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

• Label: 1440.2.w
• Level: $1440$
• Weight: $2$
• Character orbit: 1440.w
• Rep. character: $\chi_{1440}(737,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $7$
• Sturm bound: $576$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(576\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	640	48	592
Cusp forms	512	48	464
Eisenstein series	128	0	128

Trace form

\( 48 q - 16 q^{37} + 32 q^{73} - 16 q^{85} + 96 q^{97}+O(q^{100}) \)

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.w.a	$1440$	$2$	1440.w	15.e	$4$	$4$	$2$	$11.498$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1440.2.w.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-5-5\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)
1440.2.w.b	$1440$	$2$	1440.w	15.e	$4$	$4$	$2$	$11.498$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1440.2.w.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-1-\zeta_{8}^{2})q^{13}+\cdots\)
1440.2.w.c	$1440$	$2$	1440.w	15.e	$4$	$4$	$2$	$11.498$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1440.2.w.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(1+\zeta_{8}^{2})q^{13}+\cdots\)
1440.2.w.d	$1440$	$2$	1440.w	15.e	$4$	$4$	$2$	$11.498$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1440.2.w.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(5-5\zeta_{8}^{2})q^{13}+\cdots\)
1440.2.w.e	$1440$	$2$	1440.w	15.e	$4$	$8$	$4$	$11.498$	\(\Q(\zeta_{24})\)	None		✓			1440.2.w.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2\beta_{3}-\beta_1)q^{5}+\beta_{5} q^{7}-\beta_{7} q^{11}+\cdots\)
1440.2.w.f	$1440$	$2$	1440.w	15.e	$4$	$12$	$6$	$11.498$	12.0.\(\cdots\).1	None		✓			1440.2.w.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{5}+(-1+\beta _{2}+\beta _{5})q^{7}+(\beta _{6}+\cdots)q^{11}+\cdots\)
1440.2.w.g	$1440$	$2$	1440.w	15.e	$4$	$12$	$6$	$11.498$	12.0.\(\cdots\).1	None		✓			1440.2.w.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{5}+(1-\beta _{2}-\beta _{5})q^{7}+(\beta _{6}+\beta _{8}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)