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

• Label: 18.11.d
• Level: $18$
• Weight: $11$
• Character orbit: 18.d
• Rep. character: $\chi_{18}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• 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.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
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	64	20	44
Cusp forms	56	20	36
Eisenstein series	8	0	8

Trace form

20 * q - 84 * q^3 + 5120 * q^4 - 9918 * q^5 + 12864 * q^6 + 12238 * q^7 + 79248 * q^9 - 327582 * q^11 + 9216 * q^12 - 280550 * q^13 + 175680 * q^14 - 2685042 * q^15 - 2621440 * q^16 + 3925632 * q^18 - 2966240 * q^19 - 5078016 * q^20 - 11895726 * q^21 + 3473472 * q^22 + 10446606 * q^23 + 2752512 * q^24 + 9609944 * q^25 + 2340576 * q^27 + 12531712 * q^28 + 32440806 * q^29 + 37556352 * q^30 - 40069958 * q^31 - 35367930 * q^33 + 30746496 * q^34 - 32695296 * q^36 - 127390400 * q^37 + 370567296 * q^38 + 153125550 * q^39 - 245419398 * q^41 - 344505600 * q^42 - 86593094 * q^43 + 394622766 * q^45 - 366913920 * q^46 + 1094979330 * q^47 + 26738688 * q^48 - 598072056 * q^49 - 456606720 * q^50 - 2329772724 * q^51 + 143641600 * q^52 + 1623484224 * q^54 - 262510308 * q^55 + 89948160 * q^56 + 311135772 * q^57 + 249515904 * q^58 - 2125085130 * q^59 - 2357738496 * q^60 + 312021586 * q^61 + 5475513858 * q^63 - 2684354560 * q^64 + 13076821350 * q^65 + 2185467264 * q^66 - 1200881210 * q^67 - 2610487296 * q^68 - 11765922354 * q^69 + 1138681152 * q^70 + 1554382848 * q^72 + 5213376328 * q^73 + 9118122624 * q^74 + 13244996208 * q^75 - 759357440 * q^76 - 33678720774 * q^77 - 14572366080 * q^78 - 3396212726 * q^79 + 14546869128 * q^81 + 3667214592 * q^82 + 16739541378 * q^83 + 1518514176 * q^84 + 7141101588 * q^85 - 11512304064 * q^86 - 32778228834 * q^87 - 1778417664 * q^88 + 16769410560 * q^90 - 10426841884 * q^91 + 5348662272 * q^92 - 4843832814 * q^93 + 6416128320 * q^94 - 26494427340 * q^95 - 1962934272 * q^96 + 6721893598 * q^97 + 41160676842 * q^99

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.d.a	$18$	$11$	18.d	9.d	$6$	$20$	$10$	$11.436$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	18.11.d.a	$2$	$0$	\(0\)	\(-84\)	\(-9918\)	\(12238\)	$2^{46}\cdot 3^{37}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-2-4\beta _{1}+\beta _{3}-\beta _{4})q^{3}+\cdots\)

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

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