Modular Forms and Elliptic Curves over the Field of Fifth Roots of Unity

References

• Ash , [Ash 77] A. 1977 . Deformation Retracts with Lowest Possible Dimension of Arithmetic Quotients of Self-Adjoint Homogeneous Cones . Math. Ann. , 225 ( 1 ) : 69 – 76 .
   Google Scholar
• Ash , [Ash 84] A. 1984 . Small-Dimensional Classifying Spaces for Arithmetic Subgroups of General Linear Groups . Duke Math. J. , 51 ( 2 ) : 459 – 468 .
   Google Scholar
• Ash , [Ash 94] A. 1994 . Unstable Cohomology of . J. Algebra , 167 ( 2 ) : 330 – 342 .
   Web of Science ®Google Scholar
• Ash , [Ash et al. 02] A. , Gunnells , P. E. and McConnell , M. 2002 . Cohomology of Congruence Subgroups of . J. Number Theory , 94 ( 1 ) : 181 – 212 .
   Web of Science ®Google Scholar
• Borel , [Borel 06] A. 2006 . “ Introduction to the Cohomology of Arithmetic Groups ” . In Lie Groups and Automorphic Forms , 51 – 86 . Amer. Math. Soc. . AMS/IP Stud. Adv. Math. 37
   Google Scholar
• Borel , [Borel and Serre 73] A. and Serre , J.-P. 1973 . Corners and Arithmetic Groups . Comment. Math. Helv. , 48 : 436 – 491 .
   Web of Science ®Google Scholar
• Borel , [Borel and Wallach 00] A. and Wallach , N. 2000 . Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups, second edition , American Mathematical Society . Mathematical Surveys and Monographs 67
   Google Scholar
• Bygott , [Bygott 99] J. 1999 . Modular Forms and Modular Symbols over Imaginary Quadratic Fields . PhD thesis, Exeter
   Google Scholar
• Cremona , [Cremona 84] J. E. 1984 . Hyperbolic Tessellations, Modular Symbols, and Elliptic Curves over Complex Quadratic Fields . Compositio Math. , 51 ( 3 ) : 275 – 324 .
   Web of Science ®Google Scholar
• Cremona , [Cremona 92] J. E. 1992 . Abelian Varieties with Extra Twist, Cusp Forms, and Elliptic Curves over Imaginary Quadratic Fields . J. London Math. Soc. (2) , 45 ( 3 ) : 404 – 416 .
   Google Scholar
• Cremona , [Cremona 06] J. E. 2006 . “ The Elliptic Curve Database for Conductors to 130000 ” . In Algorithmic Number Theory , 11 – 29 . Sci. 4076. Springer . Lecture Notes in Comput
   Google Scholar
• Cremona , [Cremona and Lingham 07] J. E. and Lingham , M. P. 2007 . Finding all Elliptic Curves with Good Reduction outside a Given Set of Primes . Experiment. Math. , 16 ( 3 ) : 303 – 312 .
   Web of Science ®Google Scholar
• Cremona , [Cremona and Whitley 94] J. E. and Whitley , E. 1994 . Periods of Cusp Forms and Elliptic Curves over Imaginary Quadratic Fields . Math. Comp. , 62 ( 205 ) : 407 – 429 .
   Web of Science ®Google Scholar
• Dembélé , [Dembélé 05] L. 2005 . Explicit Computations of Hilbert Modular Forms on . Experiment. Math. , 14 ( 4 ) : 457 – 466 .
   Web of Science ®Google Scholar
• Dembélé , [Dembélé and Voight 10] L. and Voight , J. 2010 . Explicit Methods for Hilbert Modular Forms . Preprint
   Google Scholar
• Franke , [Franke 98] J. 1998 . Harmonic Analysis in Weighted L 2-Spaces . Ann. Sci. École Norm. Sup. (4) , 31 ( 2 ) : 181 – 279 .
   Web of Science ®Google Scholar
• Gunnells , [Gunnells 99] P. E. 1999 . Modular Symbols for Q-Rank One Groups and Voronoi Reduction . J. Number Theory , 75 ( 2 ) : 198 – 219 .
   Web of Science ®Google Scholar
• Gunnells , [Gunnells 00] P. E. 2000 . Computing Hecke Eigenvalues below the Cohomological Dimension . Experiment. Math. , 9 ( 3 ) : 351 – 367 .
   Web of Science ®Google Scholar
• Gunnells , [Gunnells and Yasaki 08] P. E. and Yasaki , D. 2008 . “ Hecke Operators and Hilbert Modular Forms ” . In Algorithmic Number Theory , 387 – 401 . Springer . Lecture Notes in Comput. Sci. 5011
   Google Scholar
• Harder , [Harder 87] G. 1987 . Eisenstein Cohomology of Arithmetic Groups: The Case GL2 . Invent. Math. , 89 ( 1 ) : 37 – 118 .
   Web of Science ®Google Scholar
• Harder , [Harder 12] G. 2012 . Cohomology of Arithmetic Groups . Available online (http://www.math.uni-bonn.de/people/harder/Manuscripts/buch/chap2.pdf)
   Google Scholar
• Koecher , [Koecher 60] M. 1960 . Beiträge zu einer Reduktionstheorie in Positivitätsbereichen. I . Math. Ann. , 141 : 384 – 432 .
   Web of Science ®Google Scholar
• Li , [Li and Schwermer 01] J.-S. and Schwermer , J. 2001 . “ Automorphic Representations and Cohomology of Arithmetic Groups ” . In Challenges for the 21st Century (Singapore, 2000) , 102 – 137 . World Sci. Publ. .
   Google Scholar
• Lingham , [Lingham 05] M. 2005 . Modular Forms and Elliptic Curves over Imaginary Quadratic Fields . PhD thesis, Nottingham
   Google Scholar
• Socrates , [Socrates and Whitehouse 05] J. and Whitehouse , D. 2005 . Unramified Hilbert Modular Forms, with Examples Relating to Elliptic Curves . Pacific J. Math. , 219 ( 2 ) : 333 – 364 .
   Google Scholar
• Voronoi , [Voronoi 08] G. 1908 . Sur quelques propriétés des formes quadratiques positives parfaites . J. Reine Angew. Math. , 133 : 97 – 178 .
   Google Scholar
• Yasaki , [Yasaki 09] D. 2009 . Binary Hermitian Forms over a Cyclotomic Field . J. Algebra , 322 : 4132 – 4142 .
   Google Scholar