LMFDB - Space of modular forms of level 9800, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9800.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 81 $
Sturm bound:			$3360$
Trace bound:			$23$
Distinguishing $T_p$:			$3$, $11$, $13$, $19$, $23$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9800))$.

	Total	New	Old
Modular forms	1776	195	1581
Cusp forms	1585	195	1390
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.

$2$	$5$	$7$	Fricke	Dim.
$+$	$+$	$+$	$+$	$19$
$+$	$+$	$-$	$-$	$26$
$+$	$-$	$+$	$-$	$28$
$+$	$-$	$-$	$+$	$24$
$-$	$+$	$+$	$-$	$25$
$-$	$+$	$-$	$+$	$22$
$-$	$-$	$+$	$+$	$24$
$-$	$-$	$-$	$-$	$27$
Plus space			$+$	$89$
Minus space			$-$	$106$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9800))$ 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	5	7	$q$-expansion
9800.2.a.a	$1$	$78.253$	$\Q$	None	$0$	$-3$	$0$	$0$	$-$	$+$	$-$	$q-3q^{3}+6q^{9}-5q^{11}-5q^{13}-7q^{17}+\cdots$
9800.2.a.b	$1$	$78.253$	$\Q$	None	$0$	$-3$	$0$	$0$	$+$	$+$	$+$	$q-3q^{3}+6q^{9}-q^{11}-2q^{13}-3q^{17}+\cdots$
9800.2.a.c	$1$	$78.253$	$\Q$	None	$0$	$-3$	$0$	$0$	$-$	$+$	$-$	$q-3q^{3}+6q^{9}+q^{11}+4q^{13}+5q^{17}+\cdots$
9800.2.a.d	$1$	$78.253$	$\Q$	None	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$q-2q^{3}+q^{9}-4q^{11}-4q^{13}+4q^{19}+\cdots$
9800.2.a.e	$1$	$78.253$	$\Q$	None	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$q-2q^{3}+q^{9}-3q^{11}+2q^{13}-4q^{17}+\cdots$
9800.2.a.f	$1$	$78.253$	$\Q$	None	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$q-2q^{3}+q^{9}-3q^{11}+2q^{13}-4q^{17}+\cdots$
9800.2.a.g	$1$	$78.253$	$\Q$	None	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$q-2q^{3}+q^{9}-q^{11}-3q^{13}-2q^{17}+\cdots$
9800.2.a.h	$1$	$78.253$	$\Q$	None	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$q-2q^{3}+q^{9}+q^{11}-4q^{13}-6q^{19}+\cdots$
9800.2.a.i	$1$	$78.253$	$\Q$	None	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$q-2q^{3}+q^{9}+4q^{11}-2q^{13}+2q^{19}+\cdots$
9800.2.a.j	$1$	$78.253$	$\Q$	None	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$q-2q^{3}+q^{9}+4q^{11}+2q^{13}+3q^{17}+\cdots$
9800.2.a.k	$1$	$78.253$	$\Q$	None	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$q-2q^{3}+q^{9}+4q^{11}+2q^{13}+3q^{17}+\cdots$
9800.2.a.l	$1$	$78.253$	$\Q$	None	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$q-2q^{3}+q^{9}+5q^{11}-8q^{17}+2q^{19}+\cdots$
9800.2.a.m	$1$	$78.253$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{9}-5q^{11}-7q^{13}+3q^{17}+\cdots$
9800.2.a.n	$1$	$78.253$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{9}-5q^{11}+q^{13}+3q^{17}+\cdots$
9800.2.a.o	$1$	$78.253$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{9}-2q^{11}+4q^{13}-6q^{19}+\cdots$
9800.2.a.p	$1$	$78.253$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$-$	$-$	$q-q^{3}-2q^{9}-q^{11}+q^{13}+3q^{17}+\cdots$
9800.2.a.q	$1$	$78.253$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$-$	$-$	$q-q^{3}-2q^{9}-q^{11}+6q^{13}-7q^{17}+\cdots$
9800.2.a.r	$1$	$78.253$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$q-q^{3}-2q^{9}+2q^{11}-4q^{17}-2q^{19}+\cdots$
9800.2.a.s	$1$	$78.253$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{9}+3q^{11}-6q^{13}-5q^{17}+\cdots$
9800.2.a.t	$1$	$78.253$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{9}+3q^{11}+q^{13}-5q^{17}+\cdots$
9800.2.a.u	$1$	$78.253$	$\Q$	None	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$q-3q^{9}-4q^{11}+2q^{13}-6q^{17}-8q^{19}+\cdots$
9800.2.a.v	$1$	$78.253$	$\Q$	None	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$q-3q^{9}+q^{11}-2q^{13}-4q^{17}+2q^{19}+\cdots$
9800.2.a.w	$1$	$78.253$	$\Q$	None	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$q-3q^{9}+q^{11}+2q^{13}+4q^{17}+2q^{19}+\cdots$
9800.2.a.x	$1$	$78.253$	$\Q$	None	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$q-3q^{9}+4q^{11}-2q^{13}+2q^{17}-4q^{19}+\cdots$
9800.2.a.y	$1$	$78.253$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$+$	$-$	$q+q^{3}-2q^{9}-5q^{11}+7q^{13}-3q^{17}+\cdots$
