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Some neon tetras would look nice in there, maybe a couple or corydoras You have to be careful with bettas though, as they can be temperamental with certain types of fish
I'd leave out the cores as they are quite active and a 10 is on the small side. Have you had time to observe how your betta acts with the tetras and shrimp? Give it a week or two to really study how it reacts. I have shrimp with my betta and all seamed good, but I've caught him hunting the shrimp and eating them. If it's cool with your tetras, then you could up them to 6.