LMFDB - Space of modular forms of level 8550, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8550.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 76 $
Sturm bound:			$3600$
Trace bound:			$23$
Distinguishing $T_p$:			$7$, $11$, $13$, $17$, $23$, $53$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8550))$.

	Total	New	Old
Modular forms	1848	143	1705
Cusp forms	1753	143	1610
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.

$2$	$3$	$5$	$19$	Fricke	Dim.
$+$	$+$	$+$	$+$	$+$	$7$
$+$	$+$	$+$	$-$	$-$	$6$
$+$	$+$	$-$	$+$	$-$	$7$
$+$	$+$	$-$	$-$	$+$	$9$
$+$	$-$	$+$	$+$	$-$	$12$
$+$	$-$	$+$	$-$	$+$	$8$
$+$	$-$	$-$	$+$	$+$	$10$
$+$	$-$	$-$	$-$	$-$	$12$
$-$	$+$	$+$	$+$	$-$	$7$
$-$	$+$	$+$	$-$	$+$	$6$
$-$	$+$	$-$	$+$	$+$	$7$
$-$	$+$	$-$	$-$	$-$	$9$
$-$	$-$	$+$	$+$	$+$	$8$
$-$	$-$	$+$	$-$	$-$	$13$
$-$	$-$	$-$	$+$	$-$	$13$
$-$	$-$	$-$	$-$	$+$	$9$
Plus space				$+$	$64$
Minus space				$-$	$79$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8550))$ 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	19	$q$-expansion
8550.2.a.a	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-4q^{11}+4q^{14}+\cdots$
8550.2.a.b	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$-4$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-2q^{13}+4q^{14}+\cdots$
8550.2.a.c	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$-4$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+q^{11}+4q^{14}+\cdots$
8550.2.a.d	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{11}-2q^{13}+\cdots$
8550.2.a.e	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{13}+2q^{14}+\cdots$
8550.2.a.f	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+3q^{11}-6q^{13}+\cdots$
8550.2.a.g	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+6q^{11}+2q^{14}+\cdots$
8550.2.a.h	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{8}-q^{11}-4q^{13}+q^{16}+\cdots$
8550.2.a.i	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{8}+2q^{11}+4q^{13}+\cdots$
8550.2.a.j	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{8}+4q^{11}-4q^{13}+\cdots$
8550.2.a.k	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{8}+4q^{11}+2q^{13}+\cdots$
8550.2.a.l	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{13}-q^{14}+\cdots$
8550.2.a.m	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}-5q^{13}+\cdots$
8550.2.a.n	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+2q^{7}-q^{8}-4q^{11}+6q^{13}+\cdots$
8550.2.a.o	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}-2q^{14}+\cdots$
8550.2.a.p	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$2$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}+4q^{13}+\cdots$
8550.2.a.q	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$4$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-6q^{11}-4q^{14}+\cdots$
8550.2.a.r	$1$	$68.272$	$\Q$	None	$-1$	$0$	$0$	$4$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}+4q^{7}-q^{8}+4q^{11}+6q^{13}+\cdots$
8550.2.a.s	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$-4$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}-4q^{7}+q^{8}+6q^{13}-4q^{14}+\cdots$
8550.2.a.t	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$-4$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-4q^{7}+q^{8}+4q^{11}+2q^{13}+\cdots$
8550.2.a.u	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$-3$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-3q^{7}+q^{8}-2q^{11}+q^{13}+\cdots$
8550.2.a.v	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots$
8550.2.a.w	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+4q^{11}-6q^{13}+\cdots$
8550.2.a.x	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}+q^{8}-4q^{11}-2q^{13}+\cdots$
8550.2.a.y	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}+q^{8}-2q^{11}+4q^{13}+\cdots$
8550.2.a.z	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}+q^{8}-q^{11}+4q^{13}+q^{16}+\cdots$
8550.2.a.ba	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}+q^{8}+4q^{11}-2q^{13}+\cdots$
8550.2.a.bb	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}+q^{8}+4q^{11}-2q^{13}+\cdots$
8550.2.a.bc	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}+q^{8}+4q^{11}+4q^{13}+\cdots$
8550.2.a.bd	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+q^{13}+q^{14}+\cdots$
8550.2.a.be	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{11}+2q^{13}+\cdots$
8550.2.a.bf	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots$
8550.2.a.bg	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+4q^{13}+\cdots$