9800.2.a.z	$1$	$78.253$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$+$	$+$	$q+q^{3}-2q^{9}-2q^{11}-4q^{13}+6q^{19}+\cdots$
9800.2.a.ba	$1$	$78.253$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$+$	$-$	$q+q^{3}-2q^{9}-q^{11}-6q^{13}+7q^{17}+\cdots$
9800.2.a.bb	$1$	$78.253$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}-2q^{9}-q^{11}-q^{13}-3q^{17}+\cdots$
9800.2.a.bc	$1$	$78.253$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$+$	$-$	$q+q^{3}-2q^{9}+2q^{11}+4q^{17}+2q^{19}+\cdots$
9800.2.a.bd	$1$	$78.253$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$+$	$-$	$q+q^{3}-2q^{9}+3q^{11}-q^{13}+5q^{17}+\cdots$
9800.2.a.be	$1$	$78.253$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$+$	$+$	$q+q^{3}-2q^{9}+3q^{11}+6q^{13}+5q^{17}+\cdots$
9800.2.a.bf	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$q+2q^{3}+q^{9}-4q^{11}+4q^{13}+4q^{19}+\cdots$
9800.2.a.bg	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$q+2q^{3}+q^{9}-3q^{11}-2q^{13}+4q^{17}+\cdots$
9800.2.a.bh	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$+$	$-$	$-$	$q+2q^{3}+q^{9}-3q^{11}-2q^{13}+4q^{17}+\cdots$
9800.2.a.bi	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$+$	$+$	$+$	$q+2q^{3}+q^{9}-q^{11}+3q^{13}+2q^{17}+\cdots$
9800.2.a.bj	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$q+2q^{3}+q^{9}-2q^{17}+2q^{19}-8q^{23}+\cdots$
9800.2.a.bk	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$q+2q^{3}+q^{9}+q^{11}+4q^{13}-6q^{19}+\cdots$
9800.2.a.bl	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$q+2q^{3}+q^{9}+4q^{11}-2q^{13}-3q^{17}+\cdots$
9800.2.a.bm	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$+$	$-$	$+$	$q+2q^{3}+q^{9}+4q^{11}-2q^{13}-3q^{17}+\cdots$
9800.2.a.bn	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$+$	$+$	$-$	$q+2q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{19}+\cdots$
9800.2.a.bo	$1$	$78.253$	$\Q$	None	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$q+2q^{3}+q^{9}+5q^{11}+8q^{17}+2q^{19}+\cdots$
9800.2.a.bp	$1$	$78.253$	$\Q$	None	$0$	$3$	$0$	$0$	$+$	$+$	$-$	$q+3q^{3}+6q^{9}-q^{11}+2q^{13}+3q^{17}+\cdots$
9800.2.a.bq	$1$	$78.253$	$\Q$	None	$0$	$3$	$0$	$0$	$+$	$-$	$-$	$q+3q^{3}+6q^{9}+q^{11}-4q^{13}-5q^{17}+\cdots$
9800.2.a.br	$2$	$78.253$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$q+(-1+\beta )q^{3}-2\beta q^{9}+(-2+2\beta )q^{11}+\cdots$
9800.2.a.bs	$2$	$78.253$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$+$	$+$	$+$	$q+(-1+\beta )q^{3}-2\beta q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots$
9800.2.a.bt	$2$	$78.253$	$\Q(\sqrt{17}) $	None	$0$	$-1$	$0$	$0$	$-$	$-$	$-$	$q-\beta q^{3}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots$
9800.2.a.bu	$2$	$78.253$	$\Q(\sqrt{33}) $	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-\beta q^{3}+(5+\beta )q^{9}+(4-\beta )q^{11}+(2+\cdots)q^{13}+\cdots$
9800.2.a.bv	$2$	$78.253$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$q+\beta q^{3}-q^{9}+6q^{11}-4\beta q^{13}+\beta q^{17}+\cdots$
9800.2.a.bw	$2$	$78.253$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$q+\beta q^{3}+5q^{9}-4q^{11}-\beta q^{13}-2\beta q^{17}+\cdots$
9800.2.a.bx	$2$	$78.253$	$\Q(\sqrt{17}) $	None	$0$	$1$	$0$	$0$	$+$	$+$	$-$	$q+\beta q^{3}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots$
9800.2.a.by	$2$	$78.253$	$\Q(\sqrt{17}) $	None	$0$	$1$	$0$	$0$	$+$	$+$	$-$	$q+\beta q^{3}+(1+\beta )q^{9}-\beta q^{11}+(2-3\beta )q^{13}+\cdots$
9800.2.a.bz	$2$	$78.253$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$+$	$+$	$+$	$q+(1+\beta )q^{3}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots$
9800.2.a.ca	$2$	$78.253$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$+$	$+$	$+$	$q+(1+\beta )q^{3}+2\beta q^{9}-q^{11}+(1-\beta )q^{13}+\cdots$
9800.2.a.cb	$3$	$78.253$	$\Q(\zeta_{18})^+$	None	$0$	$-3$	$0$	$0$	$-$	$+$	$-$	$q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+\cdots$
