I'm not sure so don't take my word on this. If you run it perpendicular to the joists and near an outside wall you might be OK but you should probably consult a building engineer of some sort to be sure.
I knew a guy who put his 90g on the main floor and although it's perpendicular to the joists, there was a disturbing amount of flex in the floor when someone would walk by the tank. Think he ended up installing a telepost underneath the tank.
So if that's an option I would look into that.
I know in my own case, I don't have a tank on the main floor, but I am building an inwall tank in the basement where the canopy is suspended from the ceiling. I have a 1/2" gap above the tank to the canopy (it will eventually be covered by the finishing carpentry, but structurally, it is 1/2" above the tank). I had to reinforce the floor joists over the tank (took a 2x10 and glued and bolted it to the floor joist running over the front of the tank) because if someone walked over the "magic spot" in the living room, my canopy would bounce down that whole 1/2" and contact the tank.
Slightly different situation to yours but I bring it up because it illustrates how much flex there can be in a floor. 130 gallons is a lot heavier than the average person.
So again you might be OK if near an outside wall but if it were me I'd still feel better if I could somehow install a telepost underneath.
I know that's probably not an ideal option for you so you might still want to consult with a structural engineer before going forward.