Quadratic forms representing all integers coprime to 3

Following Bhargava and Hanke’s celebrated 290-theorem, we prove a universality theorem for all positive-definite integer-valued quadratic forms that represent all positive integers coprime to 3. In particular, if a positive-definite quadratic form represents all positive integers coprime to 3 and ≤ 290, then it represents all positive integers coprime to 3. We use similar methods to those used by Rouse to prove (assuming GRH) that a positive-definite quadratic form representing every odd integer between 1 and 451 represents all positive odd integers.