Space of modular forms of level 2880, weight 2, and Character 2880.k

• Label: 2880.2.k
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.k
• Rep. character: $\chi_{2880}(1441,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $12$
• Sturm bound: $1152$
• Trace bound: $47$

Defining parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1152\)
Trace bound:			\(47\)
Distinguishing \(T_p\):			\(7\), \(11\), \(23\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).

	Total	New	Old
Modular forms	624	40	584
Cusp forms	528	40	488
Eisenstein series	96	0	96

Trace form

\( 40 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2880, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2880.2.k.a	$2880$	$2$	2880.k	8.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{5}-4q^{7}-4iq^{11}-2iq^{13}+\cdots\)
2880.2.k.b	$2880$	$2$	2880.k	8.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{5}+6iq^{13}+2iq^{19}-6q^{23}+\cdots\)
2880.2.k.c	$2880$	$2$	2880.k	8.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-6iq^{13}+2iq^{19}+6q^{23}+\cdots\)
2880.2.k.d	$2880$	$2$	2880.k	8.b	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+4q^{7}-4iq^{11}+2iq^{13}+\cdots\)
2880.2.k.e	$2880$	$2$	2880.k	8.b	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{5}+(-3-\zeta_{12}^{3})q^{7}+2\zeta_{12}^{2}q^{11}+\cdots\)
2880.2.k.f	$2880$	$2$	2880.k	8.b	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{5}-2q^{7}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{11}+\cdots\)
2880.2.k.g	$2880$	$2$	2880.k	8.b	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2880.2.k.h	$2880$	$2$	2880.k	8.b	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{5}-\zeta_{12}^{2}q^{11}-\zeta_{12}^{2}q^{13}+\cdots\)
2880.2.k.i	$2880$	$2$	2880.k	8.b	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{5}+\zeta_{12}^{2}q^{11}-\zeta_{12}^{2}q^{13}+\cdots\)
2880.2.k.j	$2880$	$2$	2880.k	8.b	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2880.2.k.k	$2880$	$2$	2880.k	8.b	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{5}+2q^{7}+(2\zeta_{12}-\zeta_{12}^{2})q^{11}+\cdots\)
2880.2.k.l	$2880$	$2$	2880.k	8.b	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{5}+(3+\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)