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

• Label: 560.2.bn
• Level: $560$
• Weight: $2$
• Character orbit: 560.bn
• Rep. character: $\chi_{560}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $184$
• 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.bn (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 560 \)
Character field:			\(\Q(i)\)
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	200	200	0
Cusp forms	184	184	0
Eisenstein series	16	16	0

Trace form

184 * q - 4 * q^2 + 8 * q^8 + 168 * q^9 - 8 * q^11 - 8 * q^15 - 8 * q^16 - 24 * q^18 - 4 * q^21 + 4 * q^22 + 12 * q^28 - 4 * q^30 + 16 * q^32 - 40 * q^36 - 48 * q^39 - 36 * q^42 - 8 * q^43 - 24 * q^44 - 8 * q^46 - 4 * q^50 - 8 * q^51 - 8 * q^53 - 4 * q^56 - 24 * q^57 - 68 * q^58 - 32 * q^63 - 8 * q^65 - 56 * q^67 + 80 * q^70 - 8 * q^72 - 40 * q^74 + 24 * q^77 - 100 * q^78 + 104 * q^81 + 48 * q^84 - 24 * q^85 + 8 * q^86 - 16 * q^88 - 20 * q^91 - 56 * q^92 - 56 * q^95 + 52 * q^98 - 24 * 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.bn.a	$560$	$2$	560.bn	560.an	$4$	$184$	$92$	$4.472$		None		✓	✓	✓	560.2.r.a	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$