Space of modular forms of level 189, weight 4, and Character 189.e

• Label: 189.4.e
• Level: $189$
• Weight: $4$
• Character orbit: 189.e
• Rep. character: $\chi_{189}(109,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $8$
• Sturm bound: $96$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(96\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(189, [\chi])\).

	Total	New	Old
Modular forms	156	64	92
Cusp forms	132	64	68
Eisenstein series	24	0	24

Trace form

\( 64 q - 128 q^{4} - 20 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(189, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
189.4.e.a	$189$	$4$	189.e	7.c	$3$	$2$	$1$	$11.151$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-3\)	\(0\)	\(6\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+6\zeta_{6}q^{5}+\cdots\)
189.4.e.b	$189$	$4$	189.e	7.c	$3$	$2$	$1$	$11.151$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+(8-8\zeta_{6})q^{4}+(19-18\zeta_{6})q^{7}-19q^{13}+\cdots\)
189.4.e.c	$189$	$4$	189.e	7.c	$3$	$2$	$1$	$11.151$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+(8-8\zeta_{6})q^{4}+(1+18\zeta_{6})q^{7}+89q^{13}+\cdots\)
189.4.e.d	$189$	$4$	189.e	7.c	$3$	$2$	$1$	$11.151$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(0\)	\(-6\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-6\zeta_{6}q^{5}+\cdots\)
189.4.e.e	$189$	$4$	189.e	7.c	$3$	$12$	$6$	$11.151$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-26\)	$2^{4}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{3}q^{2}+(-6-6\beta _{2}+\beta _{4}+\beta _{7}-\beta _{11})q^{4}+\cdots\)
189.4.e.f	$189$	$4$	189.e	7.c	$3$	$14$	$7$	$11.151$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-1\)	\(0\)	\(1\)	\(20\)	$3^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-4\beta _{5}+\beta _{9})q^{4}+\cdots\)
189.4.e.g	$189$	$4$	189.e	7.c	$3$	$14$	$7$	$11.151$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(20\)	$3^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-4\beta _{5}+\beta _{9})q^{4}+\cdots\)
189.4.e.h	$189$	$4$	189.e	7.c	$3$	$16$	$8$	$11.151$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-60\)	$2^{10}\cdot 3^{9}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{5})q^{2}+(6\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

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