LMFDB - Space of Modular Forms of Level 2880, Weight 2, and Trivial Character

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	Dim.
$+$	$+$	$+$	$+$	$4$
$+$	$+$	$-$	$-$	$4$
$+$	$-$	$+$	$-$	$7$
$+$	$-$	$-$	$+$	$5$
$-$	$+$	$+$	$-$	$4$
$-$	$+$	$-$	$+$	$4$
$-$	$-$	$+$	$+$	$5$
$-$	$-$	$-$	$-$	$7$
Plus space			$+$	$18$
Minus space			$-$	$22$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(2880))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	3	5	$q$-expansion
2880.2.a.a	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$-4$	$+$	$-$	$+$	$q-q^{5}-4q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots$
2880.2.a.b	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$-4$	$-$	$-$	$+$	$q-q^{5}-4q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots$
2880.2.a.c	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$-4$	$+$	$-$	$+$	$q-q^{5}-4q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots$
2880.2.a.d	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$-2$	$+$	$-$	$+$	$q-q^{5}-2q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots$
2880.2.a.e	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$-2$	$-$	$+$	$+$	$q-q^{5}-2q^{7}-2q^{11}-4q^{13}+2q^{17}+\cdots$
2880.2.a.f	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$-2$	$-$	$-$	$+$	$q-q^{5}-2q^{7}-2q^{13}+6q^{17}-4q^{19}+\cdots$
2880.2.a.g	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$-2$	$+$	$+$	$+$	$q-q^{5}-2q^{7}+2q^{11}-2q^{17}+4q^{19}+\cdots$
2880.2.a.h	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$-2$	$-$	$+$	$+$	$q-q^{5}-2q^{7}+6q^{11}+4q^{13}-6q^{17}+\cdots$
2880.2.a.i	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$0$	$-$	$-$	$+$	$q-q^{5}-4q^{11}-2q^{13}+2q^{17}+8q^{19}+\cdots$
2880.2.a.j	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$0$	$-$	$-$	$+$	$q-q^{5}+4q^{11}-2q^{13}+2q^{17}-8q^{19}+\cdots$
2880.2.a.k	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$2$	$+$	$+$	$+$	$q-q^{5}+2q^{7}-6q^{11}+4q^{13}-6q^{17}+\cdots$
2880.2.a.l	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$2$	$+$	$+$	$+$	$q-q^{5}+2q^{7}-2q^{11}-2q^{17}-4q^{19}+\cdots$
2880.2.a.m	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$2$	$+$	$-$	$+$	$q-q^{5}+2q^{7}-2q^{13}+6q^{17}+4q^{19}+\cdots$
2880.2.a.n	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$2$	$+$	$+$	$+$	$q-q^{5}+2q^{7}+2q^{11}-4q^{13}+2q^{17}+\cdots$
2880.2.a.o	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$2$	$+$	$-$	$+$	$q-q^{5}+2q^{7}+4q^{11}+6q^{13}-2q^{17}+\cdots$
2880.2.a.p	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$4$	$+$	$-$	$+$	$q-q^{5}+4q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots$
