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

• Label: 24.9.h
• Level: $24$
• Weight: $9$
• Character orbit: 24.h
• Rep. character: $\chi_{24}(5,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $3$
• Sturm bound: $36$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	24.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(36\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	34	34	0
Cusp forms	30	30	0
Eisenstein series	4	4	0

Trace form

\( 30 q + 236 q^{4} + 1360 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \)

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.h.a	$24$	$9$	24.h	24.h	$2$	$1$	$1$	$9.777$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(-16\)	\(-81\)	\(-866\)	\(-4798\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-866q^{5}+\cdots\)
24.9.h.b	$24$	$9$	24.h	24.h	$2$	$1$	$1$	$9.777$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(16\)	\(81\)	\(866\)	\(-4798\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+866q^{5}+\cdots\)
24.9.h.c	$24$	$9$	24.h	24.h	$2$	$28$	$28$	$9.777$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(9592\)		$\mathrm{SU}(2)[C_{2}]$