Quaternionic modular groups

Vector valued hermitian and quaternionic modular forms

Multiple Holomorphs of Dihedral and Quaternionic Groups

The holomorph of a group G is NormB(λ(G)), the normalizer of the left regular representation λ(G) in its group of permutations B = Perm(G). The multiple holomorph of G is the normalizer of the holomorph in B. The multiple holomorph and its quotient by the holomorph encodes a great deal of information about the holomorph itself and about the group λ(G) and its conjugates within the holomorph. We...

Presentations for Quaternionic S-Unit Groups

In this paper, we give an algorithm for presenting S-unit groups of an order O in a definite rational quaternion algebra B such that, for every p ∈ S at which B splits, the localization of O at p is maximal and all left ideals of O of norm p are principal. We then apply this to give presentations for projective S-unit groups of the Hurwitz order in Hamilton’s quaternions over the rational field...

Quaternionic Manin symbols, Brandt matrices, and Hilbert modular forms

In this paper, we propose a generalization of the algorithm developed in [4]. Along the way, we also develop a theory of quaternionic M -symbols whose definition bears some resemblance with the classical M -symbols, except for their combinatorial nature. The theory gives a more efficient way to compute Hilbert modular forms over totally fields, especially quadratic fields, and we have illustrat...

Genus two curves with quaternionic multiplication and modular Jacobian

We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces Af with quaternionic multiplication attached to a normalized newform f without complex multiplication. We include an example of Af with quaternionic multiplication for which we find numerically a curve C whose Jacobian is Af up to numerical approximation, and we prove that it...