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

• Label: 560.2.x
• Level: $560$
• Weight: $2$
• Character orbit: 560.x
• Rep. character: $\chi_{560}(127,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.x (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	216	36	180
Cusp forms	168	36	132
Eisenstein series	48	0	48

Trace form

\( 36 q + 12 q^{13} + 12 q^{17} + 12 q^{25} - 60 q^{37} - 60 q^{45} + 36 q^{53} + 48 q^{57} + 36 q^{65} - 12 q^{73} - 36 q^{81} + 60 q^{85} - 12 q^{97}+O(q^{100}) \)

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.x.a	$560$	$2$	560.x	20.e	$4$	$12$	$6$	$4.472$	12.0.\(\cdots\).1	None		✓			560.2.x.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{4}-\beta _{8})q^{3}+(-\beta _{6}+\beta _{9})q^{5}+\cdots\)
560.2.x.b	$560$	$2$	560.x	20.e	$4$	$24$	$12$	$4.472$		None		✓	✓		560.2.x.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(560, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)