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ちょうど昼過ぎの為か、よく空いていた車内。
According to Jisho.org, 為 means "sake; purpose", "consequence; result", "regarding, concerning", but I can't say what meaning is in this sentence, and also I don't know what is the meaning of か in this case. I know that か can make a question as a relative clause, but I'm not sure if it is the case here, and if so, I don't understand the relationship of the first clause with か and the following sentence.
If we remove か from the sentence we get 「ちょうど昼過ぎの為、よく空いていた車内。」'a car that was very empty, because it was just after noon'. The か here removes some amount of certainty, almost like saying 'perhaps because it was just after noon'.
