Space of modular forms of level 8, weight 10, and Character 8.b

• Label: 8.10.b
• Level: $8$
• Weight: $10$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(8, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	8	8	0
Eisenstein series	2	2	0

Trace form

8 * q - 18 * q^2 - 428 * q^4 + 4684 * q^6 + 4800 * q^7 - 3384 * q^8 - 39368 * q^9 + 26392 * q^10 + 54760 * q^12 - 72336 * q^14 - 163136 * q^15 + 185616 * q^16 - 102000 * q^17 - 23614 * q^18 + 1245264 * q^20 - 2373124 * q^22 + 3412032 * q^23 - 3961456 * q^24 - 2423384 * q^25 + 4551240 * q^26 + 7509920 * q^28 - 15284368 * q^30 + 803584 * q^31 - 14113248 * q^32 + 58272 * q^33 + 27757244 * q^34 + 57226188 * q^36 - 63661140 * q^38 - 17590208 * q^39 - 93063648 * q^40 - 2180784 * q^41 + 127541344 * q^42 + 114013320 * q^44 - 131840944 * q^46 + 7432320 * q^47 - 217917408 * q^48 + 24436680 * q^49 + 231784902 * q^50 + 219270896 * q^52 - 362934280 * q^54 + 7056832 * q^55 - 358503360 * q^56 + 134003744 * q^57 + 375425192 * q^58 + 516952992 * q^60 - 344291904 * q^62 - 223198400 * q^63 - 316815296 * q^64 - 146501760 * q^65 + 239713176 * q^66 + 79875048 * q^68 - 56202048 * q^70 + 560234688 * q^71 + 112273016 * q^72 - 523987120 * q^73 - 65773608 * q^74 - 87532760 * q^76 + 318117968 * q^78 - 248943744 * q^79 + 890441280 * q^80 + 231960296 * q^81 - 1051981172 * q^82 - 1275608768 * q^84 + 1492810428 * q^86 + 540527424 * q^87 + 1544767952 * q^88 + 744827856 * q^89 - 3218579800 * q^90 - 2959012128 * q^92 + 3068552352 * q^94 - 1465245504 * q^95 + 4296343616 * q^96 - 9932784 * q^97 - 3062604162 * q^98

Decomposition of \(S_{10}^{\mathrm{new}}(8, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.10.b.a	$8$	$10$	8.b	8.b	$2$	$8$	$8$	$4.120$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓	✓	8.10.b.a	$2$	$0$	\(-18\)	\(0\)	\(0\)	\(4800\)	$2^{28}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots\)