You bought 4 ohms for your 510 battery? I would not fill it - I would see if I could return it. 4 ohms is for high voltage devices. A 510 battery (3.4v) is unlikely to being able to vaporize anything with a 4 ohm coil.
Slim 510's (which is what 510 means here) use 2.5 to 3 ohm atomizers and cartomizers aka standard resistance with 2.5 being the hotter end. I recommend Boge 510 3 ohms cartomizers as first cartomizers and Boge are the most popular cartos for 510 threaded devices.
If you mean a fat (14mm+ diameter) battery models like Ego, Riva 510 etc (450mah+ batteries) then you can use 2 ohms to 3 ohms and some will go as low as 1.7, some go down to 1.5 but that has killed some Egos. Mods can go that low though.
--- and here is how I fill 1ml cartomizers
How I fill Vapor4Life/Bloog/Volt KR8 cartos and Boge 510 cartos
With the carto off the battery... Pop out the soft cap with an unbent paperclip in the mouth hole, very careful not to catch stuffing or the wire loop.
Shake and open the eliquid
Fill
Hold a bit of tissue on the threaded end hole, tilt the carto, and add 18 drops per ml of capacity into the stuffing (Boges and most KR8 cartos are about 1ml).
Wait 15 seconds or so then see how many more drops the carto stuffing will soak in easily.
Cleanup
Clean up the threaded end, tilt open end down into tissue, puff into threaded end to clear air channel (Boges and the KR8 cartos I use have a defined center air channel and I want to see light through that) While the carto is still open end down, touch a soft bunch of tissue to the top of the stuffing to get the loose juice - this will help prevent leaks.
Settle (first fill only)
Cap and let it settle - I lay it on different sides for 15-20 minutes to make sure every bit of stuffing gets damp so I won't singe the carto. if you use thicker juice than me (I use 20% Vg or less) then you may need to wait much longer.
While vaping
While vaping, if the vapor gets a bit light or a bit dry or the carto is getting hotter than normal, I take the carto off the battery and add eliquid. Also, I use such light sediment-free juices, I can look at the stuffing and see if it needs juice because the stuffing goes back to near-white.
I often use a plastic or delrin drip tip as a mouthpiece on Boge and KR8 cartos (not to drip into since the juice would head for the central air channel). Easy to pop out to add juice.