I'm trying to understand the concept (definition) of the fundamental characters of level 1,2, etc. as Serre defined those in his Inventiones'72 paper and how they are related to Serre's conjecture. The paper is in French and hard to read, I would greatly appreciate clarifications and more detailed explanations. My background is algebraic number theory at the level of Marcus and Milnes's note and some class field theory from Milne's notes.

Edit: link to the paper.