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

• Label: 8.8.b
• Level: $8$
• Weight: $8$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	8	8	0
Cusp forms	6	6	0
Eisenstein series	2	2	0

Trace form

6 * q + 6 * q^2 + 116 * q^4 + 268 * q^6 - 688 * q^7 + 1512 * q^8 - 2918 * q^9 - 1656 * q^10 - 4088 * q^12 + 12048 * q^14 + 17872 * q^15 + 35344 * q^16 + 1452 * q^17 - 89062 * q^18 - 114768 * q^20 + 152860 * q^22 - 1296 * q^23 + 282512 * q^24 - 39314 * q^25 - 316968 * q^26 - 480800 * q^28 + 821648 * q^30 - 89280 * q^31 + 817056 * q^32 + 53880 * q^33 - 1009108 * q^34 - 1253556 * q^36 + 974124 * q^38 - 328208 * q^39 + 954464 * q^40 + 521244 * q^41 - 1093088 * q^42 - 1096344 * q^44 + 929840 * q^46 + 1566432 * q^47 + 853920 * q^48 - 511050 * q^49 - 148626 * q^50 + 823952 * q^52 - 1077064 * q^54 - 3270256 * q^55 - 2468928 * q^56 - 1889896 * q^57 + 3130744 * q^58 + 5715168 * q^60 - 7055808 * q^62 + 5776816 * q^63 - 4792768 * q^64 + 1416480 * q^65 + 7926264 * q^66 + 6608040 * q^68 - 7406912 * q^70 - 7597104 * q^71 - 11363944 * q^72 + 2089564 * q^73 + 7744200 * q^74 + 9241288 * q^76 - 9471184 * q^78 + 16015904 * q^79 - 12600384 * q^80 - 723058 * q^81 + 10715932 * q^82 + 4220608 * q^84 - 5639076 * q^86 - 37453776 * q^87 + 1541200 * q^88 + 2169084 * q^89 - 121864 * q^90 + 669600 * q^92 + 15503712 * q^94 + 48537936 * q^95 + 21402176 * q^96 - 1088308 * q^97 - 14983242 * q^98

Decomposition of \(S_{8}^{\mathrm{new}}(8, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.8.b.a	$8$	$8$	8.b	8.b	$2$	$6$	$6$	$2.499$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓	✓	✓	8.8.b.a	$2$	$0$	\(6\)	\(0\)	\(0\)	\(-688\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{2}+\beta _{4}q^{3}+(19+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)