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

• Label: 189.2.p
• Level: $189$
• Weight: $2$
• Character orbit: 189.p
• Rep. character: $\chi_{189}(26,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $22$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
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	60	22	38
Cusp forms	36	22	14
Eisenstein series	24	0	24

Trace form

\( 22 q + 12 q^{4} - 5 q^{7} + O(q^{10}) \)

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.p.a	$189$	$2$	189.p	21.g	$6$	$2$	$1$	$1.509$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2+2\zeta_{6})q^{4}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.p.b	$189$	$2$	189.p	21.g	$6$	$4$	$2$	$1.509$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{3})q^{5}+(2+\beta _{2})q^{7}+\cdots\)
189.2.p.c	$189$	$2$	189.p	21.g	$6$	$4$	$2$	$1.509$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(-3+2\beta _{2})q^{7}+\cdots\)
189.2.p.d	$189$	$2$	189.p	21.g	$6$	$12$	$6$	$1.509$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(1-\beta _{3}-\beta _{7}+\beta _{9})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)

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

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