8550.2.a.bh	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-6q^{13}+2q^{14}+\cdots$
8550.2.a.bi	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}+2q^{7}+q^{8}+3q^{11}+6q^{13}+\cdots$
8550.2.a.bj	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$4$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+4q^{13}+4q^{14}+\cdots$
8550.2.a.bk	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$4$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+q^{11}+4q^{14}+\cdots$
8550.2.a.bl	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$4$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+6q^{11}+4q^{14}+\cdots$
8550.2.a.bm	$1$	$68.272$	$\Q$	None	$1$	$0$	$0$	$5$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+5q^{7}+q^{8}+4q^{11}+q^{13}+\cdots$
8550.2.a.bn	$2$	$68.272$	$\Q(\sqrt{2}) $	None	$-2$	$0$	$0$	$-6$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}+(-3+\beta )q^{7}-q^{8}-\beta q^{11}+\cdots$
8550.2.a.bo	$2$	$68.272$	$\Q(\sqrt{3}) $	None	$-2$	$0$	$0$	$-4$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
8550.2.a.bp	$2$	$68.272$	$\Q(\sqrt{17}) $	None	$-2$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}+(-1-\beta )q^{7}-q^{8}+2q^{11}+\cdots$
8550.2.a.bq	$2$	$68.272$	$\Q(\sqrt{10}) $	None	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}+\beta q^{7}-q^{8}+(-1-\beta )q^{11}+\cdots$
8550.2.a.br	$2$	$68.272$	$\Q(\sqrt{17}) $	None	$-2$	$0$	$0$	$1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}+\beta q^{7}-q^{8}-4q^{11}+(2+\cdots)q^{13}+\cdots$
8550.2.a.bs	$2$	$68.272$	$\Q(\sqrt{3}) $	None	$-2$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}+(-2+\cdots)q^{11}+\cdots$
8550.2.a.bt	$2$	$68.272$	$\Q(\sqrt{3}) $	None	$-2$	$0$	$0$	$2$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}-3\beta q^{11}+\cdots$
8550.2.a.bu	$2$	$68.272$	$\Q(\sqrt{6}) $	None	$-2$	$0$	$0$	$4$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+(2+\beta )q^{7}-q^{8}+(-1+\cdots)q^{11}+\cdots$
8550.2.a.bv	$2$	$68.272$	$\Q(\sqrt{6}) $	None	$2$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}+(-1+\cdots)q^{11}+\cdots$
8550.2.a.bw	$2$	$68.272$	$\Q(\sqrt{3}) $	None	$2$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
8550.2.a.bx	$2$	$68.272$	$\Q(\sqrt{17}) $	None	$2$	$0$	$0$	$-2$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}-2q^{11}+\cdots$
8550.2.a.by	$2$	$68.272$	$\Q(\sqrt{3}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+(-2+\cdots)q^{11}+\cdots$
8550.2.a.bz	$2$	$68.272$	$\Q(\sqrt{3}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+3\beta q^{11}+\cdots$
8550.2.a.ca	$2$	$68.272$	$\Q(\sqrt{10}) $	None	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}+\beta q^{7}+q^{8}+(-1+\beta )q^{11}+\cdots$
8550.2.a.cb	$2$	$68.272$	$\Q(\sqrt{2}) $	None	$2$	$0$	$0$	$6$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}+(3+\beta )q^{7}+q^{8}+\beta q^{11}+\cdots$
8550.2.a.cc	$3$	$68.272$	3.3.788.1	None	$-3$	$0$	$0$	$-2$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}+(-1+\beta _{1})q^{7}-q^{8}+(1+\cdots)q^{11}+\cdots$
8550.2.a.cd	$3$	$68.272$	3.3.564.1	None	$-3$	$0$	$0$	$-2$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{7}-q^{8}+\cdots$
8550.2.a.ce	$3$	$68.272$	3.3.148.1	None	$-3$	$0$	$0$	$0$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+\beta _{2}q^{7}-q^{8}+(-3-\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.cf	$3$	$68.272$	3.3.148.1	None	$-3$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}+\beta _{2}q^{7}-q^{8}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.cg	$3$	$68.272$	3.3.564.1	None	$-3$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{7}-q^{8}+(-2+\cdots)q^{11}+\cdots$
8550.2.a.ch	$3$	$68.272$	3.3.788.1	None	$-3$	$0$	$0$	$2$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}+(1-\beta _{1})q^{7}-q^{8}+(-1+\cdots)q^{11}+\cdots$
8550.2.a.ci	$3$	$68.272$	3.3.993.1	None	$-3$	$0$	$0$	$2$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+(1-\beta _{2})q^{7}-q^{8}-2\beta _{1}q^{11}+\cdots$
8550.2.a.cj	$3$	$68.272$	3.3.257.1	None	$-3$	$0$	$0$	$2$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}+(1-\beta _{1}+2\beta _{2})q^{7}-q^{8}+\cdots$
8550.2.a.ck	$3$	$68.272$	3.3.568.1	None	$-3$	$0$	$0$	$4$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{7}-q^{8}+(\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.cl	$3$	$68.272$	3.3.568.1	None	$3$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+(-1-\beta _{1})q^{7}+q^{8}+(\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.cm	$3$	$68.272$	3.3.788.1	None	$3$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}+(-1+\beta _{1})q^{7}+q^{8}+(-1+\cdots)q^{11}+\cdots$
