What type of wire are you using? If its copper with at least one H, then #1 can do 130 amps and #2 can do 115 amps. If this is aluminum, you're limited to 100A breaker and 90A neutral load (or perhaps 110A/100A if 310.15(B)(6) can be applied to subpanel feeders in your area). If it helps, you can run a #6 copper grounding wire instead of a #4.
Since you have used a 125A breaker, if the calculated load is 115A or less then you are fine on copper wire (you can round up the breaker to the next standard size which is 125A). If the load calculates to 125A, then you need to determine if the unbalanced load is 115A or less. All it would take would be a 240V only load of 25A or so to accomplish (and perhaps less depending on the % factor applied to the load).
A range or dryer allows a 70% factor to be applied to the neutral loads. A 240V water heater, pump, or HVAC system would provide a lot of relief to that neutral load.