Space of modular forms of level 18, weight 8, and Character 18.c

• Label: 18.8.c
• Level: $18$
• Weight: $8$
• Character orbit: 18.c
• Rep. character: $\chi_{18}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(18, [\chi])\).

	Total	New	Old
Modular forms	46	14	32
Cusp forms	38	14	24
Eisenstein series	8	0	8

Trace form

14 * q + 8 * q^2 - 39 * q^3 - 448 * q^4 + 108 * q^5 + 1272 * q^6 + 166 * q^7 - 1024 * q^8 + 57 * q^9 + 8751 * q^11 + 3694 * q^13 + 2032 * q^14 + 18360 * q^15 - 28672 * q^16 - 81762 * q^17 - 3408 * q^18 - 46778 * q^19 + 6912 * q^20 + 277854 * q^21 + 35256 * q^22 - 41682 * q^23 - 7680 * q^24 - 181369 * q^25 - 263840 * q^26 - 200880 * q^27 - 21248 * q^28 + 522930 * q^29 + 456192 * q^30 + 144892 * q^31 + 32768 * q^32 + 517473 * q^33 - 88728 * q^34 - 2580768 * q^35 - 335040 * q^36 - 278696 * q^37 + 912808 * q^38 + 2453976 * q^39 + 1697697 * q^41 - 403200 * q^42 - 384347 * q^43 - 1120128 * q^44 - 3451572 * q^45 + 602016 * q^46 + 987342 * q^47 + 159744 * q^48 - 790863 * q^49 + 1324184 * q^50 - 1970667 * q^51 + 236416 * q^52 + 66552 * q^53 - 581976 * q^54 + 1521936 * q^55 + 130048 * q^56 + 1182801 * q^57 - 346128 * q^58 + 2885649 * q^59 - 2059776 * q^60 + 4157908 * q^61 - 2344256 * q^62 - 4404036 * q^63 + 3670016 * q^64 - 2113236 * q^65 - 4022784 * q^66 - 6528545 * q^67 + 2616384 * q^68 + 9507348 * q^69 - 1620864 * q^70 + 11239752 * q^71 + 2320896 * q^72 + 13333186 * q^73 + 4648288 * q^74 - 22090299 * q^75 + 1496896 * q^76 - 12102258 * q^77 - 6015408 * q^78 - 10232468 * q^79 - 884736 * q^80 + 11656701 * q^81 - 7620624 * q^82 - 22434636 * q^83 - 8969856 * q^84 + 2938248 * q^85 - 1724696 * q^86 + 25741386 * q^87 + 2256384 * q^88 + 49866420 * q^89 + 46925568 * q^90 - 10938616 * q^91 - 2667648 * q^92 - 17811900 * q^93 - 5792592 * q^94 - 48359376 * q^95 - 4718592 * q^96 - 21483755 * q^97 - 28083408 * q^98 + 15105546 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(18, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.8.c.a	$18$	$8$	18.c	9.c	$3$	$6$	$3$	$5.623$	6.0.\(\cdots\).1	None		✓			18.8.c.a	$2$	$0$	\(-24\)	\(-27\)	\(54\)	\(210\)	$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q-8\beta _{1}q^{2}+(-14+19\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
18.8.c.b	$18$	$8$	18.c	9.c	$3$	$8$	$4$	$5.623$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		18.8.c.b	$2$	$0$	\(32\)	\(-12\)	\(54\)	\(-44\)	$2^{4}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(8-8\beta _{1})q^{2}+(-7+11\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(18, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)