Space of modular forms of level 684, weight 2, and Character 684.ch

• Label: 684.2.ch
• Level: $684$
• Weight: $2$
• Character orbit: 684.ch
• Rep. character: $\chi_{684}(47,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $696$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.ch (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 684 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(684, [\chi])\).

	Total	New	Old
Modular forms	744	744	0
Cusp forms	696	696	0
Eisenstein series	48	48	0

Trace form

696 * q - 9 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^6 - 12 * q^10 - 3 * q^12 - 6 * q^13 - 9 * q^14 - 3 * q^16 - 12 * q^18 - 18 * q^20 - 30 * q^21 - 27 * q^22 - 18 * q^24 - 6 * q^25 - 72 * q^26 - 18 * q^29 + 63 * q^30 - 9 * q^32 - 60 * q^33 - 39 * q^34 - 66 * q^36 - 48 * q^37 - 9 * q^38 - 33 * q^40 - 18 * q^41 - 27 * q^42 - 135 * q^44 - 6 * q^45 - 6 * q^46 - 18 * q^48 + 282 * q^49 - 3 * q^52 + 15 * q^54 + 45 * q^56 - 12 * q^57 - 6 * q^58 - 9 * q^60 - 6 * q^61 + 18 * q^62 + 12 * q^64 + 18 * q^66 - 9 * q^68 - 6 * q^69 - 45 * q^70 + 12 * q^72 + 12 * q^73 + 99 * q^74 - 3 * q^76 - 36 * q^77 + 69 * q^78 - 72 * q^81 - 12 * q^82 - 45 * q^84 - 6 * q^85 - 171 * q^86 - 45 * q^88 + 27 * q^90 - 9 * q^92 + 24 * q^93 - 6 * q^94 - 87 * q^96 - 42 * q^97 - 45 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(684, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
684.2.ch.a	$684$	$2$	684.ch	684.bh	$18$	$696$	$116$	$5.462$		None		✓	✓	✓	684.2.bs.a	$4$	$0$	\(-9\)	\(0\)	\(-18\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$