Though that's still incomplete, because (more of the context stuff that you just have to know already) the "A" here refers to the frequency-weighting scheme used in the measurement, and not to the reference level (which is SPL).
It should probably be given as: dB(A) SPL, or dB SPL (A-weighted).
It should probably be given as: dB(A) SPL, or dB SPL (A-weighted).