WordNet sense 1 (the number of elements in a mathematical set; denotes a quantity but not the order):

cardinal number

WordNet sense 2 (a variable color averaging a vivid red):

carmine

WordNet sense 3 (crested thick-billed North American finch having bright red plumage in the male):

redbird, cardinal grosbeak, Cardinalis cardinalis, Richmondena Cardinalis

WordNet sense 4 (serving as an essential component):

central, fundamental, key, primal

WordNet sense 5 (of great significance or value):

important, of import