Space of modular forms of level 1440, weight 1, and Character 1440.p

• Label: 1440.1.p
• Level: $1440$
• Weight: $1$
• Character orbit: 1440.p
• Rep. character: $\chi_{1440}(559,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1440.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1440, [\chi])\).

	Total	New	Old
Modular forms	40	4	36
Cusp forms	8	2	6
Eisenstein series	32	2	30

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1440, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1440.1.p.a	$1440$	$1$	1440.p	40.e	$2$	$1$	$1$	$0.719$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-q^{5}+2q^{19}+2q^{23}+q^{25}-2q^{47}+\cdots\)
1440.1.p.b	$1440$	$1$	1440.p	40.e	$2$	$1$	$1$	$0.719$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{5}+2q^{19}-2q^{23}+q^{25}+2q^{47}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1440, [\chi]) \cong \)