Space of modular forms of level 18, weight 11, and Character 18.b

• Label: 18.11.b
• Level: $18$
• Weight: $11$
• Character orbit: 18.b
• Rep. character: $\chi_{18}(17,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	18.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(18, [\chi])\).

	Total	New	Old
Modular forms	34	2	32
Cusp forms	26	2	24
Eisenstein series	8	0	8

Trace form

2 * q - 1024 * q^4 + 41272 * q^7 + 92352 * q^10 + 863056 * q^13 + 524288 * q^16 + 7511008 * q^19 - 1567488 * q^22 + 11202254 * q^25 - 21131264 * q^28 - 71943272 * q^31 - 109209024 * q^34 + 57867772 * q^37 - 47284224 * q^40 + 345932080 * q^43 + 356199168 * q^46 + 286738494 * q^49 - 441884672 * q^52 + 141367824 * q^55 + 1096058688 * q^58 - 2603985500 * q^61 - 268435456 * q^64 - 3633336944 * q^67 + 1905775872 * q^70 + 3888426208 * q^73 - 3845636096 * q^76 - 4575639512 * q^79 + 4638595008 * q^82 + 9849288852 * q^85 + 802553856 * q^88 + 17810023616 * q^91 - 7577667840 * q^94 + 6795139552 * q^97

Decomposition of \(S_{11}^{\mathrm{new}}(18, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.11.b.a	$18$	$11$	18.b	3.b	$2$	$2$	$2$	$11.436$	\(\Q(\sqrt{-2}) \)	None		✓	✓	✓	18.11.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(41272\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}\beta q^{2}-2^{9}q^{4}-1443\beta q^{5}+20636q^{7}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(18, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)