LEVELS OF POSITIVE DEFINITE TERNARY QUADRATIC-FORMS

The level N and square-free character q of a positive definite ternary quadratic form are defined so that its associated modular form has level N and character chi-q . We define a collection of correspondences between classes of quadratic forms having the same level and different discriminants. This makes practical a method for finding representatives of all classes of ternary forms having a given level. We also give a formula for the number of genera of ternary forms with a given level and character.