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

• Label: 2304.1.b
• Level: $2304$
• Weight: $1$
• Character orbit: 2304.b
• Rep. character: $\chi_{2304}(127,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $384$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2304.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(384\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	68	4	64
Cusp forms	20	2	18
Eisenstein series	48	2	46

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{25} + 2 q^{49} + 4 q^{73} - 4 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2304.1.b.a	$2304$	$1$	2304.b	8.d	$2$	$2$	$2$	$1.150$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{3}) \)			✓	✓	144.1.g.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q-2 i q^{13}+q^{25}-2 i q^{37}+q^{49}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2304, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)