I am self studying Analytic number theory from Tom M Apostol Modular functions and Dirichlet series in number theory and I have a doubt in an argument in Chapter -6 .
Doubt is If $ M_k $ denotes set of all entire forms of weight k . Then it's a Linear Space but I don't know how Apostol deduced that dimension of $ M_k $ is [ k / 12 ] when k = 2+ 12r , [ x ] denotes Greatest integer less than or equal to x. But why when k=2+12r , dimension is not [k/12] +1 as when k $\neq $ 2+12r then dimension is equal to [k/12] +1 .
Why does dimension changes when k = 2+12r . Can somebody please explain.
Apostol uses this formula whose image I am adding as image 