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

• Label: 189.2.g
• Level: $189$
• Weight: $2$
• Character orbit: 189.g
• Rep. character: $\chi_{189}(100,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	60	20	40
Cusp forms	36	12	24
Eisenstein series	24	8	16

Trace form

12 * q - q^2 - 3 * q^4 + 10 * q^5 + 12 * q^8 - 6 * q^10 - 2 * q^11 - 3 * q^13 - 11 * q^14 + 3 * q^16 - 9 * q^17 - 4 * q^20 - 6 * q^22 - 6 * q^25 - 16 * q^26 - 6 * q^28 - 8 * q^29 - 3 * q^31 + 7 * q^32 - 4 * q^35 - 3 * q^37 + 38 * q^38 + 12 * q^40 - 10 * q^41 - 6 * q^43 + 5 * q^44 - 27 * q^47 + 12 * q^49 - 23 * q^50 + 30 * q^52 + 12 * q^53 - 6 * q^55 + 48 * q^56 + 18 * q^58 - 30 * q^59 + 12 * q^62 - 36 * q^64 + 16 * q^65 - 6 * q^67 + 60 * q^68 - 24 * q^70 + 30 * q^71 + 12 * q^73 - 78 * q^74 + 6 * q^76 + 26 * q^77 - 12 * q^79 - 19 * q^80 - 18 * q^83 - 3 * q^85 - 14 * q^86 + 6 * q^88 - 41 * q^89 + 21 * q^91 - 30 * q^92 - 3 * q^94 + 13 * q^95 - 3 * q^97 - 61 * q^98

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.g.a	$189$	$2$	189.g	63.g	$3$	$2$	$1$	$1.509$	\(\Q(\sqrt{-3}) \)	None					63.2.g.a	$2$	$0$	\(1\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.g.b	$189$	$2$	189.g	63.g	$3$	$10$	$5$	$1.509$	10.0.\(\cdots\).1	None			✓		63.2.g.b	$2$	$0$	\(-2\)	\(0\)	\(8\)	\(-1\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(189, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)