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

• Label: 189.2.e
• Level: $189$
• Weight: $2$
• Character orbit: 189.e
• Rep. character: $\chi_{189}(109,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $22$
• Newform subspaces: $6$
• Sturm bound: $48$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
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	22	38
Cusp forms	36	22	14
Eisenstein series	24	0	24

Trace form

\( 22 q - 12 q^{4} + 9 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
189.2.e.a	$189$	$2$	189.e	7.c	$3$	$2$	$1$	$1.509$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.b	$189$	$2$	189.e	7.c	$3$	$2$	$1$	$1.509$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+(2-2\zeta_{6})q^{4}+(1-3\zeta_{6})q^{7}+2q^{13}+\cdots\)
189.2.e.c	$189$	$2$	189.e	7.c	$3$	$2$	$1$	$1.509$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
189.2.e.d	$189$	$2$	189.e	7.c	$3$	$4$	$2$	$1.509$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}-\beta _{2}q^{5}+\cdots\)
189.2.e.e	$189$	$2$	189.e	7.c	$3$	$6$	$3$	$1.509$	6.0.309123.1	None		$2$	$0$	\(-2\)	\(0\)	\(-1\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
189.2.e.f	$189$	$2$	189.e	7.c	$3$	$6$	$3$	$1.509$	6.0.309123.1	None		$2$	$0$	\(2\)	\(0\)	\(1\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)

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

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