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

• Label: 680.2.cg
• Level: $680$
• Weight: $2$
• Character orbit: 680.cg
• Rep. character: $\chi_{680}(57,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $216$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cg (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	928	216	712
Cusp forms	800	216	584
Eisenstein series	128	0	128

Trace form

\( 216 q + 48 q^{27} + 32 q^{31} - 32 q^{37} + 40 q^{41} + 24 q^{53} + 48 q^{55} - 96 q^{59} - 144 q^{63} - 96 q^{67} - 32 q^{73} + 48 q^{77} + 32 q^{79} - 48 q^{83} + 32 q^{85} - 96 q^{93} + 16 q^{95} + 96 q^{99}+O(q^{100}) \)

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.cg.a	$680$	$2$	680.cg	85.o	$16$	$104$	$13$	$5.430$		None		✓			680.2.cg.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
680.2.cg.b	$680$	$2$	680.cg	85.o	$16$	$112$	$14$	$5.430$		None		✓	✓		680.2.cg.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(680, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(680, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 2}\)