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You must not ride bicycles on the sidewalk.
Literal
Sidewalk [on-で] bicycle [on-に] ride [must not-てはいけない] (polite).
~てはいけない is the standard 'must not,' 'may not' prohibition — literally 'if (you) X, it won't do.' The polite form ~てはいけません is common on signs and rules. 自転車に乗る uses に, not を, for the thing ridden: you 'ride onto' a bike, not 'ride' it as a direct object. で marks the location of the action.