LMFDB - Space of modular forms of level 6720, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 6720 = 2^{6} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6720.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 80 $
Sturm bound:			$3072$
Trace bound:			$23$
Distinguishing $T_p$:			$11$, $13$, $17$, $19$, $23$, $29$, $31$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(6720))$.

	Total	New	Old
Modular forms	1584	96	1488
Cusp forms	1489	96	1393
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.

$2$	$3$	$5$	$7$	Fricke	Dim.
$+$	$+$	$+$	$+$	$+$	$5$
$+$	$+$	$+$	$-$	$-$	$8$
$+$	$+$	$-$	$+$	$-$	$6$
$+$	$+$	$-$	$-$	$+$	$5$
$+$	$-$	$+$	$+$	$-$	$6$
$+$	$-$	$+$	$-$	$+$	$5$
$+$	$-$	$-$	$+$	$+$	$5$
$+$	$-$	$-$	$-$	$-$	$8$
$-$	$+$	$+$	$+$	$-$	$7$
$-$	$+$	$+$	$-$	$+$	$4$
$-$	$+$	$-$	$+$	$+$	$6$
$-$	$+$	$-$	$-$	$-$	$7$
$-$	$-$	$+$	$+$	$+$	$6$
$-$	$-$	$+$	$-$	$-$	$7$
$-$	$-$	$-$	$+$	$-$	$7$
$-$	$-$	$-$	$-$	$+$	$4$
Plus space				$+$	$40$
Minus space				$-$	$56$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(6720))$ 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	7	$q$-expansion
6720.2.a.a	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
6720.2.a.b	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.c	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
6720.2.a.d	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
6720.2.a.e	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
6720.2.a.f	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots$
6720.2.a.g	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots$
6720.2.a.h	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.i	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.j	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.k	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.l	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$
6720.2.a.m	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$1$	$-$	$+$	$+$	$-$	$q-q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.n	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$1$	$+$	$+$	$+$	$-$	$q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots$
6720.2.a.o	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$1$	$-$	$+$	$+$	$-$	$q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots$
6720.2.a.p	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$1$	$+$	$+$	$+$	$-$	$q-q^{3}-q^{5}+q^{7}+q^{9}+6q^{13}+q^{15}+\cdots$
6720.2.a.q	$1$	$53.659$	$\Q$	None	$0$	$-1$	$-1$	$1$	$+$	$+$	$+$	$-$	$q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.r	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$-1$	$-$	$+$	$-$	$+$	$q-q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
6720.2.a.s	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$-1$	$+$	$+$	$-$	$+$	$q-q^{3}+q^{5}-q^{7}+q^{9}-6q^{13}-q^{15}+\cdots$
6720.2.a.t	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$-1$	$-$	$+$	$-$	$+$	$q-q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
6720.2.a.u	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$-1$	$-$	$+$	$-$	$+$	$q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots$
6720.2.a.v	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$-1$	$-$	$+$	$-$	$+$	$q-q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
6720.2.a.w	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$-1$	$+$	$+$	$-$	$+$	$q-q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
6720.2.a.x	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots$
6720.2.a.y	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
6720.2.a.z	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$-$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.ba	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$-$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}-q^{15}+\cdots$
6720.2.a.bb	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
6720.2.a.bc	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
6720.2.a.bd	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$-$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
6720.2.a.be	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$-$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.bf	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.bg	$1$	$53.659$	$\Q$	None	$0$	$-1$	$1$	$1$	$-$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
6720.2.a.bh	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$-1$	$+$	$-$	$+$	$+$	$q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.bi	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$-1$	$-$	$-$	$+$	$+$	$q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
6720.2.a.bj	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$-1$	$+$	$-$	$+$	$+$	$q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
6720.2.a.bk	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$-1$	$-$	$-$	$+$	$+$	$q+q^{3}-q^{5}-q^{7}+q^{9}+6q^{13}-q^{15}+\cdots$
6720.2.a.bl	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$-1$	$+$	$-$	$+$	$+$	$q+q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.bm	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots$
