Space of modular forms of level 8, weight 4, and Character 8.b

• Label: 8.4.b
• Level: $8$
• Weight: $4$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(8, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

Trace form

2 * q - 2 * q^2 - 12 * q^4 + 28 * q^6 - 16 * q^7 + 40 * q^8 - 2 * q^9 - 56 * q^10 - 56 * q^12 + 16 * q^14 + 112 * q^15 + 16 * q^16 - 28 * q^17 + 2 * q^18 + 112 * q^20 - 84 * q^22 - 304 * q^23 - 112 * q^24 + 26 * q^25 + 280 * q^26 + 96 * q^28 - 112 * q^30 + 448 * q^31 - 352 * q^32 + 168 * q^33 + 28 * q^34 + 12 * q^36 - 196 * q^38 - 560 * q^39 + 224 * q^40 - 140 * q^41 - 224 * q^42 + 168 * q^44 + 304 * q^46 + 672 * q^47 + 672 * q^48 - 558 * q^49 - 26 * q^50 - 560 * q^52 + 728 * q^54 - 336 * q^55 - 320 * q^56 + 392 * q^57 - 840 * q^58 - 672 * q^60 - 448 * q^62 + 16 * q^63 + 576 * q^64 + 1120 * q^65 - 168 * q^66 + 168 * q^68 + 448 * q^70 - 144 * q^71 - 40 * q^72 - 588 * q^73 + 1288 * q^74 + 392 * q^76 + 560 * q^78 - 928 * q^79 - 1344 * q^80 - 1510 * q^81 + 140 * q^82 + 448 * q^84 - 2324 * q^86 + 1680 * q^87 + 336 * q^88 + 532 * q^89 + 56 * q^90 + 1824 * q^92 - 672 * q^94 - 784 * q^95 - 448 * q^96 + 1988 * q^97 + 558 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.4.b.a	$8$	$4$	8.b	8.b	$2$	$2$	$2$	$0.472$	\(\Q(\sqrt{-7}) \)	None		✓	✓	✓	8.4.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)