 Note that, as first noticed by J. McKay, the coefficient of the linear term of "j"("τ") almost equals formula_9, which is the degree of the smallest nontrivial irreducible representation of the Monster group.Similar phenomena will be observed in the other levels.Define

Then the two modular functions and sequences are related by

if the series converges and the sign chosen appropriately, though squaring both sides easily removes the ambiguity.