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

• Label: 560.2.ch
• Level: $560$
• Weight: $2$
• Character orbit: 560.ch
• Rep. character: $\chi_{560}(117,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $368$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	400	400	0
Cusp forms	368	368	0
Eisenstein series	32	32	0

Trace form

\( 368 q - 2 q^{2} - 6 q^{5} - 20 q^{8} - 168 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.2.ch.a	$560$	$2$	560.ch	560.bh	$12$	$4$	$1$	$4.472$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(-2\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\)
560.2.ch.b	$560$	$2$	560.ch	560.bh	$12$	$4$	$1$	$4.472$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(2\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\)
560.2.ch.c	$560$	$2$	560.ch	560.bh	$12$	$360$	$90$	$4.472$		None		$4$	$0$	\(2\)	\(0\)	\(-6\)	\(8\)		$\mathrm{SU}(2)[C_{12}]$