Space of modular forms of level 8, weight 14, and Character 8.b

• Label: 8.14.b
• Level: $8$
• Weight: $14$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(14\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(8, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	12	12	0
Eisenstein series	2	2	0

Trace form

\( 12 q - 2 q^{2} - 8556 q^{4} + 58444 q^{6} + 235296 q^{7} + 1076872 q^{8} - 5314412 q^{9} + O(q^{10}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(8, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.14.b.a	$8$	$14$	8.b	8.b	$2$	$2$	$2$	$8.578$	\(\Q(\sqrt{-79}) \)	None		$2$	$1$	\(-112\)	\(0\)	\(0\)	\(-351664\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-56-4\beta )q^{2}+129\beta q^{3}+(-1920+\cdots)q^{4}+\cdots\)
8.14.b.b	$8$	$14$	8.b	8.b	$2$	$10$	$10$	$8.578$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(110\)	\(0\)	\(0\)	\(586960\)	$2^{48}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(11+\beta _{1})q^{2}+(3\beta _{1}+\beta _{3})q^{3}+(-472+\cdots)q^{4}+\cdots\)