Metaplectic cusp forms on the group SL2(Q(i))

• Main Author: Campbell-Platt, N.
• Published: University College London (University of London) 2013
• Subjects: 510
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.587792

The aim of this thesis is to contribute to the understanding of genuine cusp forms on the group SL2=Q(i), from a computational point of view. We show, via the generalised Eichler-Shimura-Harder isomorphism, that a genuine cusp form of cohomological type exists at level SL2(Z[i]; 4)SL2(Z). We show, by calculating cohomology groups, that such a form exists at weight (2; 2). Finally, we compute the genuine quotient of the Hecke algebra acting on representations of SL2(Q2(i)) containing non-zero SL2(Z2[i]; 4)SL2(Z2)- xed vectors. When such a representation $ corresponds to an unrami ed representation of SL2(Q2(i)), we show that the space of SL2(Z2[i]; 4)SL2(Z2)- xed vectors in $ is a sum of two 1-dimensional components. We determine which 1-dimensional representations arise in this way.