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

• Label: 840.2.cl
• Level: $840$
• Weight: $2$
• Character orbit: 840.cl
• Rep. character: $\chi_{840}(451,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $128$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cl (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(4\)
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	128	272
Cusp forms	368	128	240
Eisenstein series	32	0	32

Trace form

128 * q + 4 * q^2 + 4 * q^4 - 8 * q^8 + 64 * q^9 - 16 * q^11 + 16 * q^14 - 4 * q^16 - 4 * q^18 + 40 * q^22 + 36 * q^24 - 64 * q^25 + 60 * q^26 + 8 * q^28 + 24 * q^32 + 8 * q^36 + 12 * q^42 + 32 * q^43 - 16 * q^44 - 20 * q^46 - 16 * q^49 - 8 * q^50 + 36 * q^52 - 52 * q^56 - 32 * q^57 - 28 * q^58 + 96 * q^59 - 56 * q^64 + 36 * q^66 + 16 * q^67 - 60 * q^68 - 28 * q^70 - 4 * q^72 + 48 * q^73 - 24 * q^78 - 64 * q^81 + 12 * q^82 + 12 * q^84 - 84 * q^86 - 40 * q^88 - 80 * q^91 + 184 * q^92 - 108 * q^94 - 40 * q^98 - 32 * q^99

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.cl.a	$840$	$2$	840.cl	56.m	$6$	$64$	$32$	$6.707$		None		✓			840.2.cl.a	$2$	$0$	\(2\)	\(0\)	\(32\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
840.2.cl.b	$840$	$2$	840.cl	56.m	$6$	$64$	$32$	$6.707$		None		✓			840.2.cl.a	$2$	$0$	\(2\)	\(0\)	\(-32\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)