LMFDB - Space of modular forms of level 9600, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 9600 = 2^{7} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9600.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 100 $
Sturm bound:			$3840$
Trace bound:			$17$
Distinguishing $T_p$:			$7$, $11$, $13$, $17$, $29$, $31$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9600))$.

	Total	New	Old
Modular forms	2016	152	1864
Cusp forms	1825	152	1673
Eisenstein series	191	0	191

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.
$+$	$+$	$+$	$+$	$17$
$+$	$+$	$-$	$-$	$22$
$+$	$-$	$+$	$-$	$19$
$+$	$-$	$-$	$+$	$18$
$-$	$+$	$+$	$-$	$19$
$-$	$+$	$-$	$+$	$18$
$-$	$-$	$+$	$+$	$17$
$-$	$-$	$-$	$-$	$22$
Plus space			$+$	$70$
Minus space			$-$	$82$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9600))$ 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
9600.2.a.a	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$-4$	$+$	$+$	$+$	$q-q^{3}-4q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots$
9600.2.a.b	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$-4$	$-$	$+$	$+$	$q-q^{3}-4q^{7}+q^{9}-2q^{11}+4q^{21}+\cdots$
9600.2.a.c	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$-4$	$+$	$+$	$-$	$q-q^{3}-4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots$
9600.2.a.d	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$-4$	$+$	$+$	$-$	$q-q^{3}-4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots$
9600.2.a.e	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$-2$	$-$	$+$	$+$	$q-q^{3}-2q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
9600.2.a.f	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$-2$	$-$	$+$	$+$	$q-q^{3}-2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$
9600.2.a.g	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$-2$	$+$	$+$	$+$	$q-q^{3}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
9600.2.a.h	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$-2$	$-$	$+$	$+$	$q-q^{3}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
9600.2.a.i	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$-2$	$-$	$+$	$+$	$q-q^{3}-2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots$
9600.2.a.j	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}-4q^{11}-2q^{13}+2q^{17}+\cdots$
9600.2.a.k	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots$
9600.2.a.l	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$q-q^{3}+q^{9}-2q^{11}-4q^{13}-q^{27}+\cdots$
9600.2.a.m	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{9}-2q^{11}-2q^{13}-2q^{17}+\cdots$
9600.2.a.n	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}-2q^{11}+2q^{13}-2q^{17}+\cdots$
9600.2.a.o	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$q-q^{3}+q^{9}-2q^{11}+4q^{13}-q^{27}+\cdots$
9600.2.a.p	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}+2q^{11}-2q^{13}+2q^{17}+\cdots$
9600.2.a.q	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}+2q^{11}+2q^{13}+2q^{17}+\cdots$
9600.2.a.r	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots$
9600.2.a.s	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots$
9600.2.a.t	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$2$	$+$	$+$	$+$	$q-q^{3}+2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
9600.2.a.u	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$2$	$-$	$+$	$+$	$q-q^{3}+2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots$
9600.2.a.v	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$2$	$+$	$+$	$+$	$q-q^{3}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
9600.2.a.w	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$2$	$-$	$+$	$+$	$q-q^{3}+2q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
9600.2.a.x	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$2$	$+$	$+$	$+$	$q-q^{3}+2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots$
9600.2.a.y	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$4$	$-$	$+$	$+$	$q-q^{3}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots$
9600.2.a.z	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$4$	$-$	$+$	$+$	$q-q^{3}+4q^{7}+q^{9}-2q^{11}-4q^{21}+\cdots$
9600.2.a.ba	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$4$	$-$	$+$	$-$	$q-q^{3}+4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots$
9600.2.a.bb	$1$	$76.656$	$\Q$	None	$0$	$-1$	$0$	$4$	$+$	$+$	$-$	$q-q^{3}+4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots$
9600.2.a.bc	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$-4$	$-$	$-$	$-$	$q+q^{3}-4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots$
9600.2.a.bd	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$-4$	$+$	$-$	$-$	$q+q^{3}-4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots$
9600.2.a.be	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$-4$	$-$	$-$	$+$	$q+q^{3}-4q^{7}+q^{9}+2q^{11}-4q^{21}+\cdots$
9600.2.a.bf	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$-4$	$+$	$-$	$+$	$q+q^{3}-4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$
9600.2.a.bg	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$-2$	$+$	$-$	$+$	$q+q^{3}-2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
9600.2.a.bh	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$-2$	$+$	$-$	$+$	$q+q^{3}-2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
9600.2.a.bi	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$-2$	$-$	$-$	$+$	$q+q^{3}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
9600.2.a.bj	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$-2$	$+$	$-$	$+$	$q+q^{3}-2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
9600.2.a.bk	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$-2$	$+$	$-$	$+$	$q+q^{3}-2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
9600.2.a.bl	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots$
9600.2.a.bm	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots$
9600.2.a.bn	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}-2q^{11}-2q^{13}+2q^{17}+\cdots$
9600.2.a.bo	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots$
9600.2.a.bp	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$q+q^{3}+q^{9}+2q^{11}-4q^{13}+q^{27}+\cdots$
