Space of modular forms of level 24, weight 22, and Character 24.f

• Label: 24.22.f
• Level: $24$
• Weight: $22$
• Character orbit: 24.f
• Rep. character: $\chi_{24}(11,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $2$
• Sturm bound: $88$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
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:			\(88\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(24, [\chi])\).

	Total	New	Old
Modular forms	86	86	0
Cusp forms	82	82	0
Eisenstein series	4	4	0

Trace form

\( 82 q - 2 q^{3} - 1212044 q^{4} - 69283304 q^{6} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(24, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
24.22.f.a	$24$	$22$	24.f	24.f	$2$	$2$	$2$	$67.075$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-71810\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{10}\beta q^{2}+(-35905+67717\beta )q^{3}+\cdots\)
24.22.f.b	$24$	$22$	24.f	24.f	$2$	$80$	$80$	$67.075$		None		$4$	$0$	\(0\)	\(71808\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$