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We report on the light sterile neutrino search from the first four-weekscience run of the KATRIN experiment in~2019. Beta-decay electrons from ahigh-purity gaseous molecular tritium source are analyzed by a high-resolutionMAC-E filter down to 40 eV below the endpoint at 18.57 keV. We consider theframework with three active neutrinos and one sterile neutrino of mass $m_{4}$.The analysis is sensitive to a fourth mass state $m^2_{4} \lesssim$ 1000 eV$^2$and to active-to-sterile neutrino mixing down to $|U_{e4}|^2 \gtrsim2\cdot10^{-2}$. No significant spectral distortion is observed and exclusionbounds on the sterile mass and mixing are reported. These new limits supersedethe Mainz results and improve the Troitsk bound for $m^2_{4} <$ 30 eV$^2$. Thereactor and gallium anomalies are constrained for $ 100 < \Delta{m}^2_{41} <1000$ eV$^2$.

Bound on 3+1 active-sterile neutrino mixing from the first four-week science run of KATRIN