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

• Label: 684.2.bb
• Level: $684$
• Weight: $2$
• Character orbit: 684.bb
• Rep. character: $\chi_{684}(293,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

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 + q^7 - 2 * q^9 + 3 * q^11 - 3 * q^15 + 3 * q^17 - q^19 + 20 * q^25 - 9 * q^27 - 9 * q^29 + 6 * q^31 + 27 * q^33 - 9 * q^39 - 3 * q^41 + 8 * q^43 - 4 * q^45 + 12 * q^47 - 21 * q^49 + 9 * q^51 + 12 * q^53 - 18 * q^57 + 36 * q^59 + 7 * q^61 + 14 * q^63 + 6 * q^65 - 42 * q^69 - 9 * q^71 - 4 * q^73 - 6 * q^75 - 48 * q^77 - 50 * q^81 - 3 * q^83 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 24 * q^93 - 24 * q^95 - 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.bb.a	$684$	$2$	684.bb	171.t	$6$	$2$	$1$	$5.462$	\(\Q(\sqrt{-3}) \)	None		✓			684.2.n.a	$2$	$1$	\(0\)	\(-3\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
684.2.bb.b	$684$	$2$	684.bb	171.t	$6$	$38$	$19$	$5.462$		None		✓	✓		684.2.n.b	$2$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{6}]$

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

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