Space of modular forms of level 889, weight 2, and Character 889.v

• Label: 889.2.v
• Level: $889$
• Weight: $2$
• Character orbit: 889.v
• Rep. character: $\chi_{889}(37,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $498$
• Newform subspaces: $1$
• Sturm bound: $170$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.v (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 889 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(170\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(889, [\chi])\).

	Total	New	Old
Modular forms	522	522	0
Cusp forms	498	498	0
Eisenstein series	24	24	0

Trace form

\( 498 q - 6 q^{2} - 3 q^{3} - 246 q^{4} + 15 q^{5} + 6 q^{8} - 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(889, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
889.2.v.a	$889$	$2$	889.v	889.v	$9$	$498$	$83$	$7.099$		None		$2$	$0$	\(-6\)	\(-3\)	\(15\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$