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

• Label: 189.2.f
• Level: $189$
• Weight: $2$
• Character orbit: 189.f
• Rep. character: $\chi_{189}(64,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(2\)
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	12	48
Cusp forms	36	12	24
Eisenstein series	24	0	24

Trace form

12 * q + 2 * q^2 - 6 * q^4 - 2 * q^5 + 4 * q^11 + 4 * q^14 - 6 * q^16 + 12 * q^17 - 12 * q^19 - 22 * q^20 + 6 * q^22 + 12 * q^23 + 8 * q^26 + 10 * q^29 + 6 * q^31 - 8 * q^32 - 6 * q^34 - 16 * q^35 - 12 * q^37 + 14 * q^38 - 12 * q^40 - 22 * q^41 + 6 * q^43 - 76 * q^44 + 24 * q^46 - 6 * q^47 - 6 * q^49 + 4 * q^50 + 18 * q^52 + 24 * q^53 - 12 * q^55 + 12 * q^56 + 18 * q^58 - 12 * q^59 + 96 * q^62 + 10 * q^65 + 12 * q^67 + 12 * q^68 - 36 * q^71 - 36 * q^73 - 24 * q^74 + 6 * q^76 + 8 * q^77 + 6 * q^79 + 8 * q^80 - 30 * q^83 - 18 * q^85 + 40 * q^86 - 6 * q^88 - 20 * q^89 - 12 * q^91 + 18 * q^92 - 6 * q^94 + 4 * q^95 - 4 * 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.f.a	$189$	$2$	189.f	9.c	$3$	$6$	$3$	$1.509$	6.0.309123.1	None					63.2.f.b	$2$	$0$	\(-1\)	\(0\)	\(-5\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
189.2.f.b	$189$	$2$	189.f	9.c	$3$	$6$	$3$	$1.509$	\(\Q(\zeta_{18})\)	None					63.2.f.a	$2$	$0$	\(3\)	\(0\)	\(3\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{5}-\beta_{4}-\beta_{3}+\beta_1)q^{2}+(2\beta_{5}-\beta_{3}+\beta_{2}+\cdots-1)q^{4}+\cdots\)

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

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