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

• Label: 1440.2.f
• Level: $1440$
• Weight: $2$
• Character orbit: 1440.f
• Rep. character: $\chi_{1440}(289,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $10$
• Sturm bound: $576$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(576\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(19\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	320	30	290
Cusp forms	256	30	226
Eisenstein series	64	0	64

Trace form

\( 30 q + 2 q^{5} + O(q^{10}) \)

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.f.a	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2-i)q^{5}+4iq^{13}-2iq^{17}+\cdots\)
1440.2.f.b	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-i)q^{5}+2iq^{7}-2iq^{13}-8q^{19}+\cdots\)
1440.2.f.c	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-i)q^{5}+2iq^{13}+4iq^{17}+\cdots\)
1440.2.f.d	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{5}+2iq^{7}+2iq^{13}+8q^{19}+\cdots\)
1440.2.f.e	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-i)q^{5}+2iq^{7}-6q^{11}-2iq^{13}+\cdots\)
1440.2.f.f	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(2+i)q^{5}+4iq^{13}+2iq^{17}+(3+\cdots)q^{25}+\cdots\)
1440.2.f.g	$1440$	$2$	1440.f	5.b	$2$	$2$	$2$	$11.498$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+i)q^{5}+2iq^{7}+6q^{11}+2iq^{13}+\cdots\)
1440.2.f.h	$1440$	$2$	1440.f	5.b	$2$	$4$	$4$	$11.498$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}+2\beta _{1}q^{13}+\cdots\)
1440.2.f.i	$1440$	$2$	1440.f	5.b	$2$	$4$	$4$	$11.498$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{5}-\beta _{1}q^{7}+(-\beta _{1}+2\beta _{2})q^{23}+\cdots\)
1440.2.f.j	$1440$	$2$	1440.f	5.b	$2$	$8$	$8$	$11.498$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}^{4}q^{5}+\zeta_{24}^{5}q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)