Brandt matrix
In mathematics, Brandt matrices are matrices, introduced by, that are related to the number of ideals of given norm in an ideal class of a definite quaternion algebra over the rationals, and that give a representation of the Hecke algebra.
calculated the traces of the Brandt matrices.
Let O be an order in a quaternion algebra with class number H, and Ii,...,IH invertible left O-ideals representing the classes. Fix an integer m. Let ej denote the number of units in the right order of Ij and let Bij denote the number of α in Ij−1Ii with reduced norm N equal to mN/N. The Brandt matrix B is the H×H matrix with entries Bij. Up to conjugation by a permutation matrix it is independent of the choice of representatives Ij; it is dependent only on the level of the order O.
