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

• Label: 2240.1.bk
• Level: $2240$
• Weight: $1$
• Character orbit: 2240.bk
• Rep. character: $\chi_{2240}(223,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2240.bk (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(15\)

Dimensions

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

	Total	New	Old
Modular forms	64	16	48
Cusp forms	16	16	0
Eisenstein series	48	0	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	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.bk.a	$2240$	$1$	2240.bk	280.y	$4$	$8$	$4$	$1.118$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-14}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}-\zeta_{16}^{3}q^{5}+\cdots\)
2240.1.bk.b	$2240$	$1$	2240.bk	280.y	$4$	$8$	$4$	$1.118$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-14}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}-\zeta_{16}^{3}q^{5}+\zeta_{16}^{6}q^{7}+\cdots\)