The number of representations of squares by integral quaternary quadratic forms II

Let f be a positive definite (classic) integral quaternary quadratic form. We say f is strongly s-regular if it satisfies a strong regularity property on the number of representations of squares of integers. In this paper, we show that there are exactly 97 strongly s-regular quaternary quadratic forms representing 1. In particular, we use modular forms to prove the strong s-regularity of the quaternary quadratic form [Formula: see text], which is, in fact, of class number 3.