9600.2.a.bq	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}+2q^{11}-2q^{13}-2q^{17}+\cdots$
9600.2.a.br	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}+2q^{11}+2q^{13}-2q^{17}+\cdots$
9600.2.a.bs	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$+$	$q+q^{3}+q^{9}+2q^{11}+4q^{13}+q^{27}+\cdots$
9600.2.a.bt	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}+4q^{11}-2q^{13}+2q^{17}+\cdots$
9600.2.a.bu	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots$
9600.2.a.bv	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$2$	$+$	$-$	$+$	$q+q^{3}+2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots$
9600.2.a.bw	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$2$	$-$	$-$	$+$	$q+q^{3}+2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
9600.2.a.bx	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$2$	$+$	$-$	$+$	$q+q^{3}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
9600.2.a.by	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$2$	$-$	$-$	$+$	$q+q^{3}+2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots$
9600.2.a.bz	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$2$	$+$	$-$	$+$	$q+q^{3}+2q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
9600.2.a.ca	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$4$	$-$	$-$	$-$	$q+q^{3}+4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots$
9600.2.a.cb	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$4$	$-$	$-$	$-$	$q+q^{3}+4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots$
9600.2.a.cc	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$4$	$+$	$-$	$+$	$q+q^{3}+4q^{7}+q^{9}+2q^{11}+4q^{21}+\cdots$
9600.2.a.cd	$1$	$76.656$	$\Q$	None	$0$	$1$	$0$	$4$	$+$	$-$	$+$	$q+q^{3}+4q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots$
9600.2.a.ce	$2$	$76.656$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$-2$	$+$	$+$	$-$	$q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots$
9600.2.a.cf	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
9600.2.a.cg	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$-2$	$0$	$-2$	$-$	$+$	$-$	$q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots$
9600.2.a.ch	$2$	$76.656$	$\Q(\sqrt{10}) $	None	$0$	$-2$	$0$	$-2$	$-$	$+$	$-$	$q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$
9600.2.a.ci	$2$	$76.656$	$\Q(\sqrt{10}) $	None	$0$	$-2$	$0$	$-2$	$+$	$+$	$+$	$q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots$
9600.2.a.cj	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$-2$	$0$	$-2$	$+$	$+$	$+$	$q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$
9600.2.a.ck	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$-2$	$0$	$-2$	$-$	$+$	$-$	$q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
9600.2.a.cl	$2$	$76.656$	$\Q(\sqrt{17}) $	None	$0$	$-2$	$0$	$-2$	$+$	$+$	$+$	$q-q^{3}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots$
9600.2.a.cm	$2$	$76.656$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$-2$	$+$	$+$	$+$	$q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots$
9600.2.a.cn	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$-2$	$0$	$2$	$-$	$+$	$+$	$q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
9600.2.a.co	$2$	$76.656$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$2$	$+$	$+$	$-$	$q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots$
9600.2.a.cp	$2$	$76.656$	$\Q(\sqrt{10}) $	None	$0$	$-2$	$0$	$2$	$+$	$+$	$+$	$q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots$
9600.2.a.cq	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$-2$	$0$	$2$	$-$	$+$	$+$	$q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots$
9600.2.a.cr	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$-2$	$0$	$2$	$-$	$+$	$-$	$q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots$
9600.2.a.cs	$2$	$76.656$	$\Q(\sqrt{10}) $	None	$0$	$-2$	$0$	$2$	$+$	$+$	$-$	$q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots$
9600.2.a.ct	$2$	$76.656$	$\Q(\sqrt{17}) $	None	$0$	$-2$	$0$	$2$	$-$	$+$	$+$	$q-q^{3}+(1+\beta )q^{7}+q^{9}+2q^{11}+(1+\cdots)q^{13}+\cdots$
9600.2.a.cu	$2$	$76.656$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$2$	$-$	$+$	$+$	$q-q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots$
9600.2.a.cv	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$-2$	$0$	$2$	$+$	$+$	$-$	$q-q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
9600.2.a.cw	$2$	$76.656$	$\Q(\sqrt{17}) $	None	$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$q+q^{3}+(-1-\beta )q^{7}+q^{9}-2q^{11}+\cdots$
9600.2.a.cx	$2$	$76.656$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots$
9600.2.a.cy	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$2$	$0$	$-2$	$+$	$-$	$-$	$q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
9600.2.a.cz	$2$	$76.656$	$\Q(\sqrt{10}) $	None	$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$
9600.2.a.da	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$2$	$0$	$-2$	$+$	$-$	$+$	$q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots$
9600.2.a.db	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$2$	$0$	$-2$	$+$	$-$	$-$	$q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$
9600.2.a.dc	$2$	$76.656$	$\Q(\sqrt{10}) $	None	$0$	$2$	$0$	$-2$	$-$	$-$	$-$	$q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots$
9600.2.a.dd	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
9600.2.a.de	$2$	$76.656$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$-2$	$+$	$-$	$-$	$q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots$
9600.2.a.df	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$2$	$0$	$2$	$+$	$-$	$-$	$q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
9600.2.a.dg	$2$	$76.656$	$\Q(\sqrt{17}) $	None	$0$	$2$	$0$	$2$	$-$	$-$	$+$	$q+q^{3}+(1+\beta )q^{7}+q^{9}-2q^{11}+(-1+\cdots)q^{13}+\cdots$
9600.2.a.dh	$2$	$76.656$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$2$	$-$	$-$	$+$	$q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots$
9600.2.a.di	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$2$	$0$	$2$	$-$	$-$	$-$	$q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots$
