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

• Label: 1440.2.x
• Level: $1440$
• Weight: $2$
• Character orbit: 1440.x
• Rep. character: $\chi_{1440}(127,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $18$
• Sturm bound: $576$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.x (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(576\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	640	60	580
Cusp forms	512	60	452
Eisenstein series	128	0	128

Trace form

\( 60 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1440.2.x.a	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-2i)q^{5}+(-3+3i)q^{7}+2iq^{11}+\cdots\)
1440.2.x.b	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+2i)q^{5}+(-1+i)q^{7}+6iq^{11}+\cdots\)
1440.2.x.c	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-2i)q^{5}-4iq^{11}+(-3+3i)q^{13}+\cdots\)
1440.2.x.d	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-2i)q^{5}+4iq^{11}+(-3+3i)q^{13}+\cdots\)
1440.2.x.e	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+2i)q^{5}+(1-i)q^{7}-6iq^{11}+\cdots\)
1440.2.x.f	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-2i)q^{5}+(3-3i)q^{7}-2iq^{11}+\cdots\)
1440.2.x.g	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+2i)q^{5}+4iq^{11}+(-3+3i)q^{13}+\cdots\)
1440.2.x.h	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+2i)q^{5}-4iq^{11}+(-3+3i)q^{13}+\cdots\)
1440.2.x.i	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-i)q^{5}+(-2+2i)q^{7}+(-1+i)q^{13}+\cdots\)
1440.2.x.j	$1440$	$2$	1440.x	20.e	$4$	$2$	$1$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-i)q^{5}+(2-2i)q^{7}+(-1+i)q^{13}+\cdots\)
1440.2.x.k	$1440$	$2$	1440.x	20.e	$4$	$4$	$2$	$11.498$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{1}+\beta _{2})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
1440.2.x.l	$1440$	$2$	1440.x	20.e	$4$	$4$	$2$	$11.498$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1440.2.x.m	$1440$	$2$	1440.x	20.e	$4$	$4$	$2$	$11.498$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-1+\zeta_{8}^{2})q^{7}+\cdots\)
1440.2.x.n	$1440$	$2$	1440.x	20.e	$4$	$4$	$2$	$11.498$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots\)
1440.2.x.o	$1440$	$2$	1440.x	20.e	$4$	$4$	$2$	$11.498$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1}-\beta _{2})q^{5}+(-1+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1440.2.x.p	$1440$	$2$	1440.x	20.e	$4$	$4$	$2$	$11.498$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1}-\beta _{2})q^{5}+(1+2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1440.2.x.q	$1440$	$2$	1440.x	20.e	$4$	$8$	$4$	$11.498$	8.0.1698758656.6	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{5}+(-1+\beta _{2}+\beta _{3}+\beta _{4})q^{7}+\cdots\)
1440.2.x.r	$1440$	$2$	1440.x	20.e	$4$	$8$	$4$	$11.498$	8.0.1698758656.6	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{5}+(1+\beta _{1}+\beta _{4}-\beta _{5})q^{7}+(-\beta _{3}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)