Even if your tap water is at 4ppm the tank water can get down to 0 if it's cycled properly.
What did you dose the ammonia up to on that tank and how long ago was it?
Also, here's a thought about dealing with your ammonia. Keep a second filter running on a tank or rubbermaid tote that will hold enough water for your change. It will cycle the ammonia down to 0 so you can safely do your weekly water change. A sponge filter would be easy.