BlackTHUNDER strikes twice: Balmer-line absorption in an overmassive Little Red Dot at z = 7.04

James Webb Space Telescope (JWST) has revealed a population of ‘Little Red Dots’ (LRDs): compact, red objects at redshifts (Formula presented) with ‘v’-shaped spectral energy distributions, broad permitted lines, and, often, hydrogen Balmer absorption. We use NIRSpec/IFS data from the BlackTHUNDER survey to study the H α line in the LRD Abell2744-QSO1 at (Formula presented), which is a confirmed active galactic nucleus (AGN) due to time-variable equivalent width (EW) in its broad emission lines. The H α spectral profile is non-Gaussian, requiring at least two Gaussian components. We also detect a narrow-line Gaussian component, and strong H α absorption (EW relative to the continuum (Formula presented)), confirming a connection between the strong Balmer break and line absorption. The absorber is at rest with respect to broad H α, suggesting that the gas cannot be interpreted as an inflow or outflow, forming instead a long-lived structure. Its velocity dispersion is (Formula presented) (Formula presented), consistent with the value inferred from the analysis of the Balmer break. Based on H α, we infer a black hole mass of (Formula presented), smaller but close to the previous estimates based on H β. The Eddington ratio is 0.09. Combining the high signal-to-noise ratio of the narrow H α line with the spectral resolution (Formula presented) of the G395H grating, we infer a narrow-line intrinsic dispersion (Formula presented) (Formula presented), which places a stringent constraint on the black hole-to-dynamical mass ratio of this system to be (Formula presented), confirming the overmassive nature of the black hole and potentially leaving little room for a host galaxy.