geometry (Park City, UT, 1999), IAS/Park City Math. Ser. 9. Providence, Amer. Math. Soc., 2001.
- Fred Diamond and John Im. "Modular Forms and Modular Curves." In Seminar on Fermat's Last Theorem (Toronto, ON, 1993–1994), pp. 39–133, CMS Conf. Proc. 17. Providence, Amer. Math. Soc., 1995.
- Bas Edixhoven. "The Weight in Serre's Conjectures on Modular Forms." Invent. Math. 109:3 (1992), 563–594.
- Bas Edixhoven. "Serre's Conjecture," In Modular Forms and Fermat's Last Theorem (Boston, MA, 1995), pp. 209–242. New York: Springer, 1997.
- Bas Edixhoven. "Comparison of Integral Structures on Spaces of Modular Forms of Weight Two, and Computation of Spaces of Forms mod 2 of Weight One." J. Inst. Math. Jussieu 5:1 (2006), 1–34.
- David Eisenbud. Commutative Algebra, Graduate Texts in Mathematics, 150. New York: Springer- Verlag, 1995.
- Matthew Emerton. "Supersingular Elliptic Curves, Theta Series and Weight Two Modular Forms." J. Amer. Math. Soc. 15:3 (2002), 671–714.
- B. Gross. "A Tameness Criterion for Galois Representations Associated to Modular Forms (mod p)." Duke Math. Journal 61:2 (1990), 445–517.
- H. Hida. "On Congruence Divisors of Cusp Forms as Factors of the Special Values of Their Zeta Functions." Invent. Math. 64 (1981), 221–262.
- L. J. P. Kilford. "Some Non-Gorenstein Hecke Algebras Attached to Spaces of Modular Forms," J. Number Theory 97:1 (2002), 157–164.
- G. Malle. Personal communication, 2006.
- B. Mazur. "Modular Curves and the Eisenstein Ideal." Inst. Hautes Études Sci. Publ. Math. 47, (1977), 33–186.
- B. Mazur and K. A. Ribet. "Two- Dimensional Representations in the Arithmetic of Modular Curves." Astérisque 196–197 (1992), 215–255.
- Kenneth A. Ribet. "Multiplicities of Galois Representations in Jacobians of Shimura Curves." In Festschrift in Honor of I. I. Piatetski-Shapiro on the Occasion of his Sixtieth Birthday, Part II (Ramat Aviv, 1989), pp. 221-236, Israel Math. Conf. Proc. 3. Jerusalem: Weizmann.
- Kenneth A. Ribet and William A. Stein. "Lectures on Serre's Conjectures." In Arithmetic Algebraic Geometry (Park City, UT, 1999), pp. 143–232, IAS/Park City Math. Ser. 9. Providence: Amer. Math. Soc., 2001.
- William Stein. Modular Forms: A Computational Approach, Graduate Studies in Mathematics, 79. Providence, American Mathematical Society, 2007.
- Jacques Tilouine. "Un sous-groupe p-divisible de la jacobienne de X 1(Npr ) comme module sur l'alg`ebre de Hecke." Bull. Soc. Math. France 115:3 (1987), 329–360.
- Jacques Tilouine. "Hecke Algebras and the Gorenstein Property." In Modular Forms and Fermat's Last Theorem (Boston, MA, 1995), pp. 327–342. New York: Springer, 1997.
- Gabor Wiese. "Dihedral Galois Representations and Katz Modular Forms." Doc. Math. 9 (2004), 123–133.
- Gabor Wiese. "Multiplicities of Galois Representations of Weight One." Algebra & Number Theory 1:1 (2007), 67–85.
- Gabor Wiese. "On the Faithfulness of Parabolic Cohomology as a Hecke Module over a Finite Field." J. Reine Angew. Math. 606 (2007), 79–103.
- Gabor Wiese. "On Modular Symbols and the Cohomology of Hecke Triangle Surfaces." To appear in International J. of Number Theory, 2008.
- Andrew Wiles. "Modular Elliptic Curves and Fermat's Last Theorem." Ann. of Math. (2) 141:3 (1995), 443-551.
On the Failure of the Gorenstein Property for Hecke Algebras of Prime Weight
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