Let be the abelian variety attached by Shimura to a normalized newform . We prove that for any integer the set of pairs of endomorphism algebras obtained from all normalized newforms with complex multiplication such that is finite. We determine that this set has exactly 83 pairs for the particular case and show all of them. We also discuss a conjecture related to the finiteness of the set of number fields for the non-CM case.
Cite this article
Josep González Rovira, Finiteness of endomorphism algebras of CM modular abelian varieties. Rev. Mat. Iberoam. 27 (2011), no. 3, pp. 733–750DOI 10.4171/RMI/651