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

• Label: 980.2.bf
• Level: $980$
• Weight: $2$
• Character orbit: 980.bf
• Rep. character: $\chi_{980}(139,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $984$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.bf (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 980 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	1032	1032	0
Cusp forms	984	984	0
Eisenstein series	48	48	0

Trace form

\( 984 q - 10 q^{4} - 14 q^{5} - 14 q^{6} + 136 q^{9} + O(q^{10}) \)

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.bf.a	$980$	$2$	980.bf	980.af	$14$	$24$	$4$	$7.825$		\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{14}]$
980.2.bf.b	$980$	$2$	980.bf	980.af	$14$	$960$	$160$	$7.825$		None		$8$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$