Space of modular forms of level 2304, weight 2, and Character 2304.c

• Label: 2304.2.c
• Level: $2304$
• Weight: $2$
• Character orbit: 2304.c
• Rep. character: $\chi_{2304}(2303,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $10$
• Sturm bound: $768$
• Trace bound: $49$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2304.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(768\)
Trace bound:			\(49\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2304, [\chi])\).

	Total	New	Old
Modular forms	432	32	400
Cusp forms	336	32	304
Eisenstein series	96	0	96

Trace form

\( 32 q - 32 q^{25} + 32 q^{49} - 64 q^{73} - 64 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2304.2.c.a	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	None					1152.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2\beta q^{7}-4q^{11}-2q^{13}+\beta q^{17}+\cdots\)
2304.2.c.b	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	None					1152.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2\beta q^{7}-4q^{11}+2q^{13}-\beta q^{17}+\cdots\)
2304.2.c.c	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)					1152.2.f.c	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3\beta q^{5}-6q^{13}-5\beta q^{17}-13q^{25}+\cdots\)
2304.2.c.d	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)					1152.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-6q^{13}-3\beta q^{17}+3q^{25}+\cdots\)
2304.2.c.e	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)					1152.2.f.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3\beta q^{5}+6q^{13}+5\beta q^{17}-13q^{25}+\cdots\)
2304.2.c.f	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)					1152.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}+6q^{13}+3\beta q^{17}+3q^{25}+\cdots\)
2304.2.c.g	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	None					1152.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2\beta q^{7}+4q^{11}-2q^{13}+\beta q^{17}+\cdots\)
2304.2.c.h	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-2}) \)	None					1152.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2\beta q^{7}+4q^{11}+2q^{13}-\beta q^{17}+\cdots\)
2304.2.c.i	$2304$	$2$	2304.c	12.b	$2$	$8$	$8$	$18.398$	\(\Q(\zeta_{24})\)	None					72.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{5} q^{5}+\beta_{3} q^{7}+\beta_{6} q^{11}+\beta_{2} q^{13}+\cdots\)
2304.2.c.j	$2304$	$2$	2304.c	12.b	$2$	$8$	$8$	$18.398$	\(\Q(\zeta_{24})\)	None					576.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{5}-\beta_1 q^{7}+\beta_{6} q^{11}-\beta_{2} q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2304, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)