Space of modular forms of level 9, weight 3, and Character 9.d

• Label: 9.3.d
• Level: $9$
• Weight: $3$
• Character orbit: 9.d
• Rep. character: $\chi_{9}(2,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(9, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

Trace form

2 * q - 3 * q^2 - 3 * q^3 - q^4 + 6 * q^5 + 9 * q^6 - 2 * q^7 - 9 * q^9 - 12 * q^10 - 3 * q^11 + 6 * q^12 + 4 * q^13 + 6 * q^14 + 11 * q^16 + 22 * q^19 - 6 * q^20 - 6 * q^21 + 3 * q^22 - 48 * q^23 - 45 * q^24 - 13 * q^25 + 54 * q^27 + 4 * q^28 + 78 * q^29 + 18 * q^30 - 32 * q^31 + 27 * q^32 + 9 * q^33 - 27 * q^34 - 9 * q^36 - 68 * q^37 - 33 * q^38 - 24 * q^39 + 30 * q^40 - 21 * q^41 + 61 * q^43 - 54 * q^45 + 96 * q^46 - 84 * q^47 + 33 * q^48 + 45 * q^49 + 39 * q^50 + 81 * q^51 + 4 * q^52 - 81 * q^54 - 12 * q^55 - 30 * q^56 - 33 * q^57 - 78 * q^58 + 87 * q^59 + 18 * q^60 - 56 * q^61 + 36 * q^63 - 142 * q^64 + 24 * q^65 - 18 * q^66 + 31 * q^67 - 27 * q^68 + 12 * q^70 + 135 * q^72 + 130 * q^73 + 102 * q^74 - 39 * q^75 - 11 * q^76 + 6 * q^77 + 36 * q^78 - 38 * q^79 - 81 * q^81 + 42 * q^82 - 84 * q^83 - 6 * q^84 - 54 * q^85 - 183 * q^86 - 234 * q^87 + 15 * q^88 + 54 * q^90 - 16 * q^91 + 48 * q^92 + 192 * q^93 + 84 * q^94 + 66 * q^95 + 115 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.3.d.a	$9$	$3$	9.d	9.d	$6$	$2$	$1$	$0.245$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	9.3.d.a	$2$	$0$	\(-3\)	\(-3\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)