Space of modular forms of level 8, weight 18, and Character 8.b

• Label: 8.18.b
• Level: $8$
• Weight: $18$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(8, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	16	16	0
Eisenstein series	2	2	0

Trace form

\( 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9} + O(q^{10}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(8, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.18.b.a	$8$	$18$	8.b	8.b	$2$	$16$	$16$	$14.658$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(270\)	\(0\)	\(0\)	\(11529600\)	$2^{120}\cdot 3^{14}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(17-\beta _{1})q^{2}+(3\beta _{1}-\beta _{2})q^{3}+(-1712+\cdots)q^{4}+\cdots\)