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

• Label: 624.2.x
• Level: $624$
• Weight: $2$
• Character orbit: 624.x
• Rep. character: $\chi_{624}(157,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.x (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	232	96	136
Cusp forms	216	96	120
Eisenstein series	16	0	16

Trace form

96 * q + 8 * q^4 + 24 * q^8 + 16 * q^10 + 16 * q^11 - 8 * q^12 + 8 * q^14 + 16 * q^15 - 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^24 + 32 * q^29 + 8 * q^30 - 48 * q^31 + 40 * q^34 - 48 * q^35 + 8 * q^36 + 32 * q^37 + 56 * q^38 - 32 * q^40 + 48 * q^44 + 8 * q^46 + 32 * q^48 - 96 * q^49 + 32 * q^50 - 16 * q^51 + 8 * q^52 - 32 * q^53 - 8 * q^54 + 32 * q^58 - 32 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 48 * q^66 + 32 * q^67 - 80 * q^68 - 32 * q^69 + 24 * q^70 + 8 * q^72 - 144 * q^74 - 16 * q^75 + 16 * q^76 - 32 * q^77 - 32 * q^79 - 16 * q^80 - 96 * q^81 - 80 * q^82 + 48 * q^84 + 32 * q^85 + 64 * q^86 - 72 * q^88 + 8 * q^90 + 80 * q^92 - 56 * q^94 + 96 * q^95 + 8 * q^98 + 16 * q^99

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.x.a	$624$	$2$	624.x	16.e	$4$	$40$	$20$	$4.983$		None		✓			624.2.x.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
624.2.x.b	$624$	$2$	624.x	16.e	$4$	$56$	$28$	$4.983$		None		✓	✓		624.2.x.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(624, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)