We study p-adic families of cohomological automorphic forms for $\mathrm{GL}(2)$ over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. We show how to computationally determine when this is not the case and establish concrete examples of families interpolating only finitely many Bianchi modular forms.

中文翻译：

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Bianchi模形式的p-adic族的有限性结果

我们研究了上同调自守形式的p- adic 族$\mathrm{GL}(2)$在虚构的二次场上，并证明家庭插值 Zariski 密集的经典尖牙自守形式集仅在非常严格的条件下发生。我们展示了如何通过计算确定何时不是这种情况，并建立仅插入有限多个 Bianchi 模形式的族的具体示例。