Space of modular forms of level 18, weight 9, and Character 18.b

• Label: 18.9.b
• Level: $18$
• Weight: $9$
• Character orbit: 18.b
• Rep. character: $\chi_{18}(17,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $27$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	18.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(27\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(18, [\chi])\).

	Total	New	Old
Modular forms	28	4	24
Cusp forms	20	4	16
Eisenstein series	8	0	8

Trace form

4 * q - 512 * q^4 - 3760 * q^7 + 15360 * q^10 + 8960 * q^13 + 65536 * q^16 - 559936 * q^19 + 768000 * q^22 - 210500 * q^25 + 481280 * q^28 - 174064 * q^31 + 350208 * q^34 - 5020840 * q^37 - 1966080 * q^40 + 17916320 * q^43 - 12601344 * q^46 + 7349052 * q^49 - 1146880 * q^52 - 15691680 * q^55 + 814080 * q^58 - 6210520 * q^61 - 8388608 * q^64 + 49105760 * q^67 + 52746240 * q^70 - 121101760 * q^73 + 71671808 * q^76 + 11399024 * q^79 + 16005120 * q^82 - 245390040 * q^85 - 98304000 * q^88 + 448433152 * q^91 - 9922560 * q^94 - 62327680 * q^97

Decomposition of \(S_{9}^{\mathrm{new}}(18, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.9.b.a	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	\(\Q(\sqrt{-2}) \)	None		✓			18.9.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-7064\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+8\beta q^{2}-2^{7}q^{4}+165\beta q^{5}-3532q^{7}+\cdots\)
18.9.b.b	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	\(\Q(\sqrt{-2}) \)	None		✓			18.9.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(3304\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+8\beta q^{2}-2^{7}q^{4}-645\beta q^{5}+1652q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

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