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

• Label: 840.2.bf
• Level: $840$
• Weight: $2$
• Character orbit: 840.bf
• Rep. character: $\chi_{840}(461,\cdot)$
• Character field: $\Q$
• Dimension: $128$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bf (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 168 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	200	128	72
Cusp forms	184	128	56
Eisenstein series	16	0	16

Trace form

128 * q - 16 * q^16 - 20 * q^18 + 40 * q^22 - 128 * q^25 - 12 * q^28 + 40 * q^36 - 12 * q^42 - 16 * q^46 - 16 * q^49 + 16 * q^58 - 28 * q^60 + 40 * q^63 + 48 * q^64 + 12 * q^70 - 16 * q^72 - 68 * q^78 - 64 * q^79 - 16 * q^81 - 64 * q^84 - 64 * q^88

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.bf.a	$840$	$2$	840.bf	168.i	$2$	$8$	$8$	$6.707$	\(\Q(\zeta_{24})\)	None		✓			840.2.bf.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{2}+(-\beta_{6}+\beta_1)q^{3}-2 q^{4}+\cdots\)
840.2.bf.b	$840$	$2$	840.bf	168.i	$2$	$120$	$120$	$6.707$		None		✓	✓		840.2.bf.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)