6720.2.a.bn	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.bo	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.bp	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.bq	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.br	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
6720.2.a.bs	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
6720.2.a.bt	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
6720.2.a.bu	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$
6720.2.a.bv	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
6720.2.a.bw	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.bx	$1$	$53.659$	$\Q$	None	$0$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
6720.2.a.by	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$+$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.bz	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$+$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
6720.2.a.ca	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
6720.2.a.cb	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$+$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
6720.2.a.cc	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots$
6720.2.a.cd	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots$
6720.2.a.ce	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+q^{15}+\cdots$
6720.2.a.cf	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$+$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
6720.2.a.cg	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$+$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
6720.2.a.ch	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots$
6720.2.a.ci	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$1$	$-$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
6720.2.a.cj	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$1$	$-$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
6720.2.a.ck	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$1$	$-$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{7}+q^{9}-6q^{13}+q^{15}+\cdots$
6720.2.a.cl	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$1$	$-$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots$
6720.2.a.cm	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$1$	$+$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$
6720.2.a.cn	$1$	$53.659$	$\Q$	None	$0$	$1$	$1$	$1$	$+$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
6720.2.a.co	$2$	$53.659$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-2$	$2$	$+$	$+$	$+$	$-$	$q-q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots$
6720.2.a.cp	$2$	$53.659$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$-2$	$2$	$-$	$+$	$+$	$-$	$q-q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{13}+q^{15}+\cdots$
6720.2.a.cq	$2$	$53.659$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$2$	$-2$	$+$	$+$	$-$	$+$	$q-q^{3}+q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
6720.2.a.cr	$2$	$53.659$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$2$	$-2$	$+$	$+$	$-$	$+$	$q-q^{3}+q^{5}-q^{7}+q^{9}+\beta q^{11}+(2+\cdots)q^{13}+\cdots$
6720.2.a.cs	$2$	$53.659$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$2$	$-2$	$-$	$+$	$-$	$+$	$q-q^{3}+q^{5}-q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
6720.2.a.ct	$2$	$53.659$	$\Q(\sqrt{17}) $	None	$0$	$-2$	$2$	$2$	$-$	$+$	$-$	$-$	$q-q^{3}+q^{5}+q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots$
6720.2.a.cu	$2$	$53.659$	$\Q(\sqrt{2}) $	None	$0$	$2$	$-2$	$-2$	$-$	$-$	$+$	$+$	$q+q^{3}-q^{5}-q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots$
6720.2.a.cv	$2$	$53.659$	$\Q(\sqrt{5}) $	None	$0$	$2$	$-2$	$-2$	$-$	$-$	$+$	$+$	$q+q^{3}-q^{5}-q^{7}+q^{9}-\beta q^{13}-q^{15}+\cdots$
6720.2.a.cw	$2$	$53.659$	$\Q(\sqrt{17}) $	None	$0$	$2$	$2$	$-2$	$-$	$-$	$-$	$+$	$q+q^{3}+q^{5}-q^{7}+q^{9}+(1+\beta )q^{11}+\cdots$
6720.2.a.cx	$2$	$53.659$	$\Q(\sqrt{5}) $	None	$0$	$2$	$2$	$2$	$+$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
6720.2.a.cy	$2$	$53.659$	$\Q(\sqrt{2}) $	None	$0$	$2$	$2$	$2$	$+$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{7}+q^{9}+\beta q^{11}+(2+\cdots)q^{13}+\cdots$
6720.2.a.cz	$2$	$53.659$	$\Q(\sqrt{3}) $	None	$0$	$2$	$2$	$2$	$+$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
6720.2.a.da	$3$	$53.659$	3.3.148.1	None	$0$	$-3$	$-3$	$3$	$+$	$+$	$+$	$-$	$q-q^{3}-q^{5}+q^{7}+q^{9}+(-1+\beta _{2})q^{11}+\cdots$
6720.2.a.db	$3$	$53.659$	3.3.148.1	None	$0$	$3$	$-3$	$-3$	$+$	$-$	$+$	$+$	$q+q^{3}-q^{5}-q^{7}+q^{9}+(1-\beta _{2})q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(6720))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6720 = 2^{6} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6720.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 80 \)
Sturm bound:			\(3072\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\), \(23\), \(29\), \(31\)

