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The Maaß space for the nontrivial multiplier system over the Hurwitz quaternions. (English) Zbl 0912.11020
In this remarkable paper, the author describes the Maaß space of weight $$k$$ for the modular group over the Hurwitz order with nontrivial multiplier system, which turns out to be isomorphic to the space of elliptic modular forms of weight $$k-8$$. Consequently he gets an explicit formula for the dimension of the Maaß space. Moreover, the author constructs an embedding of the Hermitian modular group over an imaginary quadratic number field $$K$$ with discriminant $$D_K\not\equiv 1\pmod 8$$ into the modular group over the Hurwitz order. It is remarkable that this embedding is compatible with the construction of the associated Maaß space. This result will be useful in the problem of constructing generators of the graded ring of quaternion modular forms of degree 2, which is studied by E. Freitag.

##### MSC:
 11F55 Other groups and their modular and automorphic forms (several variables)
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