Space of modular forms of level 680, weight 2, and Character 680.br

• Label: 680.2.br
• Level: $680$
• Weight: $2$
• Character orbit: 680.br
• Rep. character: $\chi_{680}(189,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $416$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.br (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 680 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(680, [\chi])\).

	Total	New	Old
Modular forms	448	448	0
Cusp forms	416	416	0
Eisenstein series	32	32	0

Trace form

416 * q - 16 * q^6 - 16 * q^9 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 16 * q^16 - 20 * q^20 + 24 * q^26 - 16 * q^31 - 40 * q^34 - 8 * q^36 + 32 * q^39 + 56 * q^40 - 32 * q^41 - 24 * q^44 + 32 * q^46 - 16 * q^49 - 48 * q^50 - 64 * q^54 - 8 * q^56 - 40 * q^60 + 72 * q^65 - 112 * q^66 - 24 * q^70 + 48 * q^71 - 8 * q^74 - 40 * q^76 - 16 * q^79 - 56 * q^80 - 32 * q^84 + 96 * q^86 - 148 * q^90 + 40 * q^94 - 8 * q^95 - 160 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(680, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
680.2.br.a	$680$	$2$	680.br	680.ar	$8$	$416$	$104$	$5.430$		None		✓	✓	✓	680.2.br.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$