Space of modular forms of level 69, weight 8, and Character 69.g

• Label: 69.8.g
• Level: $69$
• Weight: $8$
• Character orbit: 69.g
• Rep. character: $\chi_{69}(5,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $540$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	69.g (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(69, [\chi])\).

	Total	New	Old
Modular forms	580	580	0
Cusp forms	540	540	0
Eisenstein series	40	40	0

Trace form

\( 540 q - 35 q^{3} + 3362 q^{4} - 1280 q^{6} - 22 q^{7} - 659 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(69, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
69.8.g.a	$69$	$8$	69.g	69.g	$22$	$540$	$54$	$21.555$		None		$4$	$0$	\(0\)	\(-35\)	\(0\)	\(-22\)		$\mathrm{SU}(2)[C_{22}]$