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

• Label: 2304.1.z
• Level: $2304$
• Weight: $1$
• Character orbit: 2304.z
• Rep. character: $\chi_{2304}(319,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2304.z (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	112	16	96
Cusp forms	16	16	0
Eisenstein series	96	0	96

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	16	0

Trace form

\( 16 q + O(q^{10}) \)

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.z.a	$2304$	$1$	2304.z	144.v	$12$	$8$	$2$	$1.150$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{24}^{5}q^{3}+(-\zeta_{24}^{4}+\zeta_{24}^{10})q^{5}+\cdots\)
2304.1.z.b	$2304$	$1$	2304.z	144.v	$12$	$8$	$2$	$1.150$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q+\zeta_{24}^{5}q^{3}+(\zeta_{24}^{4}-\zeta_{24}^{10})q^{5}+(\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)