Space of modular forms of level 1440, weight 2, and Character 1440.d

• Label: 1440.2.d
• Level: $1440$
• Weight: $2$
• Character orbit: 1440.d
• Rep. character: $\chi_{1440}(1009,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $6$
• Sturm bound: $576$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1440, [\chi])\).

	Total	New	Old
Modular forms	320	32	288
Cusp forms	256	28	228
Eisenstein series	64	4	60

Trace form

\( 28 q - 4 q^{25} + 8 q^{41} - 20 q^{49} + 8 q^{55} + 24 q^{65} - 16 q^{71} + 32 q^{79} + 16 q^{89} + 40 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1440.2.d.a	$1440$	$2$	1440.d	40.f	$2$	$4$	$4$	$11.498$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-30}) \)					360.2.d.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{5}-2\beta _{2}q^{11}-\beta _{3}q^{13}+\beta _{1}q^{17}+\cdots\)
1440.2.d.b	$1440$	$2$	1440.d	40.f	$2$	$4$	$4$	$11.498$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)					360.2.d.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-1+\cdots)q^{25}+\cdots\)
1440.2.d.c	$1440$	$2$	1440.d	40.f	$2$	$4$	$4$	$11.498$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					40.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{7}-2\beta _{2}q^{11}+\cdots\)
1440.2.d.d	$1440$	$2$	1440.d	40.f	$2$	$4$	$4$	$11.498$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)					360.2.d.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}+2\beta _{2}q^{17}-\beta _{3}q^{19}-\beta _{2}q^{23}+\cdots\)
1440.2.d.e	$1440$	$2$	1440.d	40.f	$2$	$6$	$6$	$11.498$	6.0.839056.1	None					120.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}-\beta _{1}q^{7}+(-\beta _{1}-\beta _{5})q^{11}+\cdots\)
1440.2.d.f	$1440$	$2$	1440.d	40.f	$2$	$6$	$6$	$11.498$	6.0.839056.1	None					120.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{1}q^{7}+(\beta _{1}+\beta _{5})q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)