  The main goal of this work is to provide two new formulas for the computation
of the trace per unit volume, and consequently the integrated density of states
(IDOS), for magnetic operators. These formulas also permit the use of the
Dixmier trace in the spectral analysis of magnetic operators. The second of
these formulas, named energy shell formula, permits to approximate the IDOS by
a finite sums of averaged expectation values of the spectral projections.
