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 belongs to $S_1(\Gamma_0(23),({{}\over 23}))$.

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 belongs to $S_1(\Gamma_0(23),({{}\over 23}))$.

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 belongs to $S_1(\Gamma_0(23),({{}\over 23}))$.

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  belongs to $S_1(\Gamma_0(23),({{}\over 23}))$.