Space of modular forms of level 561, weight 2, and Character 561.q

• Label: 561.2.q
• Level: $561$
• Weight: $2$
• Character orbit: 561.q
• Rep. character: $\chi_{561}(32,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $272$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.q (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 561 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(561, [\chi])\).

	Total	New	Old
Modular forms	304	304	0
Cusp forms	272	272	0
Eisenstein series	32	32	0

Trace form

\( 272 q - 8 q^{3} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(561, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
561.2.q.a	$561$	$2$	561.q	561.q	$8$	$272$	$68$	$4.480$		None		$8$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$