The sensitivity of experiments searching for the electron electric-dipole moment ($e\mathrm{EDM}$) using the symmetric top molecules can be greatly enhanced by laser cooling. A detailed understanding of the Zeeman structure of the $e\mathrm{EDM}$-sensitive levels is crucial for controlling systematic effects. We develop a method for calculating the $g$ factors of $K$-doublet levels in symmetric top molecules and apply it to ${\mathrm{RaOCH}}_3$. The electric-field-dependent $g$ factors of the first excited rotational level of ${\mathrm{RaOCH}}_3$ are calculated. We find that the $K$ doublet with a total angular momentum projection $M_F=2$ has a ratio $\mathrm{\Delta }g/g\sim {10}^{-6}$ for an electric field in the range from 500 mV/cm to 1 V/cm, where $\mathrm{\Delta }g$ is the difference in the $g$ factors for the $K$-doublet components.

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• Fine & hyperfine structure
• Rotational states
• Zeeman effect
• Spacetime symmetries