Space of modular forms of level 24, weight 2, and Character 24.d

• Label: 24.2.d
• Level: $24$
• Weight: $2$
• Character orbit: 24.d
• Rep. character: $\chi_{24}(13,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	24.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(24, [\chi])\).

	Total	New	Old
Modular forms	6	2	4
Cusp forms	2	2	0
Eisenstein series	4	0	4

Trace form

2 * q - 2 * q^2 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^9 + 4 * q^10 + 4 * q^12 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 4 * q^17 + 2 * q^18 - 8 * q^20 + 8 * q^23 - 4 * q^24 + 2 * q^25 - 8 * q^26 - 4 * q^30 + 4 * q^31 + 8 * q^32 + 4 * q^34 + 8 * q^38 - 8 * q^39 + 8 * q^40 + 4 * q^41 + 4 * q^42 - 8 * q^46 - 24 * q^47 - 6 * q^49 - 2 * q^50 + 16 * q^52 + 2 * q^54 - 8 * q^56 + 8 * q^57 - 12 * q^58 - 4 * q^62 + 4 * q^63 + 16 * q^65 - 8 * q^70 + 24 * q^71 - 4 * q^72 - 12 * q^73 + 16 * q^74 - 16 * q^76 + 8 * q^78 + 20 * q^79 + 2 * q^81 - 4 * q^82 - 8 * q^84 - 8 * q^86 - 12 * q^87 - 20 * q^89 - 4 * q^90 + 24 * q^94 - 16 * q^95 + 8 * q^96 - 4 * q^97 + 6 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(24, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
24.2.d.a	$24$	$2$	24.d	8.b	$2$	$2$	$2$	$0.192$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	24.2.d.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-1)q^{2}+i q^{3}-2 i q^{4}-2 i q^{5}+\cdots\)