Corrigendum to "On traces of the Brandt-Eichler matrices"
Journal article, 2017
Abstract. This is a correction to my paper . It corrects a formula in Proposition 2.2. The corrected result says that the number ı(n, m) of principal left ideals with norm qm in the Eichler order of level n over a discrete valuation ring R with residue field of cardinality q is ı(n, m) = (m + 1)qm if m < n and ı(n, m) = (n + 1)qm + 2qm−1 + · · · + 2qⁿ + qn−1 when m ≥ n. The proof of the Proposition was not given in my paper (as “tedious but straightforward”). Unfortunately, some coefficients in the second case were erroneous. A complete proof follows below.
Quaternion algebra, Eichler order