Space of modular forms of level 567, weight 2, and Character 567.bl

• Label: 567.2.bl
• Level: $567$
• Weight: $2$
• Character orbit: 567.bl
• Rep. character: $\chi_{567}(47,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $1260$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bl (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 567 \)
Character field:			\(\Q(\zeta_{54})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(567, [\chi])\).

	Total	New	Old
Modular forms	1332	1332	0
Cusp forms	1260	1260	0
Eisenstein series	72	72	0

Trace form

\( 1260 q - 9 q^{2} - 27 q^{3} - 9 q^{4} - 27 q^{5} - 18 q^{7} - 36 q^{8} - 9 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(567, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
567.2.bl.a	$567$	$2$	567.bl	567.al	$54$	$1260$	$70$	$4.528$		None		$2$	$0$	\(-9\)	\(-27\)	\(-27\)	\(-18\)		$\mathrm{SU}(2)[C_{54}]$