How much money should I have in my checking account?

Lately I've been struggling with how much money I should have in my checking account. As of today, I have roughly 3-4 months worth of expenses in my checking. I'm thinking that's too much, since the account is essentially dead money at 0% interest. Should I keep it at this level, or should I move some to my 'emergency' savings account at Ally (1.05% interest, and also at about 3-4 months of expense right now) or to my brokerage account at Fidelity? I'm getting adequate exposure to the market already, so anything I move to Fidelity would be in addition to what's in there.