Modularity of an odd icosahedral representation

Jehanne, Arnaud; Müller, Michael

Jehanne, Arnaud ; Müller, Michael

Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 475-482.

Résumé
Abstract

Dans cet article, nous démontrons que la représentation $ρ$ de $G_{ℚ}$ dans GL $_{2} (ℂ)$ d’image $A_{5}$ dans PGL $_{2} (A_{5})$ correspondant à l’exemple $16$ dans [B-K] est modulaire. Cette représentation est de conducteur $5203$ et de déterminant $χ_{- 43}$ . La modularité de cette représentation n’était pas encore prouvée ; en effet, elle ne vérifie pas les hypothèses des théorèmes de [B-D-SB-T] et [Tay2].

In this paper, we prove that the representation $ρ$ from $G_{ℚ}$ in GL $_{2} (ℂ)$ with image $A_{5}$ in PGL $_{2} (A_{5})$ corresponding to the example $16$ in [B-K] is modular. This representation has conductor $5203$ and determinant $χ_{- 43}$ ; its modularity was not yet proved, since this representation does not satisfy the hypothesis of the theorems of [B-D-SB-T] and [Tay2].

MR Zbl

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     author = {Jehanne, Arnaud and M\"uller, Michael},
     title = {Modularity of an odd icosahedral representation},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {475--482},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {2},
     year = {2000},
     mrnumber = {1823197},
     zbl = {01626657},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_2000__12_2_475_0/}
}

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Jehanne, Arnaud; Müller, Michael. Modularity of an odd icosahedral representation. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 475-482. http://archive.numdam.org/item/JTNB_2000__12_2_475_0/

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