The Maa� space for the non-trivial multiplier system over the Hurwitz quaternions

Abstract

It is known that the modular group of degree n over the Hurwitz quaternions admits two (conjugate) non-trivial multiplier systems. We describe the attached Maas space of modular forms of degree 2 and weight k, which turns out to be isomorphic to the full space of elliptic modular forms of weight k - 8. ¶Moreover we construct an embedding of the Hermitian modular group over an imaginary-quadratic number field K with discriminant \( D_K \not \equiv 1 (\hbox {mod}\, 8) \) into the modular group over the Hurwitz order. This embedding is compatible with the construction of Maas spaces.