References of "Wiese, Gabor 50003330"
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See detailOn projective linear groups over finite fields as Galois groups over the rational numbers
Wiese, Gabor UL

in Modular forms on Schiermonnikoog (2008)

Ideas and techniques from Khare's and Wintenberger's article on the proof of Serre's conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups PSL_2(F_{l^r ... [more ▼]

Ideas and techniques from Khare's and Wintenberger's article on the proof of Serre's conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups PSL_2(F_{l^r}) (for r running) occur as Galois groups over the rationals such that the corresponding number fields are unramified outside a set consisting of l, the infinite place and only one other prime. [less ▲]

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See detailOn the generation of the coefficient field of a newform by a single Hecke eigenvalue
Koo, Koopa Tak-Lun; Stein, William; Wiese, Gabor UL

in Journal de Théorie des Nombres de Bordeaux (2008), 20(2), 373--384

# Let f be a non-CM newform of weight k>1 without nontrivial inner twists. In this article we study the set of primes p such that the eigenvalue a_p(f) of the Hecke operator T_p acting on f generates the ... [more ▼]

# Let f be a non-CM newform of weight k>1 without nontrivial inner twists. In this article we study the set of primes p such that the eigenvalue a_p(f) of the Hecke operator T_p acting on f generates the field of coefficients of f. We show that this set has density 1, and prove a natural analogue for newforms having inner twists. We also present some new data on reducibility of Hecke polynomials, which suggest questions for further investigation. [less ▲]

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See detailZahlentheorie und Geometrie vereint in der Serre-Vermutung
Wiese, Gabor UL

in Essener Unikate (2008), 33

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See detailOn the failure of the Gorenstein property for Hecke algebras of prime weight
Kilford, L. J. P.; Wiese, Gabor UL

in Experimental Mathematics (2008), 17(1), 37--52

In this article we report on extensive calculations concerning the Gorenstein defect for Hecke algebras of spaces of modular forms of prime weight p at maximal ideals of residue characteristic p such that ... [more ▼]

In this article we report on extensive calculations concerning the Gorenstein defect for Hecke algebras of spaces of modular forms of prime weight p at maximal ideals of residue characteristic p such that the attached mod p Galois representation is unramified at p and the Frobenius at p acts by scalars. The results lead us to the ask the question whether the Gorenstein defect and the multplicity of the attached Galois representation are always equal to 2. We review the literature on the failure of the Gorenstein property and multiplicity one, discuss in some detail a very important practical improvement of the modular symbols algorithm over finite fields and include precise statements on the relationship between the Gorenstein defect and the multiplicity of Galois representations. The Magma package, instructions for its use, generated tables and the complete data are available as supplemental material. [less ▲]

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See detailMultiplicities of Galois representations of weight one
Wiese, Gabor UL

in Algebra Number Theory (2007), 1(1), 67--85

In this article we consider mod p modular Galois representations which are unramified at p such that the Frobenius element at p acts through a scalar matrix. The principal result states that the ... [more ▼]

In this article we consider mod p modular Galois representations which are unramified at p such that the Frobenius element at p acts through a scalar matrix. The principal result states that the multiplicity of any such representation is bigger than 1. [less ▲]

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See detailOn the faithfulness of parabolic cohomology as a Hecke module over a finite field
Wiese, Gabor UL

in Journal für die Reine und Angewandte Mathematik (2007), 606

In this article we prove that under certain conditions the Hecke algebra of cuspidal modular forms over F_p coincides with the Hecke algebra of a certain parabolic group cohomology group with coefficients ... [more ▼]

In this article we prove that under certain conditions the Hecke algebra of cuspidal modular forms over F_p coincides with the Hecke algebra of a certain parabolic group cohomology group with coefficients in F_p. These results can e.g. be used to compute Katz modular forms of weight one over an algebraic closure of F_p with methods of linear algebra over F_p. [less ▲]

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See detailDihedral Galois representations and Katz modular forms
Wiese, Gabor UL

in Documenta Mathematica (2004), 9

We show that any two-dimensional odd dihedral representation \rho over a finite field of characteristic p>0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of ... [more ▼]

We show that any two-dimensional odd dihedral representation \rho over a finite field of characteristic p>0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of level N, character \epsilon and weight k, where N is the conductor, \epsilon is the prime-to-p part of the determinant and k is the so-called minimal weight of \rho. In particular, k=1 if and only if \rho is unramified at p. Direct arguments are used in the exceptional cases, where general results on weight and level lowering are not available. [less ▲]

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See detailA database of invariant rings
Kemper, Gregor; Körding, Elmar; Malle, Gunter et al

in Experimental Mathematics (2001), 10(4), 537--542

We announce the creation of a database of invariant rings. This database contains a large number of invariant rings of finite groups, mostly in the modular case. It gives information on generators and ... [more ▼]

We announce the creation of a database of invariant rings. This database contains a large number of invariant rings of finite groups, mostly in the modular case. It gives information on generators and structural properties of the invariant rings. The main purpose is to provide a tool for researchers in invariant theory. [less ▲]

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