I hadn't heard of this guy, but when I looked him up, he's right smack in an area I do know a decent amount (if I can keep the facts straight), which is the 5th century revolt of Illus (which is a clusterfuck if there ever was one). So thank you for highlighting this guy. (Also can I ask where you found the mention of this guy? Because this is quite niche).

In essence, in one text he is said to describe himself as a goēta (bewitcher/sorceror) and a teleotēn (initiator of mystic rites), and in the fragmentary history of Malchus, he's described as a hellene/pagan.

The state of "paganism" in the 5th century, and especially late 5th century Constantinople, is quite unknown, but remarked to be in the minority and scandalous for someone to state openly. The equivalent would be if Senator today openly stated that they were a Satanist. One might understand that "Satanism" constituted another religion that should be given equal deference under the constitution (since LaVey-an Satanism is not a new or a threatening thing), but for someone to openly state it, would raise eyebrows and stir a moral panic fear among religious conservatives, who would still be restrained by modern laws on freedom of religion.

Those heavy eyebrow raises are the context of who Pamprepius is, an unabashed and self-declared "pagan" in an openly Christian world, that people suspect of communing with daimons/demons.

So what kind of magic was he performing? This would've actually been the fairly standard fare magic of the pre-Christian Roman world, divination by birds/entrails, incantations and binding spells, enchantments and charms. Basically he would've been seen as someone who could appeal to the dark/secret powers to aid him and those who requested his assistance. For him to achieve the ranks of power that he did, he likely wasn't your common street sorceror that you could get for a dime a dozen in Egypt, he was doing this for people in the inner political circle.

In short, there were no 5D6 fireballs being cast here. He was basically a fortune teller, an enchanter, and a demon-manipulator (which is ultimately what the vast bulk of ancient magic was), except that everyone took him seriously. And this is precisely what made him powerful, and apparently led to his eventual downfall, when some of his predictions proved wrong later.

Divining the future, especially the future fate of the emperor, was serious and subversive business, and was specifically listed as a criminal act worthy of the death penalty in the Theodosian Code (Book 9, Title 16). But it was so serious that people kept risking the death sentence to do it, and so it continued to be done, with continued legislation being indicative of the law's weak enforceability and high demand.

tl;dr - He was doing the fortune-telling kind of magic, not the David Copperfield kind of magic, and not the Dungeons and Dragons kind of evocation magic.

And of course, if I'm missing anything, feel free to follow up and ask away.

EDIT: I should also add, his day job wasn't a sorceror. His day job was being a learned "Greek" intellectual, the kind that was always around in the Roman state as a sort of think-tank advisor. It's just that his knowledge included darker stuff, so a think-tank person who may have Illuminati connections and could get things done the "other" way...