Space of modular forms of level 560, weight 5, and Character 560.j

• Label: 560.5.j
• Level: $560$
• Weight: $5$
• Character orbit: 560.j
• Rep. character: $\chi_{560}(239,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	560.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(560, [\chi])\).

	Total	New	Old
Modular forms	396	72	324
Cusp forms	372	72	300
Eisenstein series	24	0	24

Trace form

\( 72 q + 72 q^{5} + 1944 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(560, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
560.5.j.a	$560$	$5$	560.j	20.d	$2$	$24$	$24$	$57.887$		None		$4$	$0$	\(0\)	\(0\)	\(36\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
560.5.j.b	$560$	$5$	560.j	20.d	$2$	$48$	$48$	$57.887$		None		$4$	$0$	\(0\)	\(0\)	\(36\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)