9600.2.a.dj	$2$	$76.656$	$\Q(\sqrt{10}) $	None	$0$	$2$	$0$	$2$	$-$	$-$	$-$	$q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots$
9600.2.a.dk	$2$	$76.656$	$\Q(\sqrt{10}) $	None	$0$	$2$	$0$	$2$	$+$	$-$	$+$	$q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots$
9600.2.a.dl	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$2$	$0$	$2$	$+$	$-$	$+$	$q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots$
9600.2.a.dm	$2$	$76.656$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$2$	$-$	$-$	$-$	$q+q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots$
9600.2.a.dn	$2$	$76.656$	$\Q(\sqrt{6}) $	None	$0$	$2$	$0$	$2$	$+$	$-$	$+$	$q+q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
9600.2.a.do	$3$	$76.656$	3.3.148.1	None	$0$	$-3$	$0$	$-4$	$-$	$+$	$-$	$q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots$
9600.2.a.dp	$3$	$76.656$	3.3.148.1	None	$0$	$-3$	$0$	$-4$	$+$	$+$	$-$	$q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots$
9600.2.a.dq	$3$	$76.656$	3.3.148.1	None	$0$	$-3$	$0$	$4$	$+$	$+$	$-$	$q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots$
9600.2.a.dr	$3$	$76.656$	3.3.148.1	None	$0$	$-3$	$0$	$4$	$+$	$+$	$-$	$q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots$
9600.2.a.ds	$3$	$76.656$	3.3.148.1	None	$0$	$3$	$0$	$-4$	$-$	$-$	$-$	$q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots$
9600.2.a.dt	$3$	$76.656$	3.3.148.1	None	$0$	$3$	$0$	$-4$	$-$	$-$	$-$	$q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots$
9600.2.a.du	$3$	$76.656$	3.3.148.1	None	$0$	$3$	$0$	$4$	$+$	$-$	$-$	$q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots$
9600.2.a.dv	$3$	$76.656$	3.3.148.1	None	$0$	$3$	$0$	$4$	$-$	$-$	$-$	$q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9600))$ 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:	\( N \)	\(=\)	\( 9600 = 2^{7} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9600.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 100 \)
Sturm bound:			\(3840\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(29\), \(31\)

\(2\)	\(3\)	\(5\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(17\)
\(+\)	\(+\)	\(-\)	\(-\)	\(22\)
\(+\)	\(-\)	\(+\)	\(-\)	\(19\)
\(+\)	\(-\)	\(-\)	\(+\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	\(19\)
\(-\)	\(+\)	\(-\)	\(+\)	\(18\)
\(-\)	\(-\)	\(+\)	\(+\)	\(17\)
\(-\)	\(-\)	\(-\)	\(-\)	\(22\)
Plus space			\(+\)	\(70\)
Minus space			\(-\)	\(82\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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Learn more about

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9600))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9600))\) 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	9600.2.a

Level	$9600$
Weight	$2$
Character orbit	9600.a
Rep. character	$\chi_{9600}(1,\cdot)$
Character field	$\Q$
Dimension	$152$
Newform subspaces	$100$
Sturm bound	$3840$
Trace bound	$17$

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
9600.2.a.a	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-4\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-4q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
9600.2.a.b	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-4\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-4q^{7}+q^{9}-2q^{11}+4q^{21}+\cdots\)
9600.2.a.c	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-4\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9600.2.a.d	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-4\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
9600.2.a.e	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-2q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
9600.2.a.f	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
9600.2.a.g	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
9600.2.a.h	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9600.2.a.i	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
9600.2.a.j	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.k	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.l	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+q^{9}-2q^{11}-4q^{13}-q^{27}+\cdots\)
9600.2.a.m	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}-2q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.n	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}-2q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.o	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+q^{9}-2q^{11}+4q^{13}-q^{27}+\cdots\)
9600.2.a.p	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.q	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}+2q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.r	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.s	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.t	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9600.2.a.u	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
9600.2.a.v	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
9600.2.a.w	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+2q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
9600.2.a.x	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
9600.2.a.y	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(4\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
9600.2.a.z	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(4\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+4q^{7}+q^{9}-2q^{11}-4q^{21}+\cdots\)
9600.2.a.ba	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(4\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
9600.2.a.bb	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(4\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
9600.2.a.bc	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-4\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
9600.2.a.bd	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}-4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
9600.2.a.be	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-4\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-4q^{7}+q^{9}+2q^{11}-4q^{21}+\cdots\)