9800.2.a.cc	$3$	$78.253$	$\Q(\zeta_{18})^+$	None	$0$	$-3$	$0$	$0$	$+$	$-$	$+$	$q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+\cdots$
9800.2.a.cd	$3$	$78.253$	3.3.568.1	None	$0$	$-1$	$0$	$0$	$+$	$-$	$-$	$q-\beta _{1}q^{3}+(1+2\beta _{1}+\beta _{2})q^{9}+(2-\beta _{2})q^{11}+\cdots$
9800.2.a.ce	$3$	$78.253$	3.3.1944.1	None	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$q+\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
9800.2.a.cf	$3$	$78.253$	3.3.1944.1	None	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$q-\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
9800.2.a.cg	$3$	$78.253$	3.3.568.1	None	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$q+\beta _{1}q^{3}+(1+2\beta _{1}+\beta _{2})q^{9}+(2-\beta _{2})q^{11}+\cdots$
9800.2.a.ch	$3$	$78.253$	$\Q(\zeta_{18})^+$	None	$0$	$3$	$0$	$0$	$+$	$-$	$-$	$q+(1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+(-2+\cdots)q^{11}+\cdots$
9800.2.a.ci	$3$	$78.253$	$\Q(\zeta_{18})^+$	None	$0$	$3$	$0$	$0$	$-$	$+$	$+$	$q+(1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+(-2+\cdots)q^{11}+\cdots$
9800.2.a.cj	$4$	$78.253$	4.4.43449.1	None	$0$	$-3$	$0$	$0$	$-$	$-$	$+$	$q+(-1+\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots$
9800.2.a.ck	$4$	$78.253$	4.4.43449.1	None	$0$	$-3$	$0$	$0$	$+$	$+$	$-$	$q+(-1+\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots$
9800.2.a.cl	$4$	$78.253$	4.4.16448.2	None	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$q-\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
9800.2.a.cm	$4$	$78.253$	$\Q(\sqrt{2}, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$q+\beta _{1}q^{3}+\beta _{3}q^{9}-q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots$
9800.2.a.cn	$4$	$78.253$	$\Q(\sqrt{2}, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$q+\beta _{1}q^{3}+\beta _{3}q^{9}-q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots$
9800.2.a.co	$4$	$78.253$	4.4.13448.1	None	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(2+\beta _{2})q^{11}+\cdots$
9800.2.a.cp	$4$	$78.253$	4.4.13448.1	None	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(2+\beta _{2})q^{11}+\cdots$
9800.2.a.cq	$4$	$78.253$	$\Q(\sqrt{7}, \sqrt{15})$	None	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$q+\beta _{2}q^{3}+(2-\beta _{3})q^{9}+q^{11}+(\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots$
9800.2.a.cr	$4$	$78.253$	$\Q(\sqrt{7}, \sqrt{15})$	None	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$q+\beta _{2}q^{3}+(2-\beta _{3})q^{9}+q^{11}+(\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots$
9800.2.a.cs	$4$	$78.253$	4.4.16448.2	None	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$q+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
9800.2.a.ct	$4$	$78.253$	4.4.43449.1	None	$0$	$3$	$0$	$0$	$+$	$+$	$+$	$q+(1-\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
9800.2.a.cu	$4$	$78.253$	4.4.43449.1	None	$0$	$3$	$0$	$0$	$-$	$-$	$-$	$q+(1-\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
9800.2.a.cv	$6$	$78.253$	6.6.239575536.1	None	$0$	$-1$	$0$	$0$	$-$	$-$	$+$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots$
9800.2.a.cw	$6$	$78.253$	6.6.239575536.1	None	$0$	$-1$	$0$	$0$	$+$	$-$	$-$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots$
9800.2.a.cx	$6$	$78.253$	6.6.239575536.1	None	$0$	$1$	$0$	$0$	$+$	$-$	$+$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots$
9800.2.a.cy	$6$	$78.253$	6.6.239575536.1	None	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots$
9800.2.a.cz	$8$	$78.253$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$q+\beta _{1}q^{3}+(2+\beta _{2})q^{9}+(1+\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots$
9800.2.a.da	$8$	$78.253$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$q+\beta _{1}q^{3}+(2+\beta _{2})q^{9}+(1+\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots$
