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

• Label: 189.3.j
• Level: $189$
• Weight: $3$
• Character orbit: 189.j
• Rep. character: $\chi_{189}(44,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(189, [\chi])\).

	Total	New	Old
Modular forms	108	36	72
Cusp forms	84	28	56
Eisenstein series	24	8	16

Trace form

\( 28 q - 50 q^{4} + 3 q^{5} - 2 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
189.3.j.a	$189$	$3$	189.j	63.j	$6$	$6$	$3$	$5.150$	6.0.63369648.1	None		$2$	$0$	\(0\)	\(0\)	\(15\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{4}-\beta _{5})q^{2}+(-4-\beta _{1})q^{4}+\cdots\)
189.3.j.b	$189$	$3$	189.j	63.j	$6$	$22$	$11$	$5.150$		None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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