iPhone 5s does not show battery empty icon

The iphone’s battery is newly replaced 100 % capacity 1572 actual capacity, 1560 design capacity. Then I had calibrated it, but when it is drained, then I hold the power button, it turns on then turns off just after showing the apple logo instead of showing the battery empty icon. It’s like that the iphone detects the battery has still got some charge. But if I plug the iphone, it turns on immediately then turns off again after showing the apple logo, then turns on again then turns off again (repeatedly), if I leave it for a while to have a charge , it will fully boot up. How to resolve it? Btw I had also update and restored. I know I can prevent it from happening if I just charge it when it is 20% or 10% below, but it bothers me when the phone is drained and that happens, I don’t know if this is normal for a new battery.