Form Genus

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).

REFERENCES:

Cohn, H. "Compositions, Order, and Genera." Ch. 8 in Advanced Number Theory. New York: Dover, pp. 212-230, 1980.