LMFDB - Space of modular forms of level 6864, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6864.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 58 $
Sturm bound:			$2688$
Trace bound:			$17$
Distinguishing $T_p$:			$5$, $7$, $17$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(6864))$.

	Total	New	Old
Modular forms	1368	120	1248
Cusp forms	1321	120	1201
Eisenstein series	47	0	47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$2$	$3$	$11$	$13$	Fricke	Dim.
$+$	$+$	$+$	$+$	$+$	$7$
$+$	$+$	$+$	$-$	$-$	$9$
$+$	$+$	$-$	$+$	$-$	$8$
$+$	$+$	$-$	$-$	$+$	$6$
$+$	$-$	$+$	$+$	$-$	$8$
$+$	$-$	$+$	$-$	$+$	$6$
$+$	$-$	$-$	$+$	$+$	$7$
$+$	$-$	$-$	$-$	$-$	$9$
$-$	$+$	$+$	$+$	$-$	$8$
$-$	$+$	$+$	$-$	$+$	$6$
$-$	$+$	$-$	$+$	$+$	$7$
$-$	$+$	$-$	$-$	$-$	$9$
$-$	$-$	$+$	$+$	$+$	$7$
$-$	$-$	$+$	$-$	$-$	$9$
$-$	$-$	$-$	$+$	$-$	$8$
$-$	$-$	$-$	$-$	$+$	$6$
Plus space				$+$	$52$
Minus space				$-$	$68$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(6864))$ 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	11	13	$q$-expansion
6864.2.a.a	$1$	$54.809$	$\Q$	None	$0$	$-1$	$-3$	$-5$	$-$	$+$	$-$	$-$	$q-q^{3}-3q^{5}-5q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
6864.2.a.b	$1$	$54.809$	$\Q$	None	$0$	$-1$	$-3$	$-3$	$+$	$+$	$-$	$+$	$q-q^{3}-3q^{5}-3q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
6864.2.a.c	$1$	$54.809$	$\Q$	None	$0$	$-1$	$-2$	$-4$	$-$	$+$	$+$	$-$	$q-q^{3}-2q^{5}-4q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.d	$1$	$54.809$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$+$	$+$	$q-q^{3}-2q^{5}+q^{9}-q^{11}-q^{13}+2q^{15}+\cdots$
6864.2.a.e	$1$	$54.809$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$-$	$q-q^{3}-2q^{5}+q^{9}+q^{11}+q^{13}+2q^{15}+\cdots$
6864.2.a.f	$1$	$54.809$	$\Q$	None	$0$	$-1$	$-2$	$2$	$-$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+2q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.g	$1$	$54.809$	$\Q$	None	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.h	$1$	$54.809$	$\Q$	None	$0$	$-1$	$0$	$-2$	$-$	$+$	$-$	$-$	$q-q^{3}-2q^{7}+q^{9}+q^{11}+q^{13}+6q^{17}+\cdots$
6864.2.a.i	$1$	$54.809$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$q-q^{3}+q^{9}-q^{11}-q^{13}-4q^{17}+\cdots$
6864.2.a.j	$1$	$54.809$	$\Q$	None	$0$	$-1$	$0$	$4$	$-$	$+$	$-$	$-$	$q-q^{3}+4q^{7}+q^{9}+q^{11}+q^{13}+4q^{19}+\cdots$
6864.2.a.k	$1$	$54.809$	$\Q$	None	$0$	$-1$	$2$	$-4$	$-$	$+$	$+$	$+$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.l	$1$	$54.809$	$\Q$	None	$0$	$-1$	$2$	$-4$	$+$	$+$	$+$	$+$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.m	$1$	$54.809$	$\Q$	None	$0$	$-1$	$2$	$-4$	$+$	$+$	$+$	$-$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.n	$1$	$54.809$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$-$	$q-q^{3}+2q^{5}+q^{9}+q^{11}+q^{13}-2q^{15}+\cdots$
6864.2.a.o	$1$	$54.809$	$\Q$	None	$0$	$-1$	$3$	$1$	$-$	$+$	$+$	$-$	$q-q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.p	$1$	$54.809$	$\Q$	None	$0$	$-1$	$4$	$4$	$-$	$+$	$+$	$+$	$q-q^{3}+4q^{5}+4q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.q	$1$	$54.809$	$\Q$	None	$0$	$1$	$-3$	$-1$	$-$	$-$	$-$	$-$	$q+q^{3}-3q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
6864.2.a.r	$1$	$54.809$	$\Q$	None	$0$	$1$	$-2$	$0$	$+$	$-$	$+$	$-$	$q+q^{3}-2q^{5}+q^{9}-q^{11}+q^{13}-2q^{15}+\cdots$
6864.2.a.s	$1$	$54.809$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$+$	$-$	$q+q^{3}-2q^{5}+q^{9}-q^{11}+q^{13}-2q^{15}+\cdots$
6864.2.a.t	$1$	$54.809$	$\Q$	None	$0$	$1$	$-1$	$-3$	$+$	$-$	$+$	$-$	$q+q^{3}-q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.u	$1$	$54.809$	$\Q$	None	$0$	$1$	$-1$	$3$	$-$	$-$	$+$	$+$	$q+q^{3}-q^{5}+3q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.v	$1$	$54.809$	$\Q$	None	$0$	$1$	$0$	$-4$	$+$	$-$	$-$	$+$	$q+q^{3}-4q^{7}+q^{9}+q^{11}-q^{13}+8q^{17}+\cdots$
