Space of modular forms of level 5, weight 22, and Character 5.b

• Label: 5.22.b
• Level: $5$
• Weight: $22$
• Character orbit: 5.b
• Rep. character: $\chi_{5}(4,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $11$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
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:			\(11\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(5, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	10	10	0
Eisenstein series	2	2	0

Trace form

10 * q - 9273720 * q^4 - 25175970 * q^5 + 190183320 * q^6 - 46796905530 * q^9 + 42469996280 * q^10 + 150626450520 * q^11 + 1196972791560 * q^14 + 28918735560 * q^15 + 13236859984160 * q^16 - 111339219544600 * q^19 + 210425436114840 * q^20 + 153512457036120 * q^21 - 925398618703200 * q^24 + 233060326559650 * q^25 - 621077824626480 * q^26 - 2607858467637300 * q^29 - 2586594238552440 * q^30 + 2526078405859520 * q^31 + 72842119718695360 * q^34 - 39547684375393320 * q^35 - 37582575203847240 * q^36 - 96095316750417360 * q^39 + 147883293047082400 * q^40 + 178989482851615620 * q^41 - 740313984960721440 * q^44 - 170779831343975790 * q^45 + 310308437385662920 * q^46 + 337573187662879630 * q^49 - 330613273664391600 * q^50 + 425405951744829120 * q^51 + 2276512248592508400 * q^54 - 4016119665475835640 * q^55 + 9526915367282527200 * q^56 + 1994566040408748600 * q^59 - 20957050062416020320 * q^60 + 5353281898917000620 * q^61 - 53705514970438977920 * q^64 - 12495942066653666640 * q^65 + 130803500735066708640 * q^66 - 100469090770094966760 * q^69 - 72656118333436657320 * q^70 + 148239232001721288720 * q^71 + 15604199347531682160 * q^74 - 355998150662931493200 * q^75 + 574798946837845274400 * q^76 - 190143330869910604000 * q^79 - 801735065581038901920 * q^80 + 1042969689596090972610 * q^81 - 984178622121811230240 * q^84 - 881984388527483667520 * q^85 + 2442532998478428470520 * q^86 - 1194549181591936131900 * q^89 - 2604678167917323770040 * q^90 + 2759667106510781727120 * q^91 - 2807277590161309874840 * q^94 - 1062907495565755235400 * q^95 + 9073487122609823752320 * q^96 - 2282448445798673329560 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(5, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.22.b.a	$5$	$22$	5.b	5.b	$2$	$10$	$10$	$13.974$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓	✓	5.22.b.a	$2$	$0$	\(0\)	\(0\)	\(-25175970\)	\(0\)	$2^{30}\cdot 3^{10}\cdot 5^{19}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-6\beta _{1}-\beta _{4})q^{3}+(-927372+\cdots)q^{4}+\cdots\)