Space of modular forms of level 2304, weight 1, and Character 2304.q

• Label: 2304.1.q
• Level: $2304$
• Weight: $1$
• Character orbit: 2304.q
• Rep. character: $\chi_{2304}(257,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2304.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2304, [\chi])\).

	Total	New	Old
Modular forms	56	16	40
Cusp forms	8	8	0
Eisenstein series	48	8	40

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2304.1.q.a	$2304$	$1$	2304.q	9.d	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(1+\zeta_{6})q^{11}+(-\zeta_{6}+\cdots)q^{17}+\cdots\)
2304.1.q.b	$2304$	$1$	2304.q	9.d	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(-1-\zeta_{6})q^{11}+\cdots\)
2304.1.q.c	$2304$	$1$	2304.q	9.d	$6$	$4$	$2$	$1.150$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-2}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{5}q^{11}+\cdots\)