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

• Label: 189.3.d
• Level: $189$
• Weight: $3$
• Character orbit: 189.d
• Rep. character: $\chi_{189}(55,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $5$
• Sturm bound: $72$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
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	22	32
Cusp forms	42	22	20
Eisenstein series	12	0	12

Trace form

22 * q + 48 * q^4 - 5 * q^7 + 128 * q^16 - 44 * q^22 - 122 * q^25 + 6 * q^28 - 130 * q^37 - 196 * q^43 + 100 * q^46 - 131 * q^49 - 284 * q^58 + 280 * q^64 + 218 * q^67 + 150 * q^70 + 890 * q^79 + 468 * q^85 - 652 * q^88 + 345 * q^91

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.d.a	$189$	$3$	189.d	7.b	$2$	$2$	$2$	$5.150$	\(\Q(\sqrt{-3}) \)	None		✓			189.3.d.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-3q^{4}+(1-2\zeta_{6})q^{5}+(-7+7\zeta_{6})q^{7}+\cdots\)
189.3.d.b	$189$	$3$	189.d	7.b	$2$	$2$	$2$	$5.150$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			189.3.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(13\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q-4 q^{4}+(\beta+6)q^{7}+(10\beta-5)q^{13}+\cdots\)
189.3.d.c	$189$	$3$	189.d	7.b	$2$	$2$	$2$	$5.150$	\(\Q(\sqrt{-3}) \)	None		✓			189.3.d.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-3q^{4}+(1-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots\)
189.3.d.d	$189$	$3$	189.d	7.b	$2$	$8$	$8$	$5.150$	8.0.\(\cdots\).6	None		✓			189.3.d.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(3+\beta _{5})q^{4}-\beta _{3}q^{5}+(-2+\cdots)q^{7}+\cdots\)
189.3.d.e	$189$	$3$	189.d	7.b	$2$	$8$	$8$	$5.150$	8.0.\(\cdots\).14	None		✓			189.3.d.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(5-\beta _{1})q^{4}+\beta _{2}q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(189, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)