Why does my Nexus 4 die at 30-40 battery (new battery)?

[AC Question]

nexus 4: died at 30%-40% battery (new battery)

hi,

3 months ago i dropped my phone, and the screen broke.
when i fixed it, i also had the shop put it a new battery.

since then, the phone sterted to die before 0%, sometimes at 13-14, somtimes at 30%+.

i went back to the shop and they put a new battery. (this was 5 days ago).
today the phone died at 40%, when i plugged it in nothing happend, didnt turn on, tried unplugging and plugging, sometimes it gave a solid red light, sometimes nothing.

i left it charging with the solid red, after 20 min i could turn it on again.

what is this? is it fixable?
did the fall caused it or the battery replacement?

thanks