Space of modular forms of level 8, weight 30, and Character 8.b

• Label: 8.30.b
• Level: $8$
• Weight: $30$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 30 \)
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:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(8, [\chi])\).

	Total	New	Old
Modular forms	30	30	0
Cusp forms	28	28	0
Eisenstein series	2	2	0

Trace form

28 * q - 8642 * q^2 - 69796972 * q^4 - 35869200308 * q^6 + 1356446145696 * q^7 - 9960937476728 * q^8 - 594796603828988 * q^9 - 62453907924808 * q^10 - 7307924809229144 * q^12 + 78078973393134640 * q^14 - 116634443346832736 * q^15 + 383700292994789136 * q^16 + 236508787823771000 * q^17 - 5463422025028232686 * q^18 + 8100282295034264464 * q^20 - 74241827096141255876 * q^22 + 149024448719096002016 * q^23 + 20712180656567708048 * q^24 - 985560523954733380084 * q^25 + 380313139658742379432 * q^26 - 1732909439174340048608 * q^28 + 7144801785073394672432 * q^30 - 7260046134127777257856 * q^31 + 6643977062920224197408 * q^32 - 2610896914152110428752 * q^33 - 2930192868202493524772 * q^34 - 28754573920484976067764 * q^36 + 252146488468191620775980 * q^38 + 74849868421738610351584 * q^39 + 820688210793094034561952 * q^40 - 80518000617380870331368 * q^41 - 1782819030248345808659744 * q^42 - 2294598007572934677578808 * q^44 + 4638427469402659794112144 * q^46 + 121247766087237335010240 * q^47 + 6184031365810992970795296 * q^48 + 8159536578855108935060412 * q^49 - 9220400966993622071721098 * q^50 - 22597445120917837888235600 * q^52 + 30818656788479461856375672 * q^54 + 48823262031438992129145632 * q^55 + 3128328639131527389044032 * q^56 - 36164170101969527032146832 * q^57 + 36177867997628119870848904 * q^58 + 329519076781799215890952992 * q^60 - 317074609885892335052163904 * q^62 - 493740527299257821299206560 * q^63 - 500218670532924741725109184 * q^64 + 275343801437622480199359040 * q^65 + 657604928464011122019443160 * q^66 - 106459616116586500235114136 * q^68 - 602966453165460640487523648 * q^70 + 1637917847840158826077048224 * q^71 - 556537060776134471328999112 * q^72 - 1631197084836886372704831464 * q^73 - 2073796425120249162662229896 * q^74 - 676347811772827416679548184 * q^76 + 4169403080301092166733125776 * q^78 - 2323214658985225396749618624 * q^79 + 13382509145726722749974633280 * q^80 + 3743945936405161605092781740 * q^81 - 12472627196010378834371800468 * q^82 - 30031545197634704679499565504 * q^84 + 24644722942495826507852746492 * q^86 - 23673763728982249679638339488 * q^87 + 6702747736581680058989669584 * q^88 - 3845720546264709069323947304 * q^89 + 34684748345566534013885745800 * q^90 + 106057936152291016342860027744 * q^92 - 115120233998779072244940565728 * q^94 + 120167370974924948019325601696 * q^95 - 107488627072203471026633280448 * q^96 - 6191808951720963836806076616 * q^97 + 159188980666085592813609483918 * q^98

Decomposition of \(S_{30}^{\mathrm{new}}(8, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.30.b.a	$8$	$30$	8.b	8.b	$2$	$28$	$28$	$42.622$		None		✓	✓	✓	8.30.b.a	$2$	$0$	\(-8642\)	\(0\)	\(0\)	\(13\!\cdots\!96\)		$\mathrm{SU}(2)[C_{2}]$