2880.2.a.q	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$4$	$-$	$-$	$+$	$q-q^{5}+4q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots$
2880.2.a.r	$1$	$22.997$	$\Q$	None	$0$	$0$	$-1$	$4$	$+$	$-$	$+$	$q-q^{5}+4q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots$
2880.2.a.s	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$-4$	$-$	$-$	$-$	$q+q^{5}-4q^{7}+2q^{13}+6q^{17}+4q^{23}+\cdots$
2880.2.a.t	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$-4$	$+$	$-$	$-$	$q+q^{5}-4q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots$
2880.2.a.u	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$-2$	$-$	$+$	$-$	$q+q^{5}-2q^{7}-6q^{11}+4q^{13}+6q^{17}+\cdots$
2880.2.a.v	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$-2$	$+$	$+$	$-$	$q+q^{5}-2q^{7}-2q^{11}+2q^{17}+4q^{19}+\cdots$
2880.2.a.w	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$-2$	$-$	$+$	$-$	$q+q^{5}-2q^{7}+2q^{11}-4q^{13}-2q^{17}+\cdots$
2880.2.a.x	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$0$	$+$	$-$	$-$	$q+q^{5}-4q^{11}-6q^{13}+6q^{17}+4q^{19}+\cdots$
2880.2.a.y	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$0$	$+$	$-$	$-$	$q+q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots$
2880.2.a.z	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$0$	$+$	$-$	$-$	$q+q^{5}-2q^{13}-6q^{17}-4q^{19}+8q^{23}+\cdots$
2880.2.a.ba	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$0$	$+$	$-$	$-$	$q+q^{5}-2q^{13}-6q^{17}+4q^{19}-8q^{23}+\cdots$
2880.2.a.bb	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$q+q^{5}+4q^{11}-6q^{13}+6q^{17}-4q^{19}+\cdots$
2880.2.a.bc	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$q+q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots$
2880.2.a.bd	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$2$	$+$	$+$	$-$	$q+q^{5}+2q^{7}-2q^{11}-4q^{13}-2q^{17}+\cdots$
2880.2.a.be	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$2$	$+$	$+$	$-$	$q+q^{5}+2q^{7}+2q^{11}+2q^{17}-4q^{19}+\cdots$
2880.2.a.bf	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$2$	$+$	$+$	$-$	$q+q^{5}+2q^{7}+6q^{11}+4q^{13}+6q^{17}+\cdots$
2880.2.a.bg	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$4$	$-$	$-$	$-$	$q+q^{5}+4q^{7}-4q^{11}+2q^{13}-2q^{17}+\cdots$
2880.2.a.bh	$1$	$22.997$	$\Q$	None	$0$	$0$	$1$	$4$	$-$	$-$	$-$	$q+q^{5}+4q^{7}+2q^{13}+6q^{17}-4q^{23}+\cdots$
2880.2.a.bi	$2$	$22.997$	$\Q(\sqrt{5}) $	None	$0$	$0$	$-2$	$0$	$-$	$+$	$+$	$q-q^{5}-\beta q^{7}-\beta q^{11}-4q^{13}+2q^{17}+\cdots$
2880.2.a.bj	$2$	$22.997$	$\Q(\sqrt{5}) $	None	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$q+q^{5}-\beta q^{7}+\beta q^{11}-4q^{13}-2q^{17}+\cdots$
2880.2.a.bk	$2$	$22.997$	$\Q(\sqrt{2}) $	None	$0$	$0$	$2$	$0$	$-$	$-$	$-$	$q+q^{5}+\beta q^{7}+2\beta q^{11}+2q^{13}-2q^{17}+\cdots$

