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

• Label: 840.2.br
• Level: $840$
• Weight: $2$
• Character orbit: 840.br
• Rep. character: $\chi_{840}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $144$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.br (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(13\)

Dimensions

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

	Total	New	Old
Modular forms	400	144	256
Cusp forms	368	144	224
Eisenstein series	32	0	32

Trace form

144 * q - 8 * q^6 - 16 * q^10 + 16 * q^12 + 8 * q^16 - 16 * q^17 + 40 * q^20 + 56 * q^22 + 16 * q^25 - 16 * q^30 - 40 * q^32 - 8 * q^36 - 56 * q^38 + 24 * q^40 + 64 * q^43 - 48 * q^46 - 40 * q^50 + 32 * q^51 - 16 * q^52 + 48 * q^56 - 32 * q^58 - 40 * q^62 + 16 * q^65 - 56 * q^68 + 80 * q^73 - 48 * q^76 + 24 * q^78 - 80 * q^80 - 144 * q^81 - 64 * q^82 - 160 * q^83 - 16 * q^86 + 40 * q^88 + 40 * q^92 + 88 * q^96 + 16 * q^97

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.br.a	$840$	$2$	840.br	40.k	$4$	$72$	$36$	$6.707$		None		✓			840.2.br.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
840.2.br.b	$840$	$2$	840.br	40.k	$4$	$72$	$36$	$6.707$		None		✓			840.2.br.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)