Space of modular forms of level 1440, weight 4, and Character 1440.k

• Label: 1440.4.k
• Level: $1440$
• Weight: $4$
• Character orbit: 1440.k
• Rep. character: $\chi_{1440}(721,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $5$
• Sturm bound: $1152$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1440.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1152\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1440, [\chi])\).

	Total	New	Old
Modular forms	896	60	836
Cusp forms	832	60	772
Eisenstein series	64	0	64

Trace form

\( 60 q - 28 q^{7} - 52 q^{23} - 1500 q^{25} - 264 q^{31} - 40 q^{41} - 940 q^{47} + 2220 q^{49} - 440 q^{55} + 1592 q^{71} - 432 q^{73} + 1296 q^{79} + 424 q^{89} - 1520 q^{95} + 1584 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1440, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1440.4.k.a	$1440$	$4$	1440.k	8.b	$2$	$2$	$2$	$84.963$	\(\Q(\sqrt{-1}) \)	None					120.4.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-52\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-5 i q^{5}-26 q^{7}+40 i q^{11}+12 i q^{13}+\cdots\)
1440.4.k.b	$1440$	$4$	1440.k	8.b	$2$	$8$	$8$	$84.963$	8.0.\(\cdots\).4	None					120.4.k.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(80\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-5\beta _{1}q^{5}+(10-\beta _{6})q^{7}+(\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots\)
1440.4.k.c	$1440$	$4$	1440.k	8.b	$2$	$12$	$12$	$84.963$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					40.4.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-28\)	$2^{30}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(-2+\beta _{4})q^{7}+(\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots\)
1440.4.k.d	$1440$	$4$	1440.k	8.b	$2$	$14$	$14$	$84.963$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					120.4.k.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(28\)	$2^{42}$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta _{1}q^{5}+(2+\beta _{6})q^{7}+(-6\beta _{1}+\beta _{10}+\cdots)q^{11}+\cdots\)
1440.4.k.e	$1440$	$4$	1440.k	8.b	$2$	$24$	$24$	$84.963$		None			✓		360.4.k.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-56\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1440, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)