1. Fantasy setting or heavy fantasy elements, usually involving magic
While more traditional and realistic settings may have worked back in the heyday of harems like Love Hina, the incorporation of fantasy elements serves as a replacement for actually making the viewer believe that this type of romantic setup could occur in the first place. Additionally, the use of magic creates a plethora of possibilities for getting the female characters into situations of a lewd and nearly-naked nature, with very minimal effort on the part of the writer. For Trinity Seven, we end up with one of Arata's main powers being the ability to make people's clothes disappear, providing plenty of fan service fun.
2. Story still manages to take place in a high school of some kind
I'm not sure what the exact percentage is of anime that take place in high school, but I'm going to assume it's a relatively high number, and within the harem genre the reason for that is very simple: it attracts viewers who are currently in high school. Additionally, with Trinity Seven, we get bonus points added for the high school being an all-girls school (while it's never explicitly stated that this is the case, no other male students seem to appear in this school). This further allows for Arata to be given free reign over whatever love interest the series decides to throw in for our enjoyment.
3. Actual story and magic lore is incredibly convoluted and pointless
For obvious reasons, writers can't just get away with writing absolutely nothing but fan service moments, so of course there has to be some kind of story. However, writing an actual story would make it too difficult for the viewers to focus on those wonderfully-animated breasts you just shoved into frame [heavy-handed sarcasm], so the plot needs to be flimsy, shallow, and easily tradable with any other generic plot. Every magic term in Trinity Seven is practically thrown in your face one after another with little more than a one-sentence description of what it actually does. That didn't really matter though, because I couldn't even count the times where I just flat-out looked away from the screen for a minute or so and then turned back to realize that absolutely nothing has happened other than some more flashy magic terminology and a panty shot.
4. Random climactic battle at the end of the series
...yeah that's just kind of a thing I guess. I suppose they have to at least pretend that they're putting some kind of effort into their writing at the end of the series.
5. Always, ALWAYS leave room for a second season
The harem genre is surprisingly easy to market and sell to viewers, so it's important to keep the money train going until no one shows any interest in your specific series anymore.
6. Main character has some kind of power that no one else has
To be fair, this is a trait that's common even outside the harem genre, but within harems it adds something entirely different. With an action series, being the only one with a certain power or ability makes you humanity's last hope for survival. In a harem, it makes you an object of desire. Of course all the ladies want to jump your bones; you're the only person here who has this super awesome power. In the case of Trinity Seven, Arata is the "Demon Lord Candidate" who has the potential to turn into the Demon Lord, one of the most powerful beings in the world. Another important note is that the power in question is incredibly generic and normally just equates to "I'm stronger than everyone else because reasons."
7. Main character is either overtly perverted or a shy nice guy (who's still incredibly perverted on the inside), but is also incredibly noble
Again, to be fair to Trinity Seven, Arata certainly falls into the former category, and he becomes so blatant with his perversity that it's almost hard to not like him for it (almost being the important word there). As for the nobility aspects, it plays into why the girls fall for him in the first place. I mean sure he's super perverted but he's just this super nice guy that I can rely on underneath all of that [more heavy-handed sarcasm]. Everything about a harem is designed to make the main male character look awesome, and Trinity Seven certainly doesn't miss its mark.
8. Female characters have no depth other than their assigned archetypes
When you have this many female love interests on your cast, it's nearly impossible to give them enough characterization to make them feel fleshed-out while still finding time for fan service moments, so the best course of action is to flood your series with as many archetypes as you can: the childhood friend (Hijiri), the plain Jane (Lilith), the loli (Grimoire), the tsundere (Mira), the kooky one (Levi), the childish one (Yui), the tomboy (Akio), ad nauseam.
9. Primary love interest is as bland as a piece of notebook paper
If the love interest that the main character is eventually going to end up with actually has a personality, the writers run the risk of the viewers not enjoying that specific archetype, so it's always best to choose the one with the least amount of personality possible (and also the biggest cup size). Of course, the two characters in question will never actually reach the point where they could be considered to be in a relationship. I mean lord forbid that you actually do something romantically interesting with your characters.
10. All animation budget goes towards character designs and boob physics
The fan service is the main selling point of a harem, so it's absolutely vital that this is achieved, often at the cost of the rest of the animation looking terrible. Studio Seven Arcs knows this very well and gave us exactly that. While the action in Trinity Seven wasn't completely awful, the particle and light effects certainly weren't anything worthy of praise, and backgrounds and moving objects were often rendered in the most eye-jarring 3D I've seen in a long time.
11. Fan service out the wazoo
This one doesn't really need much explanation. You're certainly not watching this because the romance is so unbelievably captivating.
12. Soundtrack occupies the background for the majority of the anime's run time
I honestly can't even think of a single note from this soundtrack off the top of my head right now, and I just finished the last episode about an hour ago. In this case, the soundtrack was composed by Technoboys Pulcraft Green-Fund (Witch Craft Works), and I wouldn't necessarily blame them for the blandness of the soundtrack because this is a harem after all, and there isn't exactly a long list of standout harem soundtracks.
Overall, I do think that anime viewers should experience a simple comedic harem at least once, but Trinity Seven certainly isn't the one I would recommend as an introduction to the genre.
