Space of modular forms of level 189, weight 2, and Character 189.v

• Label: 189.2.v
• Level: $189$
• Weight: $2$
• Character orbit: 189.v
• Rep. character: $\chi_{189}(22,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $108$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.v (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(189, [\chi])\).

	Total	New	Old
Modular forms	156	108	48
Cusp forms	132	108	24
Eisenstein series	24	0	24

Trace form

108 * q - 6 * q^5 - 18 * q^8 - 6 * q^9 - 12 * q^11 - 36 * q^12 - 18 * q^15 - 30 * q^18 + 6 * q^20 - 18 * q^22 - 12 * q^23 + 72 * q^24 - 18 * q^25 - 36 * q^26 + 6 * q^27 + 36 * q^29 - 48 * q^30 - 18 * q^31 + 42 * q^32 - 48 * q^33 - 18 * q^34 - 24 * q^35 + 48 * q^36 - 24 * q^38 - 24 * q^39 - 66 * q^41 - 30 * q^42 - 18 * q^43 - 12 * q^44 + 42 * q^45 - 54 * q^47 - 78 * q^48 + 144 * q^50 + 60 * q^51 - 54 * q^52 + 72 * q^53 - 36 * q^54 + 42 * q^57 - 54 * q^58 + 42 * q^59 + 126 * q^60 - 54 * q^64 + 48 * q^65 + 6 * q^66 + 18 * q^67 + 6 * q^68 + 48 * q^69 - 72 * q^71 + 30 * q^72 + 12 * q^74 - 24 * q^75 + 108 * q^76 - 120 * q^78 + 36 * q^79 - 180 * q^80 - 42 * q^81 - 30 * q^83 - 24 * q^84 + 36 * q^85 - 24 * q^86 - 96 * q^87 + 108 * q^88 + 48 * q^89 + 6 * q^90 - 42 * q^92 + 114 * q^93 - 54 * q^94 - 36 * q^95 + 144 * q^96 - 18 * q^97 - 6 * q^98 - 66 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
189.2.v.a	$189$	$2$	189.v	27.e	$9$	$54$	$9$	$1.509$		None		✓			189.2.v.a	$2$	$0$	\(0\)	\(-3\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
189.2.v.b	$189$	$2$	189.v	27.e	$9$	$54$	$9$	$1.509$		None		✓			189.2.v.b	$2$	$0$	\(0\)	\(3\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(189, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)