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

摘要

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 Maaβ 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 embidding of the Hermitian modular group over an Imaginary -quadratic number field k with discriminant D_k≠1 (mod8) into the modular Group over the Hurwitz order. This embedding is compatible with the construction of Maaβ spaces.