Hyperfine, rotational, and vibrational structure of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:msubsup><mml:mi>Σ</mml:mi><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>state of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Rb</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>87</mml:mn></mml:mrow></mml:mmultiscripts></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow/><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We have performed high-resolution two-photon dark-state spectroscopy of an ultracold gas of $^{87}\mathrm{Rb}$${}_{2}$ molecules in the ${a}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ state at a magnetic field of about 1000 G. The vibrational ladder as well as the hyperfine and low-lying rotational structure are mapped out. Energy shifts in the spectrum are observed due to singlet-triplet mixing at binding energies as deep as a few hundred $\text{GHz}\ifmmode\times\else\texttimes\fi{}h$. This information, together with data from other sources, is used to optimize the potentials of the ${a}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ and ${X}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ states in a coupled-channel model. We find that the hyperfine structure depends weakly on the vibrational level. This provides a possible explanation for inaccuracies in recent Feshbach resonance calculations.