Unbranded single hung single coil

Unfortunately there is no branding badge on any of the windows. Only window in the house with a coil balance and both coils are broken so I don't have pictures of a full proper installation. I am unclear if the entire coil is supposed to sit inside the shoe housing or not. Shoe body is 2 5/8" tall, 1 1/4" wide, and 1/2" deep. Window is 29" tall. 

Took measurements again and mine are measuring out around .55 in thickness. Should be a perfect fit. Thank you!