*This won't fit into a comment box so here it is :*

I came across another small nugget in Kilford's book  (p.101) this afternoon.  Let $k>0$, $N>0$ be integers such that $k.(N+1)=24$, namely one of the pairs 

$(12,1)$, $(8,2)$, $(6,3)$, $(4,5)$, $(3,7)$, $(2,11)$, or $(1,23)$.  

Then $(\eta(q)\eta(q^N))^k$ is in $S_k(\Gamma_0(N))$ unless $k=1$ or $k=3$, in which case it is in $S_k(\Gamma_0(N),({{}\over N}))$.  This implies in particular that the form 

$q\prod_{n>0}(1-q^n)(1-q^{23n})$ 

which appears in [Emerton's answer ][1] belongs to $S_1(\Gamma_0(23),({{}\over 23}))$.  


 


  [1]: https://mathoverflow.net/questions/11747/galoisian-sets-of-prime-numbers/12382#12382