Space of modular forms of level 5, weight 8, and Character 5.b

• Label: 5.8.b
• Level: $5$
• Weight: $8$
• Character orbit: 5.b
• Rep. character: $\chi_{5}(4,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(5, [\chi])\).

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

Trace form

2 * q + 24 * q^4 + 150 * q^5 - 696 * q^6 + 2286 * q^9 + 5800 * q^10 - 13656 * q^11 + 9048 * q^14 + 17400 * q^15 - 29408 * q^16 + 13720 * q^19 + 1800 * q^20 + 27144 * q^21 - 97440 * q^24 - 133750 * q^25 + 218544 * q^26 + 51180 * q^29 - 52200 * q^30 + 164224 * q^31 - 337792 * q^34 - 226200 * q^35 + 27432 * q^36 + 655632 * q^39 + 812000 * q^40 - 1066236 * q^41 - 163872 * q^44 + 171450 * q^45 - 629416 * q^46 + 1294214 * q^49 + 870000 * q^50 - 1013376 * q^51 - 2317680 * q^54 - 1024200 * q^55 + 1266720 * q^56 + 2877960 * q^59 + 208800 * q^60 + 2762044 * q^61 - 4510336 * q^64 - 5463600 * q^65 + 4752288 * q^66 - 1888248 * q^69 + 678600 * q^70 - 963216 * q^71 + 4814928 * q^74 + 2610000 * q^75 + 164640 * q^76 - 2119520 * q^79 - 2205600 * q^80 - 1953558 * q^81 + 325728 * q^84 + 8444800 * q^85 - 15270936 * q^86 + 11288340 * q^89 + 6629400 * q^90 - 8523216 * q^91 - 125512 * q^94 + 1029000 * q^95 - 2238336 * q^96 - 15608808 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(5, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.8.b.a	$5$	$8$	5.b	5.b	$2$	$2$	$2$	$1.562$	\(\Q(\sqrt{-29}) \)	None		✓	✓	✓	5.8.b.a	$2$	$0$	\(0\)	\(0\)	\(150\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots\)