On the Distribution of Frobenius of Weight 2 Eigenforms with Quadratic Coefficient Field

References

• [Bending 99] Peter R. Bending. “Curves of Genus 2 with Multiplication.” arXiv:math/9911273 [math.NT], 1999.
   Google Scholar
• [Billerey and Dieulefait 14] Nicolas Billerey and Luis V. Dieulefait. “Explicit Large Image Theorems for Modular Forms.” J. Lond. Math. Soc. (2) 89: 2 (2014), 499–523.
   Web of Science ®Google Scholar
• [Darmon et al. 97] Henri Darmon, Fred Diamond, and Richard Taylor. “Fermat’s Last Theorem.” In Elliptic Curves, Modular Forms & Fermat’s Last Theorem (Hong Kong, 1993), edited by John Coates and S. T. Yau, pp. 2–140. Cambridge, MA: International Press, 1997.
   Google Scholar
• [Diamond and Shurman 05] Fred Diamond and Jerry Shurman. A First Course in Modular Forms, Volume 228 of Graduate Texts in Mathematics. New York, NY: Springer-Verlag, 2005.
   Google Scholar
• [Fité et al. 12] Francesc Fité, Kiran S. Kedlaya, Víctor Rotger, and Andrew V. Sutherland. “Sato-Tate Distributions and Galois Endomorphism Modules in Genus 2.” Compos. Math. 148: 5 (2012), 1390–1442.
   Web of Science ®Google Scholar
• [Johansson 15] Christian Johansson. “On the Sato-Tate Conjecture for Non-Generic Abelian Surfaces.” arXiv:1307.6478v5, 2015.
   Google Scholar
• [Kedlaya and Sutherland 08] Kiran S. Kedlaya and Andrew V. Sutherland. “Computing L-Series of Hyperelliptic Curves.” In Algorithmic Number Theory, Volume 5011 of Lecture Notes in Comput. Sci., edited by Alfred J. van der Poorten, Adreas Stein, pp. 312–326. Berlin: Springer, 2008.
   Google Scholar
• [Koo et al. 08] Koopa Tak-Lun Koo, William Stein, and Gabor Wiese. “On the Generation of the Coefficient Field of a Newform by a Single Hecke Eigenvalue.” J. Théor. Nombres Bordeaux 20: 2 (2008), 373–384.
   Google Scholar
• [Lang 95] Serge Lang. Introduction to Modular Forms, Volume 222 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer-Verlag, 1995. With appendixes by D. Zagier and Walter Feit, Corrected reprint of the 1976 original.
   Google Scholar
• [Lang and Trotter 76] Serge Lang and Hale Trotter. Frobenius Distributions in GL₂-Extensions, Volume 504 of Lecture Notes in Mathematics. Berlin: Springer-Verlag, 1976. Distribution of Frobenius automorphisms in GL2-extensions of the rational numbers.
   Google Scholar
• [Loeffler 14] D. Loeffler. “Images of Adelic Galois Representations for Modular Forms.” ArXiv e-prints, November 2014.
   Google Scholar
• [Kumar Murty 99] V. Kumar Murty. “Frobenius Distributions and Galois Representations.” In Automorphic Forms, Automorphic Representations, and Arithmetic (Fort Worth, TX, 1996), Volume 66 of Proc. Sympos. Pure Math., edited by Robert S. Doran, Ze-Li Dou, George T. Gilbert, pp. 193–211. Providence, RI: American Mathematical Society, 1999.
   Google Scholar
• [Ribet 81] K. A. Ribet. “Endomorphism Algebras of Abelian Varieties Attached to Newforms of Weight 2.” In Seminar on Number Theory, Paris 1979–80, Volume 12 of Progr. Math., edited by R. V. Gamkrelidze, pp. 263–276. Boston, MA: Birkhäuser, 1981.
   Google Scholar
• [Ribet 75] Kenneth A. Ribet. “On l-Adic Representations Attached to Modular Forms.” Invent. Math. 28 (1975), 245–275.
   Web of Science ®Google Scholar
• [Ribet 80] Kenneth A. Ribet. “Twists of Modular Forms and Endomorphisms of Abelian Varieties.” Math. Ann. 253: 1 (1980), 43–62.
   Web of Science ®Google Scholar
• [Serre 13] Jean-Pierre Serre. “Un critère d’indépendance pour une famille de représentations ℓ-adiques.” Comment. Math. Helv. 88: 3 (2013), 541–554.
   Google Scholar
• [Stein 14] W. A. Stein. “Sage Mathematics Software (Version 6.3).” The Sage Development Team. Available at http://www.sagemath.org, 2014.
   Google Scholar
• [Wilson 00] John Wilson. “Explicit Moduli for Curves of Genus 2 with Real Multiplication by .” Acta Arith. 93: 2 (2000), 121–138.
   Web of Science ®Google Scholar