Space of modular forms of level 24, weight 8, and Character 24.f

• Label: 24.8.f
• Level: $24$
• Weight: $8$
• Character orbit: 24.f
• Rep. character: $\chi_{24}(11,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	24.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(24, [\chi])\).

	Total	New	Old
Modular forms	30	30	0
Cusp forms	26	26	0
Eisenstein series	4	4	0

Trace form

\( 26 q - 2 q^{3} - 28 q^{4} + 40 q^{6} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
24.8.f.a	$24$	$8$	24.f	24.f	$2$	$2$	$2$	$7.497$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-86\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+8\beta q^{2}+(-43+13\beta )q^{3}-2^{7}q^{4}+\cdots\)
24.8.f.b	$24$	$8$	24.f	24.f	$2$	$4$	$4$	$7.497$	\(\Q(\sqrt{6}, \sqrt{-26})\)	None		$4$	$0$	\(0\)	\(-36\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{1}+\beta _{2})q^{2}+(-9-9\beta _{1})q^{3}+(-80+\cdots)q^{4}+\cdots\)
24.8.f.c	$24$	$8$	24.f	24.f	$2$	$20$	$20$	$7.497$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(120\)	\(0\)	\(0\)	$2^{52}\cdot 3^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(6+\beta _{1}-\beta _{4})q^{3}+(3^{3}+\beta _{3}+\cdots)q^{4}+\cdots\)