Consider the forms for which the generic characters are equal to some preassigned array of signs or ,

subject to . There are possible arrays, where is the number of distinct prime divisors of a field discriminant , and the set of forms corresponding to each array is called a genus of forms. The forms for which all are called the principal genus of forms, and each genus is also a collection of proper equivalence classes (Cohn 1980, pp. 223-224).