8550.2.a.cn	$3$	$68.272$	3.3.564.1	None	$3$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{7}+q^{8}+\cdots$
8550.2.a.co	$3$	$68.272$	3.3.257.1	None	$3$	$0$	$0$	$-2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots$
8550.2.a.cp	$3$	$68.272$	3.3.993.1	None	$3$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+(-1+\beta _{2})q^{7}+q^{8}-2\beta _{1}q^{11}+\cdots$
8550.2.a.cq	$3$	$68.272$	3.3.148.1	None	$3$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}-\beta _{2}q^{7}+q^{8}+(-3-\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.cr	$3$	$68.272$	3.3.148.1	None	$3$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-\beta _{2}q^{7}+q^{8}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.cs	$3$	$68.272$	3.3.564.1	None	$3$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{7}+q^{8}+(2+\cdots)q^{11}+\cdots$
8550.2.a.ct	$3$	$68.272$	3.3.788.1	None	$3$	$0$	$0$	$2$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}+(1-\beta _{1})q^{7}+q^{8}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.cu	$4$	$68.272$	$\Q(\zeta_{24})^+$	None	$-4$	$0$	$0$	$0$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}+\beta _{1}q^{7}-q^{8}-\beta _{3}q^{11}+\cdots$
8550.2.a.cv	$4$	$68.272$	$\Q(\zeta_{24})^+$	None	$4$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}+\beta _{1}q^{7}+q^{8}+\beta _{3}q^{11}+\cdots$
8550.2.a.cw	$6$	$68.272$	6.6.3356224.1	None	$-6$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+\beta _{1}q^{7}-q^{8}+(-\beta _{1}+\beta _{4}+\cdots)q^{11}+\cdots$
8550.2.a.cx	$6$	$68.272$	6.6.3356224.1	None	$6$	$0$	$0$	$0$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+\beta _{1}q^{7}+q^{8}+(\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8550))$ into lower level spaces

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Level:	\( N \)	\(=\)	\( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8550.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 76 \)
Sturm bound:			\(3600\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(23\), \(53\)

\(2\)	\(3\)	\(5\)	\(19\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(7\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(9\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(10\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(12\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(7\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(13\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(13\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(9\)
Plus space				\(+\)	\(64\)
Minus space				\(-\)	\(79\)

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Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8550))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8550))\) 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	8550.2.a

Level	$8550$
Weight	$2$
Character orbit	8550.a
Rep. character	$\chi_{8550}(1,\cdot)$
Character field	$\Q$
Dimension	$143$
Newform subspaces	$76$
Sturm bound	$3600$
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	19	$q$-expansion
8550.2.a.a	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-4\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}-4q^{7}-q^{8}-4q^{11}+4q^{14}+\cdots\)
8550.2.a.b	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-4\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-4q^{7}-q^{8}-2q^{13}+4q^{14}+\cdots\)
8550.2.a.c	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}-4q^{7}-q^{8}+q^{11}+4q^{14}+\cdots\)
8550.2.a.d	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{11}-2q^{13}+\cdots\)
8550.2.a.e	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{13}+2q^{14}+\cdots\)
8550.2.a.f	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-2q^{7}-q^{8}+3q^{11}-6q^{13}+\cdots\)
8550.2.a.g	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-2q^{7}-q^{8}+6q^{11}+2q^{14}+\cdots\)
8550.2.a.h	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{8}-q^{11}-4q^{13}+q^{16}+\cdots\)
8550.2.a.i	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{8}+2q^{11}+4q^{13}+\cdots\)
8550.2.a.j	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{8}+4q^{11}-4q^{13}+\cdots\)
8550.2.a.k	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{8}+4q^{11}+2q^{13}+\cdots\)
