Space of modular forms of level 840, weight 2, and Character 840.db

• Label: 840.2.db
• Level: $840$
• Weight: $2$
• Character orbit: 840.db
• Rep. character: $\chi_{840}(109,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $192$
• Newform subspaces: $6$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.db (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(840, [\chi])\).

	Total	New	Old
Modular forms	400	192	208
Cusp forms	368	192	176
Eisenstein series	32	0	32

Trace form

192 * q - 96 * q^9 - 6 * q^10 - 4 * q^14 - 8 * q^16 + 24 * q^20 + 16 * q^26 + 8 * q^30 + 48 * q^31 - 48 * q^34 + 26 * q^40 - 32 * q^44 + 44 * q^46 + 48 * q^50 - 52 * q^56 + 2 * q^60 - 96 * q^64 + 12 * q^66 - 2 * q^70 - 64 * q^71 + 68 * q^74 - 24 * q^76 + 20 * q^80 - 96 * q^81 - 44 * q^84 + 32 * q^86 + 12 * q^90 + 12 * q^94 + 24 * q^95 - 20 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(840, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
840.2.db.a	$840$	$2$	840.db	280.af	$6$	$4$	$2$	$6.707$	\(\Q(\zeta_{12})\)	None		✓			840.2.db.a	$4$	$0$	\(-2\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\)
840.2.db.b	$840$	$2$	840.db	280.af	$6$	$4$	$2$	$6.707$	\(\Q(\zeta_{12})\)	None		✓			840.2.db.b	$4$	$0$	\(-2\)	\(2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
840.2.db.c	$840$	$2$	840.db	280.af	$6$	$4$	$2$	$6.707$	\(\Q(\zeta_{12})\)	None		✓			840.2.db.b	$4$	$0$	\(2\)	\(-2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\)
840.2.db.d	$840$	$2$	840.db	280.af	$6$	$4$	$2$	$6.707$	\(\Q(\zeta_{12})\)	None		✓			840.2.db.a	$4$	$0$	\(2\)	\(2\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
840.2.db.e	$840$	$2$	840.db	280.af	$6$	$88$	$44$	$6.707$		None		✓			840.2.db.e	$4$	$0$	\(0\)	\(-44\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
840.2.db.f	$840$	$2$	840.db	280.af	$6$	$88$	$44$	$6.707$		None		✓			840.2.db.e	$4$	$0$	\(0\)	\(44\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)