We look at genera of even unimodular lattices of rank 12 over the ring of integers of \({{\mathbb {Q}}}(\sqrt{5})\) and of rank 8 over the ring of integers of \({{\mathbb {Q}}}(\sqrt{3})\), using Kneser neighbours to diagonalise spaces of scalar-valued algebraic modular forms. We conjecture most of the global Arthur parameters, and prove several of them using theta series, in the manner of Ikeda and Yamana. We find instances of congruences for non-parallel weight Hilbert modular forms. Turning to the genus of Hermitian lattices of rank 12 over the Eisenstein integers, even and unimodular over \({{\mathbb {Z}}}\), we prove a conjecture of Hentschel, Krieg and Nebe, identifying a certain linear combination of theta series as an Hermitian Ikeda lift, and we prove that another is an Hermitian Miyawaki lift.

我们看一下\（{{\ mathbb {Q}}}（\ sqrt {5}）\）的整数环上第12位的单模晶格的属，以及\（{ {\ mathbb {Q}}}（\ sqrt {3}）\），使用Kneser邻居对角化标量值代数模块化形式的空间。我们推测了大多数全局亚瑟参数，并以池田和山名的方式使用theta级数证明了其中的几个。我们发现非平行权重希尔伯特模块化形式的全等实例。转向爱森斯坦整数上的第12位的厄米格点阵的属，在\（{{\ mathbb {Z}}} \）上的偶数和单模，我们证明了Hentschel，Krieg和Nebe的猜想，确定了theta级数的某种线性组合为Hermitian Ikeda电梯，并且证明了另一个是Hermitian Miyawaki电梯。