Space of modular forms of level 2880, weight 2, and trivial character

• Label: 2880.2.a
• Level: $2880$
• Weight: $2$
• Character orbit: 2880.a
• Rep. character: $\chi_{2880}(1,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $37$
• Sturm bound: $1152$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 37 \)
Sturm bound:			\(1152\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2880))\).

	Total	New	Old
Modular forms	624	40	584
Cusp forms	529	40	489
Eisenstein series	95	0	95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(5\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(72\)	\(4\)	\(68\)		\(61\)	\(4\)	\(57\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(80\)	\(4\)	\(76\)		\(68\)	\(4\)	\(64\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(80\)	\(7\)	\(73\)		\(68\)	\(7\)	\(61\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(80\)	\(5\)	\(75\)		\(68\)	\(5\)	\(63\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(84\)	\(4\)	\(80\)		\(72\)	\(4\)	\(68\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(76\)	\(4\)	\(72\)		\(64\)	\(4\)	\(60\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(76\)	\(5\)	\(71\)		\(64\)	\(5\)	\(59\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(76\)	\(7\)	\(69\)		\(64\)	\(7\)	\(57\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(304\)	\(18\)	\(286\)		\(257\)	\(18\)	\(239\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(320\)	\(22\)	\(298\)		\(272\)	\(22\)	\(250\)		\(48\)	\(0\)	\(48\)

Trace form

\( 40 q - 16 q^{13} + 40 q^{25} - 16 q^{29} - 32 q^{37} + 16 q^{41} + 40 q^{49} - 16 q^{53} - 16 q^{77} + 16 q^{85} + 16 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2880))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5
2880.2.a.a	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				30.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
2880.2.a.b	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				120.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
2880.2.a.c	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				480.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
2880.2.a.d	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				160.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
2880.2.a.e	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				360.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-2q^{11}-4q^{13}+2q^{17}+\cdots\)
2880.2.a.f	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				20.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-2q^{13}+6q^{17}-4q^{19}+\cdots\)
2880.2.a.g	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				1440.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+2q^{11}-2q^{17}+4q^{19}+\cdots\)
2880.2.a.h	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				90.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+6q^{11}+4q^{13}-6q^{17}+\cdots\)
2880.2.a.i	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				480.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{11}-2q^{13}+2q^{17}+8q^{19}+\cdots\)
2880.2.a.j	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				480.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{11}-2q^{13}+2q^{17}-8q^{19}+\cdots\)
2880.2.a.k	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				90.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-6q^{11}+4q^{13}-6q^{17}+\cdots\)
2880.2.a.l	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				1440.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-2q^{11}-2q^{17}-4q^{19}+\cdots\)
2880.2.a.m	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				20.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-2q^{13}+6q^{17}+4q^{19}+\cdots\)
2880.2.a.n	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				360.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+2q^{11}-4q^{13}+2q^{17}+\cdots\)
2880.2.a.o	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				160.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+4q^{11}+6q^{13}-2q^{17}+\cdots\)
2880.2.a.p	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				480.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots\)
2880.2.a.q	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				30.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
2880.2.a.r	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				120.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
2880.2.a.s	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				480.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}+2q^{13}+6q^{17}+4q^{23}+\cdots\)
2880.2.a.t	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				40.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
2880.2.a.u	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				90.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-6q^{11}+4q^{13}+6q^{17}+\cdots\)
2880.2.a.v	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				1440.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-2q^{11}+2q^{17}+4q^{19}+\cdots\)
2880.2.a.w	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				360.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+2q^{11}-4q^{13}-2q^{17}+\cdots\)
2880.2.a.x	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				120.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{11}-6q^{13}+6q^{17}+4q^{19}+\cdots\)
2880.2.a.y	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				15.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
2880.2.a.z	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				480.2.a.d	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{13}-6q^{17}-4q^{19}+8q^{23}+\cdots\)
2880.2.a.ba	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				480.2.a.d	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{13}-6q^{17}+4q^{19}-8q^{23}+\cdots\)
2880.2.a.bb	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				120.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{11}-6q^{13}+6q^{17}-4q^{19}+\cdots\)
2880.2.a.bc	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				15.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
2880.2.a.bd	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				360.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-2q^{11}-4q^{13}-2q^{17}+\cdots\)
2880.2.a.be	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				1440.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+2q^{11}+2q^{17}-4q^{19}+\cdots\)
2880.2.a.bf	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				90.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+6q^{11}+4q^{13}+6q^{17}+\cdots\)
2880.2.a.bg	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				40.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
2880.2.a.bh	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	\(\Q\)	None	✓				480.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+2q^{13}+6q^{17}-4q^{23}+\cdots\)
2880.2.a.bi	$2880$	$2$	2880.a	1.a	$1$	$2$	$2$	$22.997$	\(\Q(\sqrt{5}) \)	None	✓		✓		1440.2.a.p	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}-\beta q^{11}-4q^{13}+2q^{17}+\cdots\)
2880.2.a.bj	$2880$	$2$	2880.a	1.a	$1$	$2$	$2$	$22.997$	\(\Q(\sqrt{5}) \)	None	✓		✓		1440.2.a.p	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}+\beta q^{11}-4q^{13}-2q^{17}+\cdots\)
2880.2.a.bk	$2880$	$2$	2880.a	1.a	$1$	$2$	$2$	$22.997$	\(\Q(\sqrt{2}) \)	None	✓		✓		160.2.a.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+2\beta q^{11}+2q^{13}-2q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2880)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 2}\)