Space of modular forms of level 2240, weight 1, and Character 2240.dl

• Label: 2240.1.dl
• Level: $2240$
• Weight: $1$
• Character orbit: 2240.dl
• Rep. character: $\chi_{2240}(417,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2240.dl (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2240, [\chi])\).

	Total	New	Old
Modular forms	112	16	96
Cusp forms	16	16	0
Eisenstein series	96	0	96

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	16	0

Trace form

\( 16 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2240, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2240.1.dl.a	$2240$	$1$	2240.dl	280.at	$12$	$8$	$2$	$1.118$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{24}^{2}+\zeta_{24}^{8})q^{3}-\zeta_{24}^{7}q^{5}+\zeta_{24}^{9}q^{7}+\cdots\)
2240.1.dl.b	$2240$	$1$	2240.dl	280.at	$12$	$8$	$2$	$1.118$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{24}^{2}-\zeta_{24}^{8})q^{3}-\zeta_{24}^{7}q^{5}+\cdots\)