9800.2.a.db	$10$	$78.253$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$q+\beta _{7}q^{3}+(1-\beta _{4}-\beta _{8})q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
9800.2.a.dc	$10$	$78.253$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$q+\beta _{7}q^{3}+(1-\beta _{4}-\beta _{8})q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9800))$ into lower level spaces

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Level:	\( N \)	\(=\)	\( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9800.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 81 \)
Sturm bound:			\(3360\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\), \(19\), \(23\)

\(2\)	\(5\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(19\)
\(+\)	\(+\)	\(-\)	\(-\)	\(26\)
\(+\)	\(-\)	\(+\)	\(-\)	\(28\)
\(+\)	\(-\)	\(-\)	\(+\)	\(24\)
\(-\)	\(+\)	\(+\)	\(-\)	\(25\)
\(-\)	\(+\)	\(-\)	\(+\)	\(22\)
\(-\)	\(-\)	\(+\)	\(+\)	\(24\)
\(-\)	\(-\)	\(-\)	\(-\)	\(27\)
Plus space			\(+\)	\(89\)
Minus space			\(-\)	\(106\)

Introduction

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9800))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9800))\) 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	9800.2.a

Level	$9800$
Weight	$2$
Character orbit	9800.a
Rep. character	$\chi_{9800}(1,\cdot)$
Character field	$\Q$
Dimension	$195$
Newform subspaces	$81$
Sturm bound	$3360$
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	5	7	$q$-expansion
9800.2.a.a	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-3q^{3}+6q^{9}-5q^{11}-5q^{13}-7q^{17}+\cdots\)
9800.2.a.b	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-3q^{3}+6q^{9}-q^{11}-2q^{13}-3q^{17}+\cdots\)
9800.2.a.c	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-3q^{3}+6q^{9}+q^{11}+4q^{13}+5q^{17}+\cdots\)
9800.2.a.d	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-2q^{3}+q^{9}-4q^{11}-4q^{13}+4q^{19}+\cdots\)
9800.2.a.e	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-2q^{3}+q^{9}-3q^{11}+2q^{13}-4q^{17}+\cdots\)
9800.2.a.f	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-2q^{3}+q^{9}-3q^{11}+2q^{13}-4q^{17}+\cdots\)
9800.2.a.g	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-2q^{3}+q^{9}-q^{11}-3q^{13}-2q^{17}+\cdots\)
9800.2.a.h	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-2q^{3}+q^{9}+q^{11}-4q^{13}-6q^{19}+\cdots\)
9800.2.a.i	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-2q^{3}+q^{9}+4q^{11}-2q^{13}+2q^{19}+\cdots\)
9800.2.a.j	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-2q^{3}+q^{9}+4q^{11}+2q^{13}+3q^{17}+\cdots\)
9800.2.a.k	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-2q^{3}+q^{9}+4q^{11}+2q^{13}+3q^{17}+\cdots\)
9800.2.a.l	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-2q^{3}+q^{9}+5q^{11}-8q^{17}+2q^{19}+\cdots\)
9800.2.a.m	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{9}-5q^{11}-7q^{13}+3q^{17}+\cdots\)
9800.2.a.n	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-2q^{9}-5q^{11}+q^{13}+3q^{17}+\cdots\)
9800.2.a.o	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-2q^{9}-2q^{11}+4q^{13}-6q^{19}+\cdots\)
9800.2.a.p	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q-q^{3}-2q^{9}-q^{11}+q^{13}+3q^{17}+\cdots\)
9800.2.a.q	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q-q^{3}-2q^{9}-q^{11}+6q^{13}-7q^{17}+\cdots\)
9800.2.a.r	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-2q^{9}+2q^{11}-4q^{17}-2q^{19}+\cdots\)
9800.2.a.s	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-2q^{9}+3q^{11}-6q^{13}-5q^{17}+\cdots\)
9800.2.a.t	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-2q^{9}+3q^{11}+q^{13}-5q^{17}+\cdots\)
9800.2.a.u	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-3q^{9}-4q^{11}+2q^{13}-6q^{17}-8q^{19}+\cdots\)
9800.2.a.v	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-3q^{9}+q^{11}-2q^{13}-4q^{17}+2q^{19}+\cdots\)
9800.2.a.w	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-3q^{9}+q^{11}+2q^{13}+4q^{17}+2q^{19}+\cdots\)
