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

• Label: 1440.1.y
• Level: $1440$
• Weight: $1$
• Character orbit: 1440.y
• Rep. character: $\chi_{1440}(433,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1440.y (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	80	8	72
Cusp forms	16	4	12
Eisenstein series	64	4	60

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

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

Trace form

\( 4 q + 4 q^{7} + O(q^{10}) \)

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.y.a	$1440$	$1$	1440.y	40.i	$4$	$4$	$2$	$0.719$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-6}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)