Space of modular forms of level 12, weight 22, and Character 12.b

• Label: 12.22.b
• Level: $12$
• Weight: $22$
• Character orbit: 12.b
• Rep. character: $\chi_{12}(11,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $44$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(44\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(12, [\chi])\).

	Total	New	Old
Modular forms	44	44	0
Cusp forms	40	40	0
Eisenstein series	4	4	0

Trace form

40 * q + 1212040 * q^4 - 73477608 * q^6 + 4862757768 * q^9 + 70993722608 * q^10 + 230311800264 * q^12 + 532697931824 * q^13 - 3296861950688 * q^16 - 38138435545488 * q^18 + 6345498814320 * q^21 + 345245332418448 * q^22 + 162733136355360 * q^24 - 2870634573953208 * q^25 + 3010485857135664 * q^28 + 5225832293639088 * q^30 - 7282205643351936 * q^33 - 11653770049992256 * q^34 - 18580578856893912 * q^36 - 42230886115147792 * q^37 - 89660451263290816 * q^40 - 196777060056297264 * q^42 + 490656937607621376 * q^45 - 24590270471085024 * q^46 - 1070121602451491040 * q^48 - 1521600851011396808 * q^49 + 1474695233111072240 * q^52 - 107978656785090264 * q^54 - 410005705945522032 * q^57 + 9260173307858336144 * q^58 + 6491621502020133696 * q^60 - 5700218795673195856 * q^61 - 2949437838551773568 * q^64 + 1836224451373338192 * q^66 + 25444406037298107648 * q^69 - 24886444039106795232 * q^70 - 27969226308253542336 * q^72 + 101891967257574779024 * q^73 + 22386121373924673552 * q^76 + 76385487692811283152 * q^78 - 476218176140556806040 * q^81 + 1864686882869863520 * q^82 + 311685180307346738352 * q^84 - 605170615993311678464 * q^85 + 15063645347500158144 * q^88 - 159737520743388593232 * q^90 + 682248293569820157360 * q^93 + 242051617770611035200 * q^94 - 1187951481218430818688 * q^96 + 196191301644672463568 * q^97

Decomposition of \(S_{22}^{\mathrm{new}}(12, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.22.b.a	$12$	$22$	12.b	12.b	$2$	$40$	$40$	$33.537$		None		✓	✓	✓	12.22.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$