8550.2.a.l	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{13}-q^{14}+\cdots\)
8550.2.a.m	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}-5q^{13}+\cdots\)
8550.2.a.n	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+2q^{7}-q^{8}-4q^{11}+6q^{13}+\cdots\)
8550.2.a.o	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}-2q^{14}+\cdots\)
8550.2.a.p	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}+4q^{13}+\cdots\)
8550.2.a.q	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(4\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+4q^{7}-q^{8}-6q^{11}-4q^{14}+\cdots\)
8550.2.a.r	\(1\)	\(68.272\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(4\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+4q^{7}-q^{8}+4q^{11}+6q^{13}+\cdots\)
8550.2.a.s	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-4\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}-4q^{7}+q^{8}+6q^{13}-4q^{14}+\cdots\)
8550.2.a.t	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-4\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-4q^{7}+q^{8}+4q^{11}+2q^{13}+\cdots\)
8550.2.a.u	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-3\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-3q^{7}+q^{8}-2q^{11}+q^{13}+\cdots\)
8550.2.a.v	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}-2q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots\)
8550.2.a.w	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}-2q^{7}+q^{8}+4q^{11}-6q^{13}+\cdots\)
8550.2.a.x	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}-4q^{11}-2q^{13}+\cdots\)
8550.2.a.y	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}-2q^{11}+4q^{13}+\cdots\)
8550.2.a.z	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}-q^{11}+4q^{13}+q^{16}+\cdots\)
8550.2.a.ba	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}+4q^{11}-2q^{13}+\cdots\)
8550.2.a.bb	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}+4q^{11}-2q^{13}+\cdots\)
8550.2.a.bc	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+q^{8}+4q^{11}+4q^{13}+\cdots\)
8550.2.a.bd	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{13}+q^{14}+\cdots\)
8550.2.a.be	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{11}+2q^{13}+\cdots\)
8550.2.a.bf	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots\)
8550.2.a.bg	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+4q^{13}+\cdots\)
8550.2.a.bh	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-6q^{13}+2q^{14}+\cdots\)
8550.2.a.bi	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+2q^{7}+q^{8}+3q^{11}+6q^{13}+\cdots\)
8550.2.a.bj	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(4\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+4q^{7}+q^{8}+4q^{13}+4q^{14}+\cdots\)
8550.2.a.bk	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(4\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+4q^{7}+q^{8}+q^{11}+4q^{14}+\cdots\)
8550.2.a.bl	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(4\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+4q^{7}+q^{8}+6q^{11}+4q^{14}+\cdots\)
8550.2.a.bm	\(1\)	\(68.272\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(5\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+5q^{7}+q^{8}+4q^{11}+q^{13}+\cdots\)
8550.2.a.bn	\(2\)	\(68.272\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(0\)	\(0\)	\(-6\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}+(-3+\beta )q^{7}-q^{8}-\beta q^{11}+\cdots\)
8550.2.a.bo	\(2\)	\(68.272\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(0\)	\(0\)	\(-4\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}-2q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
8550.2.a.bp	\(2\)	\(68.272\)	\(\Q(\sqrt{17}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+(-1-\beta )q^{7}-q^{8}+2q^{11}+\cdots\)
8550.2.a.bq	\(2\)	\(68.272\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+(-1-\beta )q^{11}+\cdots\)
8550.2.a.br	\(2\)	\(68.272\)	\(\Q(\sqrt{17}) \)	None	\(-2\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}-4q^{11}+(2+\cdots)q^{13}+\cdots\)
8550.2.a.bs	\(2\)	\(68.272\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}+(-2+\cdots)q^{11}+\cdots\)
8550.2.a.bt	\(2\)	\(68.272\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}-3\beta q^{11}+\cdots\)
8550.2.a.bu	\(2\)	\(68.272\)	\(\Q(\sqrt{6}) \)	None	\(-2\)	\(0\)	\(0\)	\(4\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+(2+\beta )q^{7}-q^{8}+(-1+\cdots)q^{11}+\cdots\)