9800.2.a.x	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-3q^{9}+4q^{11}-2q^{13}+2q^{17}-4q^{19}+\cdots\)
9800.2.a.y	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+q^{3}-2q^{9}-5q^{11}+7q^{13}-3q^{17}+\cdots\)
9800.2.a.z	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-2q^{9}-2q^{11}-4q^{13}+6q^{19}+\cdots\)
9800.2.a.ba	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+q^{3}-2q^{9}-q^{11}-6q^{13}+7q^{17}+\cdots\)
9800.2.a.bb	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}-2q^{9}-q^{11}-q^{13}-3q^{17}+\cdots\)
9800.2.a.bc	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+q^{3}-2q^{9}+2q^{11}+4q^{17}+2q^{19}+\cdots\)
9800.2.a.bd	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-2q^{9}+3q^{11}-q^{13}+5q^{17}+\cdots\)
9800.2.a.be	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-2q^{9}+3q^{11}+6q^{13}+5q^{17}+\cdots\)
9800.2.a.bf	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+2q^{3}+q^{9}-4q^{11}+4q^{13}+4q^{19}+\cdots\)
9800.2.a.bg	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+2q^{3}+q^{9}-3q^{11}-2q^{13}+4q^{17}+\cdots\)
9800.2.a.bh	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+2q^{3}+q^{9}-3q^{11}-2q^{13}+4q^{17}+\cdots\)
9800.2.a.bi	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q+2q^{3}+q^{9}-q^{11}+3q^{13}+2q^{17}+\cdots\)
9800.2.a.bj	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+2q^{3}+q^{9}-2q^{17}+2q^{19}-8q^{23}+\cdots\)
9800.2.a.bk	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+2q^{3}+q^{9}+q^{11}+4q^{13}-6q^{19}+\cdots\)
9800.2.a.bl	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+2q^{3}+q^{9}+4q^{11}-2q^{13}-3q^{17}+\cdots\)
9800.2.a.bm	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+2q^{3}+q^{9}+4q^{11}-2q^{13}-3q^{17}+\cdots\)
9800.2.a.bn	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+2q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{19}+\cdots\)
9800.2.a.bo	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+2q^{3}+q^{9}+5q^{11}+8q^{17}+2q^{19}+\cdots\)
9800.2.a.bp	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+3q^{3}+6q^{9}-q^{11}+2q^{13}+3q^{17}+\cdots\)
9800.2.a.bq	\(1\)	\(78.253\)	\(\Q\)	None	\(0\)	\(3\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+3q^{3}+6q^{9}+q^{11}-4q^{13}-5q^{17}+\cdots\)
9800.2.a.br	\(2\)	\(78.253\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+(-1+\beta )q^{3}-2\beta q^{9}+(-2+2\beta )q^{11}+\cdots\)
9800.2.a.bs	\(2\)	\(78.253\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q+(-1+\beta )q^{3}-2\beta q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
9800.2.a.bt	\(2\)	\(78.253\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q-\beta q^{3}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots\)
9800.2.a.bu	\(2\)	\(78.253\)	\(\Q(\sqrt{33}) \)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-\beta q^{3}+(5+\beta )q^{9}+(4-\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
9800.2.a.bv	\(2\)	\(78.253\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q+\beta q^{3}-q^{9}+6q^{11}-4\beta q^{13}+\beta q^{17}+\cdots\)
9800.2.a.bw	\(2\)	\(78.253\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+\beta q^{3}+5q^{9}-4q^{11}-\beta q^{13}-2\beta q^{17}+\cdots\)
9800.2.a.bx	\(2\)	\(78.253\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+\beta q^{3}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots\)
9800.2.a.by	\(2\)	\(78.253\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+\beta q^{3}+(1+\beta )q^{9}-\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
9800.2.a.bz	\(2\)	\(78.253\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q+(1+\beta )q^{3}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots\)
9800.2.a.ca	\(2\)	\(78.253\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q+(1+\beta )q^{3}+2\beta q^{9}-q^{11}+(1-\beta )q^{13}+\cdots\)
9800.2.a.cb	\(3\)	\(78.253\)	\(\Q(\zeta_{18})^+\)	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+\cdots\)
