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

• Label: 684.2.j
• Level: $684$
• Weight: $2$
• Character orbit: 684.j
• Rep. character: $\chi_{684}(49,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• 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.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{3})\)
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	252	40	212
Cusp forms	228	40	188
Eisenstein series	24	0	24

Trace form

40 * q - 2 * q^3 - q^7 - 2 * q^9 - q^11 + 2 * q^13 + q^15 + 5 * q^17 + q^19 + 6 * q^21 + 8 * q^23 - 20 * q^25 + 7 * q^27 - 9 * q^29 + 2 * q^31 - q^33 - 6 * q^35 + 2 * q^37 + 3 * q^39 - 25 * q^41 - 16 * q^43 + 44 * q^45 - 10 * q^47 - 21 * q^49 + 19 * q^51 - 8 * q^53 - 22 * q^59 - 7 * q^61 + 10 * q^63 - 6 * q^65 + 20 * q^67 + 38 * q^69 - 5 * q^71 - 10 * q^73 - 10 * q^77 + 2 * q^79 + 22 * q^81 + q^83 - 52 * q^87 - 34 * q^89 + 16 * q^91 - 8 * q^93 + 36 * q^95 + 2 * q^97 + 28 * 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.j.a	$684$	$2$	684.j	171.h	$3$	$40$	$20$	$5.462$		None		✓	✓	✓	684.2.j.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-1\)		$\mathrm{SU}(2)[C_{3}]$

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

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