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

• Label: 189.2.c
• Level: $189$
• Weight: $2$
• Character orbit: 189.c
• Rep. character: $\chi_{189}(188,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	30	10	20
Cusp forms	18	10	8
Eisenstein series	12	0	12

Trace form

10 * q - 8 * q^4 - 3 * q^7 - 12 * q^16 - 28 * q^22 + 22 * q^25 + 26 * q^28 - 6 * q^37 + 12 * q^43 - 4 * q^46 - 29 * q^49 + 80 * q^58 + 36 * q^64 - 22 * q^67 - 36 * q^70 - 10 * q^79 - 36 * q^85 + 4 * q^88 + 27 * q^91

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.c.a	$189$	$2$	189.c	21.c	$2$	$2$	$2$	$1.509$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			189.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+2 q^{4}+\beta q^{7}+(-2\beta+1)q^{13}+\cdots\)
189.2.c.b	$189$	$2$	189.c	21.c	$2$	$4$	$4$	$1.509$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None		✓			189.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-3q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
189.2.c.c	$189$	$2$	189.c	21.c	$2$	$4$	$4$	$1.509$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			189.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}-2\beta _{1}q^{8}+\cdots\)

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

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