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

Introduction	Features
Universe	News

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 \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\)

\(2\)	\(3\)	\(5\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	\(7\)
Plus space			\(+\)	\(18\)
Minus space			\(-\)	\(22\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	3	5	$q$-expansion
2880.2.a.a	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-4\)	\(+\)	\(-\)	\(+\)	\(q-q^{5}-4q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
2880.2.a.b	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-4\)	\(-\)	\(-\)	\(+\)	\(q-q^{5}-4q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
2880.2.a.c	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-4\)	\(+\)	\(-\)	\(+\)	\(q-q^{5}-4q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
2880.2.a.d	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(q-q^{5}-2q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
2880.2.a.e	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(q-q^{5}-2q^{7}-2q^{11}-4q^{13}+2q^{17}+\cdots\)
2880.2.a.f	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q-q^{5}-2q^{7}-2q^{13}+6q^{17}-4q^{19}+\cdots\)
2880.2.a.g	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-q^{5}-2q^{7}+2q^{11}-2q^{17}+4q^{19}+\cdots\)
2880.2.a.h	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(q-q^{5}-2q^{7}+6q^{11}+4q^{13}-6q^{17}+\cdots\)
2880.2.a.i	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q-q^{5}-4q^{11}-2q^{13}+2q^{17}+8q^{19}+\cdots\)
2880.2.a.j	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q-q^{5}+4q^{11}-2q^{13}+2q^{17}-8q^{19}+\cdots\)
2880.2.a.k	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(2\)	\(+\)	\(+\)	\(+\)	\(q-q^{5}+2q^{7}-6q^{11}+4q^{13}-6q^{17}+\cdots\)
2880.2.a.l	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(2\)	\(+\)	\(+\)	\(+\)	\(q-q^{5}+2q^{7}-2q^{11}-2q^{17}-4q^{19}+\cdots\)
2880.2.a.m	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q-q^{5}+2q^{7}-2q^{13}+6q^{17}+4q^{19}+\cdots\)
2880.2.a.n	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(2\)	\(+\)	\(+\)	\(+\)	\(q-q^{5}+2q^{7}+2q^{11}-4q^{13}+2q^{17}+\cdots\)
2880.2.a.o	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q-q^{5}+2q^{7}+4q^{11}+6q^{13}-2q^{17}+\cdots\)
2880.2.a.p	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(4\)	\(+\)	\(-\)	\(+\)	\(q-q^{5}+4q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots\)
2880.2.a.q	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(4\)	\(-\)	\(-\)	\(+\)	\(q-q^{5}+4q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
2880.2.a.r	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(4\)	\(+\)	\(-\)	\(+\)	\(q-q^{5}+4q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
2880.2.a.s	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-4\)	\(-\)	\(-\)	\(-\)	\(q+q^{5}-4q^{7}+2q^{13}+6q^{17}+4q^{23}+\cdots\)
2880.2.a.t	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(q+q^{5}-4q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
2880.2.a.u	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q+q^{5}-2q^{7}-6q^{11}+4q^{13}+6q^{17}+\cdots\)
2880.2.a.v	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(q+q^{5}-2q^{7}-2q^{11}+2q^{17}+4q^{19}+\cdots\)
2880.2.a.w	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q+q^{5}-2q^{7}+2q^{11}-4q^{13}-2q^{17}+\cdots\)
2880.2.a.x	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{5}-4q^{11}-6q^{13}+6q^{17}+4q^{19}+\cdots\)
2880.2.a.y	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
2880.2.a.z	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{5}-2q^{13}-6q^{17}-4q^{19}+8q^{23}+\cdots\)
2880.2.a.ba	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{5}-2q^{13}-6q^{17}+4q^{19}-8q^{23}+\cdots\)
2880.2.a.bb	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{5}+4q^{11}-6q^{13}+6q^{17}-4q^{19}+\cdots\)
2880.2.a.bc	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
2880.2.a.bd	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(2\)	\(+\)	\(+\)	\(-\)	\(q+q^{5}+2q^{7}-2q^{11}-4q^{13}-2q^{17}+\cdots\)
2880.2.a.be	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(2\)	\(+\)	\(+\)	\(-\)	\(q+q^{5}+2q^{7}+2q^{11}+2q^{17}-4q^{19}+\cdots\)
2880.2.a.bf	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(2\)	\(+\)	\(+\)	\(-\)	\(q+q^{5}+2q^{7}+6q^{11}+4q^{13}+6q^{17}+\cdots\)
2880.2.a.bg	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+q^{5}+4q^{7}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
2880.2.a.bh	\(1\)	\(22.997\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+q^{5}+4q^{7}+2q^{13}+6q^{17}-4q^{23}+\cdots\)
2880.2.a.bi	\(2\)	\(22.997\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{5}-\beta q^{7}-\beta q^{11}-4q^{13}+2q^{17}+\cdots\)
2880.2.a.bj	\(2\)	\(22.997\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+q^{5}-\beta q^{7}+\beta q^{11}-4q^{13}-2q^{17}+\cdots\)
2880.2.a.bk	\(2\)	\(22.997\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{5}+\beta q^{7}+2\beta q^{11}+2q^{13}-2q^{17}+\cdots\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2880))\) into newform subspaces

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

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	2880.2.a

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