Space of modular forms of level 24, weight 6, and Character 24.f

• Label: 24.6.f
• Level: $24$
• Weight: $6$
• Character orbit: 24.f
• Rep. character: $\chi_{24}(11,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	24.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(24, [\chi])\).

	Total	New	Old
Modular forms	22	22	0
Cusp forms	18	18	0
Eisenstein series	4	4	0

Trace form

18 * q - 2 * q^3 - 12 * q^4 + 88 * q^6 - 2 * q^9 + 168 * q^10 - 92 * q^12 - 216 * q^16 + 376 * q^18 - 2364 * q^19 + 480 * q^22 - 2360 * q^24 + 6246 * q^25 - 3734 * q^27 - 6864 * q^28 + 6672 * q^30 + 3320 * q^33 + 10416 * q^34 + 7228 * q^36 + 5856 * q^40 - 16728 * q^42 - 660 * q^43 - 25056 * q^46 - 28232 * q^48 + 222 * q^49 - 7696 * q^51 - 54240 * q^52 + 56680 * q^54 - 15892 * q^57 + 58056 * q^58 + 105456 * q^60 + 159984 * q^64 - 142168 * q^66 + 48924 * q^67 - 199248 * q^70 - 184112 * q^72 - 52572 * q^73 + 57130 * q^75 - 179592 * q^76 + 251664 * q^78 - 34238 * q^81 + 297600 * q^82 + 317856 * q^84 + 385584 * q^88 - 468792 * q^90 - 32832 * q^91 - 523200 * q^94 - 572720 * q^96 + 7596 * q^97 - 51664 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(24, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
24.6.f.a	$24$	$6$	24.f	24.f	$2$	$2$	$2$	$3.849$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		✓			24.6.f.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4\beta q^{2}+(-1+11\beta )q^{3}-2^{5}q^{4}+\cdots\)
24.6.f.b	$24$	$6$	24.f	24.f	$2$	$16$	$16$	$3.849$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		24.6.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{32}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(3+\beta _{2}+\cdots)q^{4}+\cdots\)