Space of modular forms of level 8, weight 6, and Character 8.b

• Label: 8.6.b
• Level: $8$
• Weight: $6$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(8, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	4	4	0
Eisenstein series	2	2	0

Trace form

4 * q - 2 * q^2 + 20 * q^4 - 116 * q^6 + 96 * q^7 - 248 * q^8 - 164 * q^9 + 632 * q^10 + 1576 * q^12 - 2384 * q^14 - 416 * q^15 - 3312 * q^16 + 200 * q^17 + 4754 * q^18 + 4624 * q^20 - 5636 * q^22 + 2336 * q^23 - 7792 * q^24 + 1556 * q^25 + 5608 * q^26 + 5152 * q^28 - 2128 * q^30 - 12928 * q^31 + 5408 * q^32 - 2352 * q^33 - 4772 * q^34 - 10164 * q^36 + 15980 * q^38 + 35104 * q^39 + 16032 * q^40 - 4568 * q^41 - 26144 * q^42 - 29112 * q^44 + 29200 * q^46 - 54720 * q^47 + 35616 * q^48 + 9828 * q^49 - 47498 * q^50 - 36560 * q^52 + 23288 * q^54 + 85472 * q^55 + 40768 * q^56 - 2032 * q^57 + 3784 * q^58 + 2592 * q^60 + 34496 * q^62 - 153440 * q^63 - 41920 * q^64 - 19520 * q^65 + 43224 * q^66 + 10344 * q^68 - 68928 * q^70 + 206688 * q^71 - 83272 * q^72 + 39976 * q^73 + 17464 * q^74 + 99944 * q^76 - 174064 * q^78 - 247872 * q^79 - 35520 * q^80 + 29684 * q^81 + 161132 * q^82 + 196672 * q^84 - 18500 * q^86 + 307872 * q^87 - 167216 * q^88 - 84632 * q^89 + 142280 * q^90 - 49056 * q^92 - 98784 * q^94 - 259744 * q^95 - 115648 * q^96 - 99576 * q^97 - 117042 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(8, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.6.b.a	$8$	$6$	8.b	8.b	$2$	$4$	$4$	$1.283$	4.0.218489.1	None		✓	✓	✓	8.6.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(96\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)