Space of modular forms of level 490, weight 2, and Character 490.w

• Label: 490.2.w
• Level: $490$
• Weight: $2$
• Character orbit: 490.w
• Rep. character: $\chi_{490}(3,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $672$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.w (of order \(84\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 245 \)
Character field:			\(\Q(\zeta_{84})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(490, [\chi])\).

	Total	New	Old
Modular forms	2112	672	1440
Cusp forms	1920	672	1248
Eisenstein series	192	0	192

Trace form

\( 672 q + 12 q^{5} - 28 q^{6} - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(490, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
490.2.w.a	$490$	$2$	490.w	245.x	$84$	$672$	$28$	$3.913$		None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(-8\)		$\mathrm{SU}(2)[C_{84}]$

Decomposition of \(S_{2}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(490, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)