Space of modular forms of level 980, weight 2, and Character 980.bs

• Label: 980.2.bs
• Level: $980$
• Weight: $2$
• Character orbit: 980.bs
• Rep. character: $\chi_{980}(23,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $3936$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.bs (of order \(84\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 980 \)
Character field:			\(\Q(\zeta_{84})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(336\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(980, [\chi])\).

	Total	New	Old
Modular forms	4128	4128	0
Cusp forms	3936	3936	0
Eisenstein series	192	192	0

Trace form

\( 3936 q - 26 q^{2} - 52 q^{5} - 40 q^{6} - 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(980, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
980.2.bs.a	$980$	$2$	980.bs	980.as	$84$	$3936$	$164$	$7.825$		None		$8$	$0$	\(-26\)	\(0\)	\(-52\)	\(0\)		$\mathrm{SU}(2)[C_{84}]$