This phrase in Luke gives us a great example of how words have bundles of meanings, and you have to move beyond the one or two word glosses in your first year Greek grammar.
In Jesus’ parable of the Pharisee and the tax collector, the arrogant Pharisee parades his accomplishments in his prayer: “I fast twice a week (νηστεύω δὶς τοῦ σαββάτου).” δίς is an adverb meaning “twice,” and in this verse σαββάτου is singular.
A related idiom is the more common, “the first day of the week” (Τῇ δὲ μιᾷ τῶν σαββάτων, Luke 24:1; cf. Matt 28:1; Mark 16:2; John 20:1, 19; Acts 20:7) and “for three Sabbath days” (ἐπὶ σάββατα τρία, Acts 17:2).
Added to the mix is the unusual use of the plural τὰ σάββατα when referring to a single day. σάββατον occurs 68x in the New Testament, 25x in the plural. BDAG does not distinguish a difference in meaning between the singular and plural.
The fact of the matter is that σάββατον can refer to a single day (whether it is singular of plural) and it can refer to a week; this is BDAG’s second entry.
One of the primary tasks in second year Greek is to increase your Greek vocabulary, not just the number of words but also coming to understand the flexibility there is in words.