9600.2.a.bf	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-4\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}-4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
9600.2.a.bg	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}-2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
9600.2.a.bh	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}-2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9600.2.a.bi	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
9600.2.a.bj	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}-2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
9600.2.a.bk	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}-2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9600.2.a.bl	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.bm	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.bn	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.bo	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.bp	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{9}+2q^{11}-4q^{13}+q^{27}+\cdots\)
9600.2.a.bq	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}+2q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.br	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}+2q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.bs	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+q^{9}+2q^{11}+4q^{13}+q^{27}+\cdots\)
9600.2.a.bt	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.bu	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.bv	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
9600.2.a.bw	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
9600.2.a.bx	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
9600.2.a.by	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
9600.2.a.bz	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+2q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
9600.2.a.ca	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9600.2.a.cb	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
9600.2.a.cc	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(4\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+4q^{7}+q^{9}+2q^{11}+4q^{21}+\cdots\)
9600.2.a.cd	\(1\)	\(76.656\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(4\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+4q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
9600.2.a.ce	\(2\)	\(76.656\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
9600.2.a.cf	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
9600.2.a.cg	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.ch	\(2\)	\(76.656\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.ci	\(2\)	\(76.656\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.cj	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.ck	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
9600.2.a.cl	\(2\)	\(76.656\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots\)
9600.2.a.cm	\(2\)	\(76.656\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots\)
9600.2.a.cn	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9600.2.a.co	\(2\)	\(76.656\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots\)
9600.2.a.cp	\(2\)	\(76.656\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
9600.2.a.cq	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.cr	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.cs	\(2\)	\(76.656\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
9600.2.a.ct	\(2\)	\(76.656\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+2q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.cu	\(2\)	\(76.656\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
9600.2.a.cv	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(-2\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
9600.2.a.cw	\(2\)	\(76.656\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1-\beta )q^{7}+q^{9}-2q^{11}+\cdots\)
9600.2.a.cx	\(2\)	\(76.656\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
9600.2.a.cy	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
9600.2.a.cz	\(2\)	\(76.656\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.da	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.db	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.dc	\(2\)	\(76.656\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.dd	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
9600.2.a.de	\(2\)	\(76.656\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots\)
9600.2.a.df	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9600.2.a.dg	\(2\)	\(76.656\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(1+\beta )q^{7}+q^{9}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.dh	\(2\)	\(76.656\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots\)
9600.2.a.di	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.dj	\(2\)	\(76.656\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
9600.2.a.dk	\(2\)	\(76.656\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
9600.2.a.dl	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.dm	\(2\)	\(76.656\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
9600.2.a.dn	\(2\)	\(76.656\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
9600.2.a.do	\(3\)	\(76.656\)	3.3.148.1	None	\(0\)	\(-3\)	\(0\)	\(-4\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dp	\(3\)	\(76.656\)	3.3.148.1	None	\(0\)	\(-3\)	\(0\)	\(-4\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.dq	\(3\)	\(76.656\)	3.3.148.1	None	\(0\)	\(-3\)	\(0\)	\(4\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dr	\(3\)	\(76.656\)	3.3.148.1	None	\(0\)	\(-3\)	\(0\)	\(4\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.ds	\(3\)	\(76.656\)	3.3.148.1	None	\(0\)	\(3\)	\(0\)	\(-4\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dt	\(3\)	\(76.656\)	3.3.148.1	None	\(0\)	\(3\)	\(0\)	\(-4\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.du	\(3\)	\(76.656\)	3.3.148.1	None	\(0\)	\(3\)	\(0\)	\(4\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dv	\(3\)	\(76.656\)	3.3.148.1	None	\(0\)	\(3\)	\(0\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)