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

• Label: 840.2.w
• Level: $840$
• Weight: $2$
• Character orbit: 840.w
• Rep. character: $\chi_{840}(139,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $2$
• 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.w (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(17\)

Dimensions

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

	Total	New	Old
Modular forms	200	96	104
Cusp forms	184	96	88
Eisenstein series	16	0	16

Trace form

\( 96 q + 96 q^{9} - 4 q^{14} + 16 q^{16} + 16 q^{30} + 24 q^{35} + 8 q^{44} - 16 q^{46} - 24 q^{50} - 28 q^{56} + 8 q^{60} + 48 q^{64} - 48 q^{70} - 112 q^{74} + 96 q^{81} + 28 q^{84} - 40 q^{86} - 32 q^{91}+O(q^{100}) \)

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.w.a	$840$	$2$	840.w	280.n	$2$	$48$	$48$	$6.707$		None		✓			840.2.w.a	$4$	$0$	\(0\)	\(-48\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
840.2.w.b	$840$	$2$	840.w	280.n	$2$	$48$	$48$	$6.707$		None		✓			840.2.w.a	$4$	$0$	\(0\)	\(48\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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