The corresponding maximum dimensions for vessels that will transit these {new panama} locks are 366 meters LOA, 49 meters in beam and 15.2 meters in tropical freshwater (TFW) draft.
Dimensions for Future Lock Chambers and New Panamax Vessels
http://www.pancanal.com/common/maritime/advisories/2009/a-02-2009.pdf
Tanker Size
Class | Length | Beam | Draft | Overview |
Coastal Tanker | 205 m | 29 m | 16 m | Less than 50,000 dwt, mainly used for transportation of refined products (gasoline, gasoil). |
Aframax | 245 m | 34 m | 20 m | Approximately 80,000 dwt (Average Freight Rate Assessment). |
Suezmax | 285 m | 45 m | 23 m | Between 125,000 and 180,000 dwt, originally the maximum capacity of the Suez Canal. |
VLCC | 330 m | 55 m | 28 m | Very Large Crude Carrier. Up to around 320,000 dwt. Can be accommodated by the expanded dimensions of the Suez Canal. The most common length is in the range of 300 to 330 meters. |
ULCC | 415 m | 63 m | 35 m | Ultra Large Crude Carrier. Capacity exceeding 320,000 dwt. The largest tankers ever built have a deadweight of over 550,000 dwt. |
Source: http://people.hofstra.edu/geotrans/eng/ch5en/appl5en/tankers.html
Key phrase is "some will be unable" which infers that some will be able to transit. However I don't know how many "some" is nor do I know how many ULCC's there are or how many there are relative to other tankers