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

• Label: 1224.1.m
• Level: $1224$
• Weight: $1$
• Character orbit: 1224.m
• Rep. character: $\chi_{1224}(305,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1224.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 51 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	28	4	24
Cusp forms	12	4	8
Eisenstein series	16	0	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	4	0

Trace form

\( 4 q + O(q^{10}) \)

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.m.a	$1224$	$1$	1224.m	51.c	$2$	$2$	$2$	$0.611$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-q^{5}-\beta q^{7}-q^{11}-q^{13}-q^{17}+\cdots\)
1224.1.m.b	$1224$	$1$	1224.m	51.c	$2$	$2$	$2$	$0.611$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+q^{5}-\beta q^{7}+q^{11}-q^{13}+q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1224, [\chi]) \cong \)