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

• Label: 560.2.cr
• Level: $560$
• Weight: $2$
• Character orbit: 560.cr
• Rep. character: $\chi_{560}(109,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $368$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cr (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 560 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

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 - 4 * q^4 - 2 * q^5 - 16 * q^6 - 8 * q^10 - 4 * q^11 + 16 * q^14 - 16 * q^15 - 4 * q^16 - 4 * q^19 - 8 * q^20 + 4 * q^21 - 4 * q^24 - 4 * q^26 - 16 * q^29 + 22 * q^30 - 56 * q^31 - 96 * q^34 + 18 * q^35 + 32 * q^36 - 14 * q^40 - 12 * q^44 - 16 * q^45 + 12 * q^46 - 16 * q^49 - 12 * q^50 - 28 * q^51 - 8 * q^54 - 64 * q^56 + 12 * q^59 - 54 * q^60 - 4 * q^61 - 88 * q^64 - 4 * q^65 - 44 * q^66 + 8 * q^69 + 88 * q^70 - 72 * q^74 + 10 * q^75 + 104 * q^76 - 8 * q^79 + 48 * q^80 + 112 * q^81 + 68 * q^84 - 28 * q^85 + 44 * q^86 - 92 * q^90 - 80 * q^91 - 20 * q^94 + 20 * q^95 - 36 * q^96 - 112 * q^99

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.cr.a	$560$	$2$	560.cr	560.br	$12$	$368$	$92$	$4.472$		None		✓	✓	✓	560.2.cr.a	$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$