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

• Label: 2880.2.b
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.b
• Rep. character: $\chi_{2880}(2591,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $1152$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1152\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(7\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	624	32	592
Cusp forms	528	32	496
Eisenstein series	96	0	96

Trace form

\( 32 q + 32 q^{25} - 96 q^{49} - 64 q^{73} + 64 q^{97}+O(q^{100}) \)

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.b.a	$2880$	$2$	2880.b	24.f	$2$	$8$	$8$	$22.997$	\(\Q(i, \sqrt{2}, \sqrt{5})\)	None		✓			2880.2.b.a	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\beta _{2}q^{13}+\cdots\)
2880.2.b.b	$2880$	$2$	2880.b	24.f	$2$	$8$	$8$	$22.997$	\(\Q(\zeta_{24})\)	None		✓			2880.2.b.b	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}-\beta_{5} q^{7}+\beta_{5} q^{11}+\beta_1 q^{13}+\cdots\)
2880.2.b.c	$2880$	$2$	2880.b	24.f	$2$	$8$	$8$	$22.997$	\(\Q(\zeta_{24})\)	None		✓			2880.2.b.b	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}-\beta_{6} q^{7}-\beta_{6} q^{11}-\beta_1 q^{13}+\cdots\)
2880.2.b.d	$2880$	$2$	2880.b	24.f	$2$	$8$	$8$	$22.997$	\(\Q(i, \sqrt{2}, \sqrt{5})\)	None		✓			2880.2.b.a	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}+\beta _{3}q^{7}+(\beta _{1}-\beta _{3})q^{11}-\beta _{2}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)