\(2\)	\(3\)	\(5\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(8\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(5\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(6\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(4\)
Plus space				\(+\)	\(40\)
Minus space				\(-\)	\(56\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6720))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6720))\) 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	6720.2.a

Level	$6720$
Weight	$2$
Character orbit	6720.a
Rep. character	$\chi_{6720}(1,\cdot)$
Character field	$\Q$
Dimension	$96$
Newform subspaces	$80$
Sturm bound	$3072$
Trace bound	$23$

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	7	$q$-expansion
6720.2.a.a	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6720.2.a.b	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.c	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6720.2.a.d	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6720.2.a.e	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6720.2.a.f	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
6720.2.a.g	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.h	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.i	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.j	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.k	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.l	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
6720.2.a.m	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.n	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.o	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.p	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
6720.2.a.q	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.r	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
6720.2.a.s	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}-q^{7}+q^{9}-6q^{13}-q^{15}+\cdots\)
6720.2.a.t	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.u	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
6720.2.a.v	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6720.2.a.w	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6720.2.a.x	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
6720.2.a.y	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6720.2.a.z	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.ba	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}-q^{15}+\cdots\)
6720.2.a.bb	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bc	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bd	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6720.2.a.be	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bf	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bg	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6720.2.a.bh	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bi	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bj	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bk	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}-q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
6720.2.a.bl	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bm	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
6720.2.a.bn	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bo	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bp	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bq	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.br	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bs	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6720.2.a.bt	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6720.2.a.bu	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
6720.2.a.bv	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6720.2.a.bw	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bx	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6720.2.a.by	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bz	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.ca	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6720.2.a.cb	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6720.2.a.cc	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.cd	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.ce	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
6720.2.a.cf	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6720.2.a.cg	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.ch	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
6720.2.a.ci	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
6720.2.a.cj	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6720.2.a.ck	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{7}+q^{9}-6q^{13}+q^{15}+\cdots\)
6720.2.a.cl	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.cm	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
6720.2.a.cn	\(1\)	\(53.659\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6720.2.a.co	\(2\)	\(53.659\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-2\)	\(2\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
6720.2.a.cp	\(2\)	\(53.659\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(-2\)	\(2\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{13}+q^{15}+\cdots\)
6720.2.a.cq	\(2\)	\(53.659\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(2\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
6720.2.a.cr	\(2\)	\(53.659\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(2\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}-q^{7}+q^{9}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
6720.2.a.cs	\(2\)	\(53.659\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(2\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+q^{5}-q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
6720.2.a.ct	\(2\)	\(53.659\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(-2\)	\(2\)	\(2\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+q^{5}+q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
6720.2.a.cu	\(2\)	\(53.659\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-2\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}-q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
6720.2.a.cv	\(2\)	\(53.659\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(2\)	\(-2\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}-q^{7}+q^{9}-\beta q^{13}-q^{15}+\cdots\)
6720.2.a.cw	\(2\)	\(53.659\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(2\)	\(2\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}-q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
6720.2.a.cx	\(2\)	\(53.659\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(2\)	\(2\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
6720.2.a.cy	\(2\)	\(53.659\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(2\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{7}+q^{9}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
6720.2.a.cz	\(2\)	\(53.659\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(2\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
6720.2.a.da	\(3\)	\(53.659\)	3.3.148.1	None	\(0\)	\(-3\)	\(-3\)	\(3\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+q^{7}+q^{9}+(-1+\beta _{2})q^{11}+\cdots\)
6720.2.a.db	\(3\)	\(53.659\)	3.3.148.1	None	\(0\)	\(3\)	\(-3\)	\(-3\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}-q^{7}+q^{9}+(1-\beta _{2})q^{11}+\cdots\)