We exhibit three double octic Calabi--Yau threefolds over the certain quadratic fields and prove their modularity. The non-rigid threefold has two conjugate Hilbert modular forms of weight [4,2] and [2,4] attached while the two rigid threefolds correspond to a Hilbert modular form of weight [4,4] and to the twist of the restriction of a classical modular form of weight 4.

中文翻译：

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一些双octic Calabi-Yau三重的希尔伯特模数

我们在某些二次场上展示了三个双octic Calabi-Yau三重并证明了它们的模块化。非刚性三重具有两个共轭希尔伯特模形式的权重 [4,2] 和 [2,4]，而两个刚性三重对应于权重 [4,4] 的希尔伯特模形式和限制的扭曲重量 4 的经典模块化形式。