= Solution
By the <state–operator correspondence>, a CFT operator of <scaling dimension> $\Delta$ creates a cylinder state of energy $E=\Delta/R$. The identity gives the vacuum; the first nontrivial low-energy single-trace operator is the conserved <stress-energy tensor>, with $\Delta=3$ in three dimensions; and one translation raises the dimension by one. Taking the scheme-dependent vacuum energy to vanish,
$$
\boxed{E_0=0,
\qquad E_1=\frac3R,
\qquad E_2=\frac4R.}
$$
All other single-trace primaries are heavy by assumption, while the first two-graviton state begins at $6/R$.
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