Space of modular forms of level 560, weight 2, and Character 560.cu

• Label: 560.2.cu
• Level: $560$
• Weight: $2$
• Character orbit: 560.cu
• Rep. character: $\chi_{560}(207,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cu (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(560, [\chi])\).

	Total	New	Old
Modular forms	432	96	336
Cusp forms	336	96	240
Eisenstein series	96	0	96

Trace form

\( 96 q + 24 q^{21} + 24 q^{33} - 48 q^{41} - 96 q^{57} + 48 q^{65} + 48 q^{73} - 24 q^{77} + 72 q^{81} - 48 q^{85} + 48 q^{93} + 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(560, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.2.cu.a	$560$	$2$	560.cu	140.w	$12$	$8$	$2$	$4.472$	\(\Q(\zeta_{24})\)	None		✓			560.2.cu.a	$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2\zeta_{24}-\zeta_{24}^{5})q^{3}+(-2\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
560.2.cu.b	$560$	$2$	560.cu	140.w	$12$	$24$	$6$	$4.472$		None		✓			560.2.cu.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
560.2.cu.c	$560$	$2$	560.cu	140.w	$12$	$32$	$8$	$4.472$		None		✓			560.2.cu.c	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)		$\mathrm{SU}(2)[C_{12}]$
560.2.cu.d	$560$	$2$	560.cu	140.w	$12$	$32$	$8$	$4.472$		None		✓			560.2.cu.c	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(560, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)