Traces of Eichler—Brandt matrices and type numbers of quaternion orders

LetA be a totally definite quaternion algebra over a totally real algebraic number fieldF andM be the ring of algebraic integers ofF. For anyM-orderG ofA we derive formulas for the massm(G) and the type numbert(G) of G and for the trace of the Eichler-Brandt matrixB(G, J) ofG and any integral idealJ ofM in terms of genus invariants ofG and of invariants ofF andJ. Applications to class numbers of quaternion orders and of ternary quadratic forms are indicated.