A new season has started. Why did my multiplier go down?

The clan multiplier is calculated as follows: (player level) × (player rating) × (item effects) × (Library factor) × (Grail factor) / 1000.
The rating used is either your current one or the one you finished the last season with, whichever is greater.
If your multiplier has gone down, that means your rating from last season is lower than your rating from the season before that.