Revista de la
Unión Matemática Argentina
An exotic example of a tensor product of a CM elliptic curve and a weight 1 form
Ariel Pacetti

Volume 65, no. 2 (2023), pp. 225–228    

Published online: October 16, 2023

https://doi.org/10.33044/revuma.2284

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Abstract

The representation obtained as a tensor product of a rational elliptic curve with a weight 1 modular form is in general an irreducible four-dimensional representation. However, there are some instances where such representation is reducible. In this short article we give an exotic way to obtain such a reducible representation.

References

  1. W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system. I: The user language, J. Symbolic Comput. 24 no. 3-4 (1997), 235–265.  DOI  MR  Zbl
  2. P. Deligne and J.-P. Serre, Formes modulaires de poids $1$, Ann. Sci. École Norm. Sup. (4) 7 (1974), 507–530.  MR  Zbl Available at http://www.numdam.org/item?id=ASENS_1974_4_7_4_507_0.
  3. G. Henniart, Représentations du groupe de Weil d'un corps local, Publications Mathématiques d'Orsay 79, 2, Université de Paris-Sud, Département de Mathématiques, Orsay, 1979.  MR  Zbl
  4. A. Pacetti and L. Villagra Torcomian, $\mathbb{Q}$-Curves, Hecke characters and some Diophantine equations, Math. Comp. 91 no. 338 (2022), 2817–2865.  DOI  MR  Zbl