The entry in the Parker serialization book, Price & Fjestad, page 221 for 58537 reads as:
D2 H 0 C 10 32
Grade 2, Damascus steel, hammerless, no extras, capped pistol grip, in 10 gauge, made with 32 inch barrels.
The numeral 2 on the water table designates the grade. Also, the letter E does too for a 10 gauge. Note the letter E referred to in the first paragraph quoted below.
If you care to really learn and want to study these guns, just go ahead and get the book as soon as you can. If you don’t get it now, you’ll get it later and wish you had it before.
https://www.amazon.com/Parker-Identi.../dp/1886768374
This is from the page on this website about the Parker Brothers grades:
“The Grade 2 production started about 1875, before the grading system was adopted and it sold for $80 (a 80 Dollar grade). As Parker introduced the named grades they named Grade 2 guns E, F, G, H, EH and GH. The GH and EH describes Grade 2 hammerless Parkers, the other names describe Grade 2 hammer guns. These names were based on various gauge and stock configurations.”
“It was a popular gun for the owner that wanted a gun with more adornment that the average gun and was willing to pay about $20 more for a gun that looked better and was well balanced. The Grade 2 had a higher quality of American walnut which has some figure.”
“Most Grade 2 guns have Damascus or Parker Special Steel barrels. They were significantly better engraved than the lower grade guns. Quail, ducks, snipe and woodcock are common figures in the engraving of the frame sides and bottom; the forend latch and screw heads are also engraved. The checkering was deeper and finer than lower grade Parkers. After about 1880, the hard rubber dogs head butt plate and a white metal shied behind the top tang became standard on the Grade 2. Because of the added embellishments, it was very popular with Parker customers.”
“Ejectors were an option on GH grade. These guns with ejectors (GHE) are desirable to collectors and can add as much as 50% to their collector value.”
Production numbers*:
Lifter Hammer 4,555
Top Lever Hammer 7,582
Hammerless 31,778
See at:
https://parkerguns.org/ Look for the link to the page titled “Parker Grades”