Space of modular forms of level 18, weight 3, and Character 18.d

• Label: 18.3.d
• Level: $18$
• Weight: $3$
• Character orbit: 18.d
• Rep. character: $\chi_{18}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(18, [\chi])\).

	Total	New	Old
Modular forms	16	4	12
Cusp forms	8	4	4
Eisenstein series	8	0	8

Trace form

4 * q + 4 * q^4 - 18 * q^5 - 12 * q^6 + 2 * q^7 + 12 * q^9 + 18 * q^11 + 12 * q^12 - 10 * q^13 + 36 * q^14 + 18 * q^15 - 8 * q^16 - 24 * q^18 - 40 * q^19 - 36 * q^20 - 42 * q^21 - 12 * q^22 + 18 * q^23 + 4 * q^25 + 8 * q^28 + 18 * q^29 + 72 * q^30 + 38 * q^31 + 54 * q^33 + 24 * q^34 + 12 * q^36 + 128 * q^37 - 72 * q^38 - 102 * q^39 - 126 * q^41 - 48 * q^42 - 46 * q^43 - 54 * q^45 - 24 * q^46 + 54 * q^47 + 24 * q^48 - 12 * q^49 - 72 * q^51 + 20 * q^52 + 36 * q^54 - 108 * q^55 + 72 * q^56 + 144 * q^57 + 24 * q^58 + 126 * q^59 - 36 * q^60 + 62 * q^61 + 222 * q^63 - 32 * q^64 + 90 * q^65 - 72 * q^66 - 106 * q^67 + 72 * q^68 + 18 * q^69 - 108 * q^70 - 96 * q^72 - 208 * q^73 + 72 * q^74 - 12 * q^75 - 40 * q^76 - 90 * q^77 + 144 * q^78 + 14 * q^79 - 252 * q^81 + 144 * q^82 - 378 * q^83 - 144 * q^84 + 108 * q^85 - 108 * q^86 - 54 * q^87 + 24 * q^88 + 412 * q^91 + 36 * q^92 + 222 * q^93 + 84 * q^94 + 180 * q^95 + 48 * q^96 + 14 * q^97 + 126 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(18, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.3.d.a	$18$	$3$	18.d	9.d	$6$	$4$	$2$	$0.490$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓	✓	✓	18.3.d.a	$2$	$0$	\(0\)	\(0\)	\(-18\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

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