Space of modular forms of level 624, weight 2, and Character 624.ch

• Label: 624.2.ch
• Level: $624$
• Weight: $2$
• Character orbit: 624.ch
• Rep. character: $\chi_{624}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $224$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.ch (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 208 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(624, [\chi])\).

	Total	New	Old
Modular forms	464	224	240
Cusp forms	432	224	208
Eisenstein series	32	0	32

Trace form

224 * q - 8 * q^10 - 32 * q^14 - 48 * q^16 - 12 * q^20 + 8 * q^22 + 12 * q^24 - 224 * q^25 - 16 * q^26 - 52 * q^28 + 40 * q^32 + 64 * q^34 - 40 * q^38 - 40 * q^40 - 16 * q^43 + 24 * q^44 + 16 * q^46 - 16 * q^50 - 16 * q^52 - 32 * q^55 - 20 * q^56 - 32 * q^58 + 96 * q^59 - 64 * q^60 - 24 * q^68 - 48 * q^70 + 64 * q^71 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 76 * q^76 - 24 * q^78 + 100 * q^80 + 112 * q^81 + 48 * q^82 - 64 * q^86 - 60 * q^88 - 16 * q^89 + 40 * q^91 - 48 * q^92 + 64 * q^94 - 56 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(624, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
624.2.ch.a	$624$	$2$	624.ch	208.af	$12$	$224$	$56$	$4.983$		None		✓	✓	✓	624.2.ch.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(624, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)