Space of modular forms of level 18, weight 5, and Character 18.d

• Label: 18.5.d
• Level: $18$
• Weight: $5$
• Character orbit: 18.d
• Rep. character: $\chi_{18}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(18, [\chi])\).

	Total	New	Old
Modular forms	28	8	20
Cusp forms	20	8	12
Eisenstein series	8	0	8

Trace form

8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9 - 720 * q^11 - 144 * q^12 + 10 * q^13 + 288 * q^14 + 1134 * q^15 - 256 * q^16 - 384 * q^18 + 100 * q^19 + 144 * q^20 + 438 * q^21 + 336 * q^22 + 1278 * q^23 + 384 * q^24 + 794 * q^25 - 1296 * q^27 - 416 * q^28 - 1854 * q^29 - 3456 * q^30 - 1478 * q^31 - 3384 * q^33 - 96 * q^34 + 1056 * q^36 - 32 * q^37 + 6768 * q^38 + 5274 * q^39 - 36 * q^41 + 2592 * q^42 - 68 * q^43 + 3402 * q^45 + 2112 * q^46 + 2214 * q^47 - 1536 * q^48 + 2442 * q^49 - 15552 * q^50 - 12006 * q^51 - 80 * q^52 + 7056 * q^54 - 3996 * q^55 + 2304 * q^56 + 10902 * q^57 - 2400 * q^58 + 9108 * q^59 + 6480 * q^60 - 4478 * q^61 - 6654 * q^63 - 4096 * q^64 - 22554 * q^65 - 19872 * q^66 + 7504 * q^67 - 11088 * q^68 - 5994 * q^69 + 6048 * q^70 + 5376 * q^72 + 20716 * q^73 + 15264 * q^74 + 16590 * q^75 + 400 * q^76 + 34434 * q^77 + 24096 * q^78 - 6050 * q^79 - 21150 * q^81 + 1152 * q^82 - 3834 * q^83 - 9600 * q^84 - 16092 * q^85 - 12528 * q^86 + 10170 * q^87 - 2688 * q^88 + 2592 * q^90 - 45868 * q^91 + 10224 * q^92 - 10926 * q^93 + 672 * q^94 + 20880 * q^95 + 31336 * q^97 - 22338 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(18, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.5.d.a	$18$	$5$	18.d	9.d	$6$	$8$	$4$	$1.861$	8.0.\(\cdots\).4	None		✓	✓	✓	18.5.d.a	$2$	$0$	\(0\)	\(6\)	\(18\)	\(-26\)	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(2+\beta _{1}-3\beta _{2}-\beta _{5})q^{3}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(18, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)