8550.2.a.bv	\(2\)	\(68.272\)	\(\Q(\sqrt{6}) \)	None	\(2\)	\(0\)	\(0\)	\(-4\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}+(-1+\cdots)q^{11}+\cdots\)
8550.2.a.bw	\(2\)	\(68.272\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(0\)	\(-4\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}-2q^{7}+q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
8550.2.a.bx	\(2\)	\(68.272\)	\(\Q(\sqrt{17}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}-2q^{11}+\cdots\)
8550.2.a.by	\(2\)	\(68.272\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+(-2+\cdots)q^{11}+\cdots\)
8550.2.a.bz	\(2\)	\(68.272\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+3\beta q^{11}+\cdots\)
8550.2.a.ca	\(2\)	\(68.272\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+\beta q^{7}+q^{8}+(-1+\beta )q^{11}+\cdots\)
8550.2.a.cb	\(2\)	\(68.272\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(0\)	\(0\)	\(6\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+(3+\beta )q^{7}+q^{8}+\beta q^{11}+\cdots\)
8550.2.a.cc	\(3\)	\(68.272\)	3.3.788.1	None	\(-3\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}+(-1+\beta _{1})q^{7}-q^{8}+(1+\cdots)q^{11}+\cdots\)
8550.2.a.cd	\(3\)	\(68.272\)	3.3.564.1	None	\(-3\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{7}-q^{8}+\cdots\)
8550.2.a.ce	\(3\)	\(68.272\)	3.3.148.1	None	\(-3\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+\beta _{2}q^{7}-q^{8}+(-3-\beta _{1}+\cdots)q^{11}+\cdots\)
8550.2.a.cf	\(3\)	\(68.272\)	3.3.148.1	None	\(-3\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}+\beta _{2}q^{7}-q^{8}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8550.2.a.cg	\(3\)	\(68.272\)	3.3.564.1	None	\(-3\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{7}-q^{8}+(-2+\cdots)q^{11}+\cdots\)
8550.2.a.ch	\(3\)	\(68.272\)	3.3.788.1	None	\(-3\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+(1-\beta _{1})q^{7}-q^{8}+(-1+\cdots)q^{11}+\cdots\)
8550.2.a.ci	\(3\)	\(68.272\)	3.3.993.1	None	\(-3\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+(1-\beta _{2})q^{7}-q^{8}-2\beta _{1}q^{11}+\cdots\)
8550.2.a.cj	\(3\)	\(68.272\)	3.3.257.1	None	\(-3\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}+(1-\beta _{1}+2\beta _{2})q^{7}-q^{8}+\cdots\)
8550.2.a.ck	\(3\)	\(68.272\)	3.3.568.1	None	\(-3\)	\(0\)	\(0\)	\(4\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+(1+\beta _{1})q^{7}-q^{8}+(\beta _{1}+\cdots)q^{11}+\cdots\)
8550.2.a.cl	\(3\)	\(68.272\)	3.3.568.1	None	\(3\)	\(0\)	\(0\)	\(-4\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+(-1-\beta _{1})q^{7}+q^{8}+(\beta _{1}+\cdots)q^{11}+\cdots\)
8550.2.a.cm	\(3\)	\(68.272\)	3.3.788.1	None	\(3\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+(-1+\beta _{1})q^{7}+q^{8}+(-1+\cdots)q^{11}+\cdots\)
8550.2.a.cn	\(3\)	\(68.272\)	3.3.564.1	None	\(3\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{7}+q^{8}+\cdots\)
8550.2.a.co	\(3\)	\(68.272\)	3.3.257.1	None	\(3\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
8550.2.a.cp	\(3\)	\(68.272\)	3.3.993.1	None	\(3\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+(-1+\beta _{2})q^{7}+q^{8}-2\beta _{1}q^{11}+\cdots\)
8550.2.a.cq	\(3\)	\(68.272\)	3.3.148.1	None	\(3\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}-\beta _{2}q^{7}+q^{8}+(-3-\beta _{1}+\cdots)q^{11}+\cdots\)
8550.2.a.cr	\(3\)	\(68.272\)	3.3.148.1	None	\(3\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-\beta _{2}q^{7}+q^{8}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8550.2.a.cs	\(3\)	\(68.272\)	3.3.564.1	None	\(3\)	\(0\)	\(0\)	\(2\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{7}+q^{8}+(2+\cdots)q^{11}+\cdots\)
8550.2.a.ct	\(3\)	\(68.272\)	3.3.788.1	None	\(3\)	\(0\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+(1-\beta _{1})q^{7}+q^{8}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
8550.2.a.cu	\(4\)	\(68.272\)	\(\Q(\zeta_{24})^+\)	None	\(-4\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}+\beta _{1}q^{7}-q^{8}-\beta _{3}q^{11}+\cdots\)
8550.2.a.cv	\(4\)	\(68.272\)	\(\Q(\zeta_{24})^+\)	None	\(4\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}+\beta _{1}q^{7}+q^{8}+\beta _{3}q^{11}+\cdots\)
8550.2.a.cw	\(6\)	\(68.272\)	6.6.3356224.1	None	\(-6\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+\beta _{1}q^{7}-q^{8}+(-\beta _{1}+\beta _{4}+\cdots)q^{11}+\cdots\)
8550.2.a.cx	\(6\)	\(68.272\)	6.6.3356224.1	None	\(6\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+\beta _{1}q^{7}+q^{8}+(\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)