Space of modular forms of level 9, weight 6, and Character 9.c

• Label: 9.6.c
• Level: $9$
• Weight: $6$
• Character orbit: 9.c
• Rep. character: $\chi_{9}(4,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(9, [\chi])\).

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

Trace form

8 * q + 3 * q^2 - 12 * q^3 - 49 * q^4 + 78 * q^5 + 171 * q^6 + 28 * q^7 - 750 * q^8 - 414 * q^9 + 60 * q^10 + 444 * q^11 + 2724 * q^12 - 182 * q^13 + 1392 * q^14 - 2052 * q^15 - 289 * q^16 - 4356 * q^17 - 8100 * q^18 + 952 * q^19 + 6684 * q^20 + 8670 * q^21 + 1011 * q^22 + 8844 * q^23 + 549 * q^24 - 1654 * q^25 - 24888 * q^26 - 10152 * q^27 - 1604 * q^28 + 12018 * q^29 + 22104 * q^30 + 1132 * q^31 + 8703 * q^32 - 8820 * q^33 + 10125 * q^34 - 16224 * q^35 - 14589 * q^36 - 15176 * q^37 - 11145 * q^38 + 8220 * q^39 - 8736 * q^40 + 1248 * q^41 + 10098 * q^42 - 6092 * q^43 + 49530 * q^44 + 43038 * q^45 + 45960 * q^46 - 60 * q^47 - 57405 * q^48 + 9090 * q^49 - 57057 * q^50 - 9396 * q^51 - 32510 * q^52 + 20952 * q^53 + 8181 * q^54 - 36120 * q^55 - 61170 * q^56 - 104298 * q^57 + 8328 * q^58 + 2076 * q^59 + 88308 * q^60 + 48142 * q^61 + 241764 * q^62 + 133524 * q^63 - 20926 * q^64 - 13146 * q^65 - 100998 * q^66 - 7148 * q^67 - 123129 * q^68 - 125982 * q^69 - 654 * q^70 - 71856 * q^71 + 35451 * q^72 + 122452 * q^73 - 160320 * q^74 - 18732 * q^75 - 49571 * q^76 + 39534 * q^77 + 181422 * q^78 - 59516 * q^79 + 124512 * q^80 + 194562 * q^81 - 233598 * q^82 + 117696 * q^83 + 108354 * q^84 + 28836 * q^85 - 15915 * q^86 - 142956 * q^87 + 104523 * q^88 - 451728 * q^89 - 539892 * q^90 + 111392 * q^91 + 134034 * q^92 + 113898 * q^93 + 169464 * q^94 + 294888 * q^95 + 42768 * q^96 + 33976 * q^97 + 57654 * q^98 + 33696 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.6.c.a	$9$	$6$	9.c	9.c	$3$	$8$	$4$	$1.443$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓	✓	9.6.c.a	$2$	$0$	\(3\)	\(-12\)	\(78\)	\(28\)	$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)