Campbell-Platt, N; (2013) Metaplectic cusp forms on the group SL2(Q(i)). Doctoral thesis , UCL (University College London).

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Abstract

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.

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