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

• Label: 2880.2.d
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.d
• Rep. character: $\chi_{2880}(289,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $11$
• Sturm bound: $1152$
• Trace bound: $41$

Defining parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(1152\)
Trace bound:			\(41\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(31\), \(41\), \(43\)

Dimensions

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

	Total	New	Old
Modular forms	624	60	564
Cusp forms	528	60	468
Eisenstein series	96	0	96

Trace form

\( 60 q + 12 q^{25} - 24 q^{41} - 60 q^{49} - 24 q^{65} + 24 q^{89}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2880.2.d.a	$2880$	$2$	2880.d	40.f	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					960.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta-1)q^{5}+\beta q^{7}-\beta q^{11}+2 q^{13}+\cdots\)
2880.2.d.b	$2880$	$2$	2880.d	40.f	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					960.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta-1)q^{5}+\beta q^{7}-\beta q^{11}+2 q^{13}+\cdots\)
2880.2.d.c	$2880$	$2$	2880.d	40.f	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					960.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta+1)q^{5}+\beta q^{7}+\beta q^{11}-2 q^{13}+\cdots\)
2880.2.d.d	$2880$	$2$	2880.d	40.f	$2$	$2$	$2$	$22.997$	\(\Q(\sqrt{-1}) \)	None					960.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta+1)q^{5}+\beta q^{7}+\beta q^{11}-2 q^{13}+\cdots\)
2880.2.d.e	$2880$	$2$	2880.d	40.f	$2$	$4$	$4$	$22.997$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-10}) \)					320.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{5}+\beta _{2}q^{7}-\beta _{1}q^{11}+2\beta _{3}q^{13}+\cdots\)
2880.2.d.f	$2880$	$2$	2880.d	40.f	$2$	$8$	$8$	$22.997$	\(\Q(\zeta_{24})\)	None		✓			2880.2.d.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{5}+\beta_{5} q^{7}-\beta_1 q^{11}+(\beta_{4}-\beta_{3})q^{13}+\cdots\)
2880.2.d.g	$2880$	$2$	2880.d	40.f	$2$	$8$	$8$	$22.997$	\(\Q(\zeta_{24})\)	None					320.2.f.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{6} q^{5}+\beta_{2} q^{7}+\beta_1 q^{11}+(2\beta_{6}+2\beta_{5})q^{13}+\cdots\)
2880.2.d.h	$2880$	$2$	2880.d	40.f	$2$	$8$	$8$	$22.997$	\(\Q(\zeta_{24})\)	None		✓			2880.2.d.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{5}+\beta_{5} q^{7}-\beta_1 q^{11}+(-\beta_{4}+\beta_{3})q^{13}+\cdots\)
2880.2.d.i	$2880$	$2$	2880.d	40.f	$2$	$8$	$8$	$22.997$	\(\Q(i, \sqrt{3}, \sqrt{7})\)	None					960.2.d.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+(-\beta _{4}+\beta _{5})q^{7}+\beta _{1}q^{11}+\cdots\)
2880.2.d.j	$2880$	$2$	2880.d	40.f	$2$	$8$	$8$	$22.997$	\(\Q(i, \sqrt{3}, \sqrt{7})\)	None					960.2.d.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(-\beta _{4}+\beta _{5})q^{7}-\beta _{1}q^{11}+\cdots\)
2880.2.d.k	$2880$	$2$	2880.d	40.f	$2$	$8$	$8$	$22.997$	\(\Q(i, \sqrt{2}, \sqrt{5})\)	\(\Q(\sqrt{-10}) \)		✓			2880.2.d.k	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{5}-\beta _{3}q^{7}-\beta _{5}q^{11}+\beta _{6}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)