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

• Label: 684.2.bq
• Level: $684$
• Weight: $2$
• Character orbit: 684.bq
• Rep. character: $\chi_{684}(85,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $120$
• 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.bq (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{9})\)
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	756	120	636
Cusp forms	684	120	564
Eisenstein series	72	0	72

Trace form

120 * q - 3 * q^3 - 3 * q^9 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 3 * q^19 - 24 * q^23 + 3 * q^27 - 9 * q^29 - 12 * q^33 + 18 * q^35 - 30 * q^39 + 3 * q^41 + 12 * q^43 + 9 * q^45 + 18 * q^47 + 120 * q^49 + 3 * q^51 + 24 * q^53 - 12 * q^57 - 42 * q^59 - 42 * q^61 + 48 * q^63 - 78 * q^65 + 30 * q^67 - 9 * q^69 + 42 * q^71 + 3 * q^73 + 3 * q^79 + 21 * q^81 + 24 * q^83 - 12 * q^87 + 18 * q^89 + 12 * q^91 + 24 * q^93 - 60 * q^95 + 9 * q^97 + 42 * q^99

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.bq.a	$684$	$2$	684.bq	171.w	$9$	$120$	$20$	$5.462$		None		✓	✓	✓	684.2.bp.a	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(684, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)