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

• Label: 2240.1.p
• Level: $2240$
• Weight: $1$
• Character orbit: 2240.p
• Rep. character: $\chi_{2240}(769,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $5$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2240.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	56	12	44
Cusp forms	32	8	24
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 4 q^{9} + O(q^{10}) \)

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.p.a	$2240$	$1$	2240.p	35.c	$2$	$1$	$1$	$1.118$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-35}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$1$		\(q-q^{3}-q^{5}-q^{7}-q^{11}+q^{13}+q^{15}+\cdots\)
2240.1.p.b	$2240$	$1$	2240.p	35.c	$2$	$1$	$1$	$1.118$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-35}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)	$1$		\(q-q^{3}+q^{5}-q^{7}+q^{11}-q^{13}-q^{15}+\cdots\)
2240.1.p.c	$2240$	$1$	2240.p	35.c	$2$	$1$	$1$	$1.118$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-35}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)	$1$		\(q+q^{3}-q^{5}+q^{7}+q^{11}+q^{13}-q^{15}+\cdots\)
2240.1.p.d	$2240$	$1$	2240.p	35.c	$2$	$1$	$1$	$1.118$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-35}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(1\)	\(1\)	$1$		\(q+q^{3}+q^{5}+q^{7}-q^{11}-q^{13}+q^{15}+\cdots\)
2240.1.p.e	$2240$	$1$	2240.p	35.c	$2$	$4$	$4$	$1.118$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)