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).
