Genuine Bianchi modular forms of higher level, at varying weight and discriminant

in Journal de Théorie des Nombres de Bordeaux (2019), 31(1), 27-48

Bianchi modular forms are automorphic forms over an imaginary quadratic field, associated to a Bianchi group. Those of the cuspidal Bianchi modular forms which are relatively well understood, namely ... [more ▼]

Bianchi modular forms are automorphic forms over an imaginary quadratic field, associated to a Bianchi group. Those of the cuspidal Bianchi modular forms which are relatively well understood, namely (twists of) base-change forms and CM-forms, are what we call non-genuine forms; the remaining forms are what we call genuine. In a preceding paper by Rahm and Şengün, an extreme paucity of genuine forms has been reported, but those and other computations were restricted to level One. In this paper, we are extending the formulas for the non-genuine Bianchi modular forms to higher levels, and we are able to spot the first, rare instances of genuine forms at higher level and higher weight. [less ▲]

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