9800.2.a.cc	\(3\)	\(78.253\)	\(\Q(\zeta_{18})^+\)	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+\cdots\)
9800.2.a.cd	\(3\)	\(78.253\)	3.3.568.1	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-\beta _{1}q^{3}+(1+2\beta _{1}+\beta _{2})q^{9}+(2-\beta _{2})q^{11}+\cdots\)
9800.2.a.ce	\(3\)	\(78.253\)	3.3.1944.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
9800.2.a.cf	\(3\)	\(78.253\)	3.3.1944.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
9800.2.a.cg	\(3\)	\(78.253\)	3.3.568.1	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{1}q^{3}+(1+2\beta _{1}+\beta _{2})q^{9}+(2-\beta _{2})q^{11}+\cdots\)
9800.2.a.ch	\(3\)	\(78.253\)	\(\Q(\zeta_{18})^+\)	None	\(0\)	\(3\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+(1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+(-2+\cdots)q^{11}+\cdots\)
9800.2.a.ci	\(3\)	\(78.253\)	\(\Q(\zeta_{18})^+\)	None	\(0\)	\(3\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(1-\beta _{1})q^{3}+(-2\beta _{1}+\beta _{2})q^{9}+(-2+\cdots)q^{11}+\cdots\)
9800.2.a.cj	\(4\)	\(78.253\)	4.4.43449.1	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+(-1+\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots\)
9800.2.a.ck	\(4\)	\(78.253\)	4.4.43449.1	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+(-1+\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots\)
9800.2.a.cl	\(4\)	\(78.253\)	4.4.16448.2	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
9800.2.a.cm	\(4\)	\(78.253\)	\(\Q(\sqrt{2}, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+\beta _{1}q^{3}+\beta _{3}q^{9}-q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
9800.2.a.cn	\(4\)	\(78.253\)	\(\Q(\sqrt{2}, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q+\beta _{1}q^{3}+\beta _{3}q^{9}-q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
9800.2.a.co	\(4\)	\(78.253\)	4.4.13448.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9800.2.a.cp	\(4\)	\(78.253\)	4.4.13448.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9800.2.a.cq	\(4\)	\(78.253\)	\(\Q(\sqrt{7}, \sqrt{15})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{2}q^{3}+(2-\beta _{3})q^{9}+q^{11}+(\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
9800.2.a.cr	\(4\)	\(78.253\)	\(\Q(\sqrt{7}, \sqrt{15})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+\beta _{2}q^{3}+(2-\beta _{3})q^{9}+q^{11}+(\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
9800.2.a.cs	\(4\)	\(78.253\)	4.4.16448.2	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
9800.2.a.ct	\(4\)	\(78.253\)	4.4.43449.1	None	\(0\)	\(3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q+(1-\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
9800.2.a.cu	\(4\)	\(78.253\)	4.4.43449.1	None	\(0\)	\(3\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+(1-\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
9800.2.a.cv	\(6\)	\(78.253\)	6.6.239575536.1	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q-\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)
9800.2.a.cw	\(6\)	\(78.253\)	6.6.239575536.1	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)
9800.2.a.cx	\(6\)	\(78.253\)	6.6.239575536.1	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)
9800.2.a.cy	\(6\)	\(78.253\)	6.6.239575536.1	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)
9800.2.a.cz	\(8\)	\(78.253\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{1}q^{3}+(2+\beta _{2})q^{9}+(1+\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots\)
9800.2.a.da	\(8\)	\(78.253\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{3}+(2+\beta _{2})q^{9}+(1+\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots\)
9800.2.a.db	\(10\)	\(78.253\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+\beta _{7}q^{3}+(1-\beta _{4}-\beta _{8})q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
9800.2.a.dc	\(10\)	\(78.253\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{7}q^{3}+(1-\beta _{4}-\beta _{8})q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)