As far as I am aware there is no such thing as a collegium Aventinum. The moniker does not seem to make much sense. Collegia, the voluntary citizen associations (as Bendlin calls them) of the Roman world, frequently had a territorial aspect, but not one such as this. Our information for collegia is rather scant, particularly in the Republic, but a few broad classifications can be made about such associations. Most collegia were either professional or religious in nature, though the distinction should not be pressed as much of our evidence for collegia of either type (often epigraphic) is religious in nature, and festivals like the Ludi Compitalicii (which, following Flambard's excellent analysis, I must conclude were organized by professional associations, not some vague, mysterious class of collegia compitalicia) were simultaneously religious and professional. There were also of course priestly and minor magisterial colleges (not, generally, of our concern here) and the notoriously mysterious collegia sodalicia, which since Mommsen have been understood to be some sort of politically-oriented organizations, an interpretation that I do not fully agree with and which has very little support in the texts. It used to be thought that a class of "collegia tenuiorum" and collegia funeraticia existed for the most impoverished (as the shopkeepers and skilled workers of the professional collegia made up the so-called plebs media) but Bendlin has recently pretty much totally dismantled that idea--no such sort of collegium existed.

Leaving aside the question of how to categorize collegia in their entirety and how to dissect them into discernible groups and types (an exercise I increasingly think is impossible, as these associations did not think of themselves so rigidly), this supposed collegium Aventinum would be totally unprecedented in what we know of Roman society. Collegia with territorial aspects existed, sure, but they did not encompass an entire hill, an area which under Augustus would become its own regio. Instead, the case of the lanii piscinenses (known from ILS 3682a, one of the few Republican collegiate inscriptions) is much more usual--while smaller Italian settlements might only contain a single collegium for all the members of a profession, the city's collegia located themselves by vici or whatever notable landmarks existed. The Aventine hill is quite out of the question. Moreover, the idea of collegia with purely territorial natures is not particularly well-supported by the texts, and we do not have the actual names of any such collegia if they existed. Territorial collegia were almost always professional, taking their names from the immediate area, almost like a city block, in which their professional members kept shop. What sort of a collegium would this collegium Aventinum be? It's unlikely it would be a professional or religious one, although that's indicated more by the name (which fails to mention any such connection) than by anything inherent to the nature of such associations--the famous Lanuvium inscription (CIL 14.2112) catalogs the lex of a collegium cultorum Dianae et Antinoi which otherwise seems to have little actual religious connection. Pretty much no other collegiate types are attested, which is not to say that they did not exist. Probably the purpose here of this invented group is to associate the Aventine in the minds of the audience with popular unrest, and to point out the supposed role of the collegia in urban violence. In fact I find pretty much no textual evidence for the direct involvement of collegia in urban political violence, though collegiati in general were certainly involved. The Aventine, however, is easier to defend. The Aventine was traditionally the location of a number of (especially foreign) cults, and many religious collegia in particular had their headquarters there. At the same time the Aventine was traditionally a symbolic location for the plebs and allies. It lay outside the pomerium, was the location of the Aventine Triad, and was originally settled as an ager publicus--Gaius Gracchus sought its safety in 121 and the site held symbolic significance for the urban plebs. The dramatic connection of the Aventine with the collegia who supposedly terrorized the city under P. Clodius (which I don't think is true and in any case is irrelevant--Clodius died before Rome even begins, though much of the series is founded on grosser anachronisms than that) is presumably what is being aimed at here, but there is no evidence for the existence of such a collegium