Space of modular forms of level 420, weight 2, and Character 420.bk

• Label: 420.2.bk
• Level: $420$
• Weight: $2$
• Character orbit: 420.bk
• Rep. character: $\chi_{420}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bk (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 140 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(420, [\chi])\).

	Total	New	Old
Modular forms	208	96	112
Cusp forms	176	96	80
Eisenstein series	32	0	32

Trace form

96 * q + 48 * q^9 + 18 * q^10 + 4 * q^14 - 8 * q^16 + 4 * q^25 - 8 * q^30 - 30 * q^40 + 16 * q^44 + 44 * q^46 - 8 * q^49 - 48 * q^50 - 52 * q^56 + 2 * q^60 - 144 * q^64 - 36 * q^66 - 42 * q^70 - 20 * q^74 - 36 * q^80 - 48 * q^81 - 20 * q^84 - 32 * q^85 - 32 * q^86 - 36 * q^94 - 60 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(420, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
420.2.bk.a	$420$	$2$	420.bk	140.s	$6$	$96$	$48$	$3.354$		None		✓	✓	✓	420.2.bk.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(420, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)