Space of modular forms of level 189, weight 3, and Character 189.b

• Label: 189.3.b
• Level: $189$
• Weight: $3$
• Character orbit: 189.b
• Rep. character: $\chi_{189}(134,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(189, [\chi])\).

	Total	New	Old
Modular forms	54	16	38
Cusp forms	42	16	26
Eisenstein series	12	0	12

Trace form

16 * q - 36 * q^4 - 20 * q^10 + 60 * q^13 + 108 * q^16 - 12 * q^19 - 128 * q^22 - 252 * q^25 + 112 * q^28 + 76 * q^31 + 204 * q^34 - 44 * q^37 + 72 * q^40 - 40 * q^43 - 12 * q^46 + 112 * q^49 - 376 * q^52 - 76 * q^55 - 92 * q^58 + 564 * q^61 - 596 * q^64 + 156 * q^67 - 28 * q^70 + 280 * q^73 + 608 * q^76 - 244 * q^79 + 92 * q^82 - 708 * q^85 + 72 * q^88 + 56 * q^91 - 468 * q^94 - 188 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(189, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
189.3.b.a	$189$	$3$	189.b	3.b	$2$	$4$	$4$	$5.150$	4.0.1166592.2	None		✓			189.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-6+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
189.3.b.b	$189$	$3$	189.b	3.b	$2$	$4$	$4$	$5.150$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		✓			189.3.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{5}+\beta _{2}q^{7}+\cdots\)
189.3.b.c	$189$	$3$	189.b	3.b	$2$	$8$	$8$	$5.150$	8.0.1997017344.2	None		✓	✓		189.3.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-1-\beta _{2}-\beta _{3})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(189, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)