Space of modular forms of level 1224, weight 1, and Character 1224.cx

• Label: 1224.1.cx
• Level: $1224$
• Weight: $1$
• Character orbit: 1224.cx
• Rep. character: $\chi_{1224}(11,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $12$

Defining parameters

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1224.cx (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1224 \)
Character field:			\(\Q(\zeta_{48})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1224, [\chi])\).

	Total	New	Old
Modular forms	96	96	0
Cusp forms	32	32	0
Eisenstein series	64	64	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1224.1.cx.a	$1224$	$1$	1224.cx	1224.bx	$48$	$16$	$1$	$0.611$	\(\Q(\zeta_{48})\)	$D_{48}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{48}^{5}q^{2}+\zeta_{48}^{14}q^{3}+\zeta_{48}^{10}q^{4}+\cdots\)
1224.1.cx.b	$1224$	$1$	1224.cx	1224.bx	$48$	$16$	$1$	$0.611$	\(\Q(\zeta_{48})\)	$D_{48}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{48}^{5}q^{2}+\zeta_{48}^{17}q^{3}+\zeta_{48}^{10}q^{4}+\cdots\)