The phrasal verb is shut up.
Shut up: To stop talking or making a noise, or to make a person or animal stop making noise:
I wish you’d shut up and listen.
Shut up! I'm trying to think.
Can you shut that dog up?
In the sentence
"Shut the fuck up down there!"
The words the fuck are most likely "semantically inert". They only serve to add emphasis. We can omit them:
Shut up down there!
The words down there reflect the position of the person(s) to whom the sentence is addressed. The person pronouncing the sentence could be on a floor that is above the addressee's, for instance.
After screaming the sentence, the book character might pick up the phone and say to his/her friend:
There are some people down there who were singing loudly. I just told them to shut up. Yes, to shut the fuck up.