Space of modular forms of level 18, weight 6, and Character 18.c

• Label: 18.6.c
• Level: $18$
• Weight: $6$
• Character orbit: 18.c
• Rep. character: $\chi_{18}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(18\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(18, [\chi])\).

	Total	New	Old
Modular forms	34	10	24
Cusp forms	26	10	16
Eisenstein series	8	0	8

Trace form

10 * q - 4 * q^2 + 9 * q^3 - 80 * q^4 - 108 * q^5 - 84 * q^6 - 58 * q^7 + 128 * q^8 + 579 * q^9 - 393 * q^11 - 384 * q^12 + 362 * q^13 - 824 * q^14 + 2664 * q^15 - 1280 * q^16 + 3882 * q^17 + 2568 * q^18 - 1018 * q^19 - 1728 * q^20 - 11310 * q^21 - 948 * q^22 - 8706 * q^23 + 576 * q^24 + 181 * q^25 + 14800 * q^26 + 18144 * q^27 + 1856 * q^28 - 9042 * q^29 - 7488 * q^30 - 3892 * q^31 - 1024 * q^32 - 405 * q^33 - 3828 * q^34 + 432 * q^35 - 7440 * q^36 + 30344 * q^37 - 11084 * q^38 - 30432 * q^39 + 20403 * q^41 + 36960 * q^42 + 1469 * q^43 + 12576 * q^44 + 7884 * q^45 - 18960 * q^46 + 37878 * q^47 + 3840 * q^48 - 22413 * q^49 - 23788 * q^50 - 44379 * q^51 + 5792 * q^52 - 128712 * q^53 - 116604 * q^54 + 56160 * q^55 - 13184 * q^56 + 89667 * q^57 - 5016 * q^58 + 84921 * q^59 + 42624 * q^60 - 72916 * q^61 + 106624 * q^62 + 55788 * q^63 + 40960 * q^64 + 121284 * q^65 + 80064 * q^66 + 3767 * q^67 - 31056 * q^68 - 68292 * q^69 - 9936 * q^70 - 277368 * q^71 - 59712 * q^72 - 110842 * q^73 - 99056 * q^74 - 86403 * q^75 + 8144 * q^76 + 110202 * q^77 + 240840 * q^78 + 74276 * q^79 + 55296 * q^80 + 173007 * q^81 + 82440 * q^82 + 123396 * q^83 - 2016 * q^84 - 23112 * q^85 - 256988 * q^86 - 170046 * q^87 - 15168 * q^88 + 47532 * q^89 - 344736 * q^90 - 202712 * q^91 - 139296 * q^92 - 87780 * q^93 - 48120 * q^94 + 68472 * q^95 + 12288 * q^96 + 15983 * q^97 + 666408 * q^98 + 601794 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(18, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.6.c.a	$18$	$6$	18.c	9.c	$3$	$4$	$2$	$2.887$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			18.6.c.a	$2$	$0$	\(8\)	\(0\)	\(-54\)	\(74\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\beta _{1}q^{2}+(-3+6\beta _{1}+\beta _{3})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
18.6.c.b	$18$	$6$	18.c	9.c	$3$	$6$	$3$	$2.887$	6.0.\(\cdots\).3	None		✓	✓		18.6.c.b	$2$	$0$	\(-12\)	\(9\)	\(-54\)	\(-132\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(18, [\chi])\) into lower level spaces

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