Kirti Joshi, Yichao Zhang
Published 2015-05-06Version 1
We prove that amongst all real quadratic fields and all spaces of Hilbert modular forms of full level and of weight $2$ or greater, the product of two Hecke eigenforms is not a Hecke eigenform except for finitely many real quadratic fields and finitely many weights. We show that for $\mathbb Q(\sqrt 5)$ there are exactly two such identities.
Explicit determination of images of Galois representations attached to Hilbert modular forms
Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields
Lifts of Hilbert modular forms and application to modularity of abelian varieties
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