Dimension C-137 is one of the many universes in the multiverse and the universe where the mainstream Rick and Morty are often identified as coming from. Given that Rick does not list his adoptive son-in-law Jerry as originating in the same dimension as him, dimension C-137 is the universe in which Earth was overrun by Cronenberg in “Rick Potion”
History
Dimension C-137 first appeared in the “Pilot” episode and appeared in every episode since then until “Rick Potion #9”, were in it made its last appearance until season 3. In Rick Potion No. 9, Rick made a love potion using vole DNA for Morty to use on Jessica. However, the side effects of the potion led to a disaster. The chemicals in the potion piggybacked on the flu virus, causing everyone in Morty’s school fall in love with him.
To counteract this, Rick mixes praying mantis DNA with a more contagious strain of the flu virus. Unfortunately, this backfires, turning not only those affected by the original potion into praying mantis monsters set on mating with Morty but the entire world (presumably due to the aggressive nature of the flu strain Rick used) into praying mantis creatures that want a mate with Morty, then kill him afterward. Rick used an antidote on them, but this again backfired, turning all of humanity into deformed, disgusting monsters known as Cronenbergs (except for Jerry, Beth, and Summer). Unable to solve this increasingly difficult problem, Rick sought out a different reality where he managed to restore humanity normal. There, that dimension’s version of Rick and Morty died, so Dimension C-137’s Rick and Morty took their places without anyone noticing.
Meanwhile, alternate versions of them from yet another dimension where everyone is born a Cronenberg, named Cronenberg Rick and Cronenberg Morty, did exactly the same thing in their dimension and turned everyone into normal humans. They left their own dimension and entered Dimension C-137, where every normal human was now a perfect Cronenberg matching their home dimension.
Meanwhile, alternate versions of them from yet another dimension where everyone is born a Cronenberg, named Cronenberg Rick and Cronenberg Morty, did exactly the same thing in their dimension and turned everyone into normal humans. They left their own dimension and entered Dimension C-137, where every normal human was now a perfect Cronenberg matching their home dimension.
The Cronenberg race and the rest of the Smith family are apparently far apart enough, that they never interact with each other, for unknown reasons, so both races don’t need to to worry about each other and the Cronenberg versions of Rick and Morty never have interacted with the real Smith family.
Dimension C-137 would be mentioned again in the episode “Rixty Minutes”, when Morty showed Summer the graves in the backyard where Rick and Morty were buried, telling her the whole story of Rick Potion #9. It was also mentioned again in “Close Rick-Counters of the Rick Kind”, by the Council of Ricks and it was also briefly seen in a screen, showing Rick’s memories. One of them was him putting the helmet on Snuffles from the episode “Lawnmower Dog”, Rick holding Morty when he was an infant, and another one was of Rick giving the love potion Morty from “Rick Potion #9”. There were also scenes of Rick and Morty flying in the space cruiser, and one of Rick, lying down on the floor, and Morty passing him his canister, but it is unknown if those took place in the old or new dimension. In the episode “Total Rickall”, there was a flashback montage to all the funny catchphrases that Rick has used. One of which was one he was using, while playing cards with Snuffles. This had to have been Dimension C-137, because Snuffles left the family in the episode “Lawnmower Dog”, before events of the dimension transition in the episode “Rick Potion #9”. There were many other flashbacks of moments in time that actually happened, but none of them proved that they were in Dimension C-137.
Dimension C-137 is briefly mentioned in the episode “Mortynight Run” when Rick is asked to identify his home dimension for identification purposes when returning to pick up his Jerry. Because Jerry is not from Rick and Morty’s home dimension of C-137, Rick marks him as “N/A”. This might mean that Rick is uncertain of their current dimension’s official alphanumeric identification.
Dimension C-137 returns in the episode The Rickshank Redemption, Morty brings the Summer from the new Dimension he and Rick came from in order to show her that Rick didn’t care about anyone and that he always left carnage in his wake. It is here, Summer met the version of herself and her family from this Dimension, who are now more tribalistic and savage than when they were previously seen.