Consider 
proper equivalence classes of forms with discriminant 
equal to the field discriminant, then they can be subdivided
equally into 
genera of 
forms which form a subgroup
of the proper equivalence class group under composition (Cohn 1980, p. 224),
where 
is the number of distinct prime divisors of 
. This theorem was proved by Gauss in 1801.
Fundamental Theorem of Genera
See also
Form Genus, Genus TheoremExplore with Wolfram|Alpha
References
Arno, S.; Robinson, M. L.; and Wheeler, F. S. "Imaginary Quadratic Fields with Small Odd Class Number." http://www.math.uiuc.edu/Algebraic-Number-Theory/0009/.Cohn, H. Advanced Number Theory. New York: Dover, 1980.Gauss, C. F. Disquisitiones Arithmeticae. New Haven, CT: Yale University Press, 1966.Referenced on Wolfram|Alpha
Fundamental Theorem of GeneraCite this as:
Weisstein, Eric W. "Fundamental Theorem of Genera." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FundamentalTheoremofGenera.html