 One verifies easily in the example that all sums of corresponding matrix elements vanish because of
the orthogonality of the given irreducible representation to the identity representation.The trace of a matrix is a sum of diagonal matrix elements,

The collection of traces is the "character" formula_38 of a representation.Often one writes for
the trace of a matrix in an irreducible representation with character formula_39

In this notation we can write several character formulas