A form genus is the set of forms 
for which the generic characters 
are equal to a preassigned array
of signs 
or 
,
 |
subject to 
.
There are 
possible form genera, where 
is the number of distinct prime divisors of a field discriminant 
. 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).
