Codimension sequence, grade, and generating degree: an operadic approach

We study several classes of operadic ideals of the unital associative algebra operad $\text{uas}$. As an application, we classify quotient operads of $\text{uas}$ of GK-dimension $\le 6$. This corresponds to a classification of all T-ideals of codimension growth $n^g$ with $g\le 5$ (or equivalently, varieties of grade $g$ with $g\le 5$).