On Artin's Conjecture for Odd 2-dimensional Representations

1. Front Matter

   Pages I-VIII

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2. On the experimental verification of the artin conjecture for 2-dimensional odd galois representations over Q liftings of 2-dimensional projective galois representations over Q

   • Ian Kiming

   Pages 1-36

3. A table of A5-fields

   • Jacques Basmaji, Ian Kiming

   Pages 37-46

4. A. Geometrical construction of 2-dimensional galois representations of A5-type. B. On the realisation of the groups PSL2(1) as galois groups over number fields by means of l-torsion points of elliptic curves

   • Martin Kinzelbach

   Pages 47-58

5. Universal Fourier expansions of modular forms

   • Loïc Merel

   Pages 59-94

6. The hecke operators on the cusp forms of Γ₀(N) with nebentype

   • Xiangdong Wang

   Pages 95-108

7. Examples of 2-dimensional, odd galois representations of A5-type over ℚ satisfying the Artin conjecture

   • Ian Kiming, Xiangdong Wang

   Pages 109-121

8. Back Matter

   Pages 122-152

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The main topic of the volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range. To do this, one has to determine the number of all representations with given Artin conductor and determinant and to compute the dimension of a corresponding space of cusp forms of weight 1 which is done by exploiting the explicit knowledge of the operation of Hecke operators on modular symbols.
It is hoped that the algorithms developed in the volume can be of use for many other problems related to modular forms.

• Artin's conjecture for L-series
• Cusp forms
• Galois group
• Modular symbols
• Volume
• algorithms
• construction
• elliptic curve
• form
• knowledge
• modular form
• presentation
• torsion
• verification

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