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

• Label: 2880.2.o
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.o
• Rep. character: $\chi_{2880}(2879,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $1152$
• Trace bound: $49$

Defining parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1152\)
Trace bound:			\(49\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	624	48	576
Cusp forms	528	48	480
Eisenstein series	96	0	96

Trace form

\( 48 q + O(q^{10}) \)

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.o.a	$2880$	$2$	2880.o	60.h	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{8}^{2}q^{5}-2\zeta_{8}q^{13}-5\zeta_{8}^{3}q^{17}+\cdots\)
2880.2.o.b	$2880$	$2$	2880.o	60.h	$2$	$4$	$4$	$22.997$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{8}^{3}q^{5}-2\zeta_{8}q^{13}+(-\zeta_{8}^{2}+2\zeta_{8}^{3})q^{17}+\cdots\)
2880.2.o.c	$2880$	$2$	2880.o	60.h	$2$	$8$	$8$	$22.997$	8.0.3317760000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{5}+\beta _{4}q^{7}-\beta _{7}q^{11}+\beta _{5}q^{13}+\cdots\)
2880.2.o.d	$2880$	$2$	2880.o	60.h	$2$	$8$	$8$	$22.997$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{24}+\zeta_{24}^{2})q^{5}-\zeta_{24}^{6}q^{7}-\zeta_{24}^{3}q^{11}+\cdots\)
2880.2.o.e	$2880$	$2$	2880.o	60.h	$2$	$12$	$12$	$22.997$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{9}q^{7}+(\beta _{2}-\beta _{3}-\beta _{4})q^{11}+\cdots\)
2880.2.o.f	$2880$	$2$	2880.o	60.h	$2$	$12$	$12$	$22.997$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+\beta _{9}q^{7}+(\beta _{2}-\beta _{3}-\beta _{4})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)