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We report the measurement of the cross sections for $e^+e^-\rightarrow {\rmhadrons}$ at center-of-mass (c.m.) energies from 3.645 to 3.871 GeV. We observea new resonance $\mathcal R(3810)$ in the cross sections for the first time,and observe the $\mathcal R(3760)$ resonance with high significance in thecross sections. The $\mathcal R(3810)$ has a mass of $(3804.5 \pm 0.9 \pm 0.9)$~MeV/$c^2$, a total width of $(5.4 \pm 3.5 \pm 3.2)$~MeV, and an electronicpartial width of $(19.4 \pm 7.4 \pm 12.1)$~eV. Its significance is $7.7\sigma$.The $\mathcal R(3810)$ could be interpreted as a hadro-charmonium resonancepredicted by Quantum Chromodynamics (QCD). In addition, we measure the mass$(3751.9\pm 3.8\pm 2.8)$ ~MeV/$c^2$, the total width $(32.8 \pm 5.8 \pm8.7)$~MeV, and the electronic partial width $(184\pm 75\pm 86)$~eV withimproved precision for the $\mathcal R(3760)$. Furthermore, for the $\mathcalR(3780)$ we measure the mass $(3778.7\pm 0.5\pm 0.3)$ ~MeV/$c^2$ and totalwidth $(20.3 \pm 0.8 \pm 1.7)$~MeV with improved precision, and the electronicpartial width $(265\pm 69\pm 83)$~eV. The $\mathcal R(3780)$ can be interpretedas the $1^3D_1$ state of charmonium. Its mass and total width differsignificantly from the corresponding fitted values given by the Particle DataGroup in 2022 by 7.1 and 3.2 times the uncertainties for $\psi(3770)$,respectively. $\psi(3770)$ has been interpreted as the $1^3D_1$ state for 45years.

Observation of $\mathcal R(3810)$ in $e^+e^-\rightarrow {\rm hadrons}$  and Improved Measurements of the Resonance Parameters of $\mathcal R(3760)$  and $\mathcal R(3780)$