Space of modular forms of level 24, weight 9, and Character 24.e

• Label: 24.9.e
• Level: $24$
• Weight: $9$
• Character orbit: 24.e
• Rep. character: $\chi_{24}(17,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	24.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(24, [\chi])\).

	Total	New	Old
Modular forms	36	8	28
Cusp forms	28	8	20
Eisenstein series	8	0	8

Trace form

\( 8 q + 56 q^{3} + 1584 q^{7} + 328 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(24, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
24.9.e.a	$24$	$9$	24.e	3.b	$2$	$8$	$8$	$9.777$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(56\)	\(0\)	\(1584\)	$2^{42}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(7+\beta _{2})q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(198+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)