I have recently coded the 1st line of an aria from an opera composed by George Gershwyn and I am ready to share with you the following information:

1. The code is a simple substitution code, ten distinct letters were replaced by the digits 0,1,2…9.
2. One letter was left uncoded.
3. The line consists of six words.
4. When coded the 1st, 4th, and the 5th words become square numbers and do not use the non-coded letter ,
5. The other words are either multiples of a square number, bigger than one, or use the uncoded letter.

I dare you to find the name of the aria, the numbers in my coding (or alternate solution complying with the above terms) and to explain how it relates to puzzle's title.