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

• Label: 2304.1.g
• Level: $2304$
• Weight: $1$
• Character orbit: 2304.g
• Rep. character: $\chi_{2304}(1279,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2304.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
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	64	7	57
Cusp forms	16	5	11
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	5	0	0	0

Trace form

\( 5 q + O(q^{10}) \)

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.g.a	$2304$	$1$	2304.g	4.b	$2$	$1$	$1$	$1.150$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-2q^{5}+3q^{25}+2q^{29}+q^{49}+2q^{53}+\cdots\)
2304.1.g.b	$2304$	$1$	2304.g	4.b	$2$	$1$	$1$	$1.150$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+2q^{17}-q^{25}+2q^{41}+q^{49}+2q^{73}+\cdots\)
2304.1.g.c	$2304$	$1$	2304.g	4.b	$2$	$1$	$1$	$1.150$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+2q^{5}+3q^{25}-2q^{29}+q^{49}-2q^{53}+\cdots\)
2304.1.g.d	$2304$	$1$	2304.g	4.b	$2$	$2$	$2$	$1.150$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{2}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q-iq^{7}-q^{25}-iq^{31}-3q^{49}+q^{73}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)