That will be with SJ?
This is SJs rules for luggages (in swedish):
"På SJs tåg får du endast ta med dig så mycket bagage som du med enkelhet själv kan bära. Grundregeln är högst två väskor per person samt datorväska/handväska. Du får även ta med dig ett specialbagage som hopfällbar barnvagn, skidor, golfbag, musikinstrument eller hopfällbar cykel. Skidor och hopfällbar cykel ska förvaras i skyddande fodral."
a fast translation to english:
On SJ's train, you are only allowed to bring as much luggage as you can carry easely. The basic rule is no more than two bags per person and a computer bag/handbag. You can also bring a special baggage such as a folding stroller, ski's, a golf bag, a musical instrument or a folding bike. Ski's and folded bikes must be stored in a protective case."
You might be allowed to bring a ordinary bike if it is dismantled and put in a protective case, but I give no guarantees.