6864.2.a.w	$1$	$54.809$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$q+q^{3}+q^{9}-q^{11}+q^{13}-4q^{17}+\cdots$
6864.2.a.x	$1$	$54.809$	$\Q$	None	$0$	$1$	$0$	$2$	$-$	$-$	$-$	$-$	$q+q^{3}+2q^{7}+q^{9}+q^{11}+q^{13}-2q^{17}+\cdots$
6864.2.a.y	$1$	$54.809$	$\Q$	None	$0$	$1$	$2$	$-4$	$-$	$-$	$-$	$+$	$q+q^{3}+2q^{5}-4q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
6864.2.a.z	$1$	$54.809$	$\Q$	None	$0$	$1$	$2$	$0$	$-$	$-$	$+$	$+$	$q+q^{3}+2q^{5}+q^{9}-q^{11}-q^{13}+2q^{15}+\cdots$
6864.2.a.ba	$1$	$54.809$	$\Q$	None	$0$	$1$	$4$	$0$	$-$	$-$	$+$	$-$	$q+q^{3}+4q^{5}+q^{9}-q^{11}+q^{13}+4q^{15}+\cdots$
6864.2.a.bb	$2$	$54.809$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-4$	$0$	$-$	$+$	$-$	$+$	$q-q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots$
6864.2.a.bc	$2$	$54.809$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-4$	$4$	$-$	$+$	$+$	$+$	$q-q^{3}+(-2+\beta )q^{5}+(2+2\beta )q^{7}+q^{9}+\cdots$
6864.2.a.bd	$2$	$54.809$	$\Q(\sqrt{41}) $	None	$0$	$-2$	$-1$	$-3$	$-$	$+$	$-$	$+$	$q-q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+q^{11}+\cdots$
6864.2.a.be	$2$	$54.809$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$4$	$+$	$+$	$-$	$-$	$q-q^{3}+\beta q^{5}+2q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
6864.2.a.bf	$2$	$54.809$	$\Q(\sqrt{41}) $	None	$0$	$-2$	$4$	$0$	$-$	$+$	$-$	$-$	$q-q^{3}+2q^{5}+q^{9}+q^{11}+q^{13}-2q^{15}+\cdots$
6864.2.a.bg	$2$	$54.809$	$\Q(\sqrt{6}) $	None	$0$	$2$	$-4$	$4$	$+$	$-$	$+$	$-$	$q+q^{3}+(-2+\beta )q^{5}+2q^{7}+q^{9}-q^{11}+\cdots$
6864.2.a.bh	$2$	$54.809$	$\Q(\sqrt{17}) $	None	$0$	$2$	$-3$	$1$	$-$	$-$	$+$	$-$	$q+q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots$
6864.2.a.bi	$2$	$54.809$	$\Q(\sqrt{3}) $	None	$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$q+q^{3}+(-1+\beta )q^{5}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.bj	$2$	$54.809$	$\Q(\sqrt{5}) $	None	$0$	$2$	$-2$	$0$	$+$	$-$	$-$	$+$	$q+q^{3}+(-1-\beta )q^{5}+q^{9}+q^{11}-q^{13}+\cdots$
6864.2.a.bk	$2$	$54.809$	$\Q(\sqrt{3}) $	None	$0$	$2$	$-2$	$4$	$-$	$-$	$-$	$+$	$q+q^{3}+(-1+\beta )q^{5}+2q^{7}+q^{9}+q^{11}+\cdots$
6864.2.a.bl	$2$	$54.809$	$\Q(\sqrt{33}) $	None	$0$	$2$	$1$	$1$	$-$	$-$	$-$	$+$	$q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
6864.2.a.bm	$2$	$54.809$	$\Q(\sqrt{3}) $	None	$0$	$2$	$2$	$0$	$+$	$-$	$+$	$-$	$q+q^{3}+(1+\beta )q^{5}-2\beta q^{7}+q^{9}-q^{11}+\cdots$
6864.2.a.bn	$3$	$54.809$	3.3.404.1	None	$0$	$-3$	$-4$	$6$	$+$	$+$	$+$	$-$	$q-q^{3}+(-1-\beta _{2})q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots$
6864.2.a.bo	$3$	$54.809$	3.3.892.1	None	$0$	$-3$	$-1$	$-5$	$+$	$+$	$-$	$-$	$q-q^{3}-\beta _{1}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots$
6864.2.a.bp	$3$	$54.809$	3.3.148.1	None	$0$	$-3$	$0$	$2$	$-$	$+$	$+$	$-$	$q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$
6864.2.a.bq	$3$	$54.809$	3.3.148.1	None	$0$	$-3$	$0$	$2$	$+$	$+$	$-$	$+$	$q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
6864.2.a.br	$3$	$54.809$	3.3.564.1	None	$0$	$-3$	$2$	$-4$	$-$	$+$	$+$	$+$	$q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots$
6864.2.a.bs	$3$	$54.809$	3.3.148.1	None	$0$	$-3$	$4$	$2$	$-$	$+$	$-$	$+$	$q-q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots$
6864.2.a.bt	$3$	$54.809$	3.3.404.1	None	$0$	$-3$	$4$	$4$	$-$	$+$	$-$	$-$	$q-q^{3}+(1+2\beta _{1}-\beta _{2})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
6864.2.a.bu	$3$	$54.809$	3.3.564.1	None	$0$	$3$	$-2$	$-2$	$-$	$-$	$+$	$+$	$q+q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+\cdots$
6864.2.a.bv	$3$	$54.809$	3.3.1620.1	None	$0$	$3$	$0$	$0$	$-$	$-$	$-$	$+$	$q+q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+q^{9}+q^{11}+\cdots$
6864.2.a.bw	$4$	$54.809$	4.4.70164.1	None	$0$	$-4$	$1$	$-1$	$+$	$+$	$+$	$+$	$q-q^{3}+(1+\beta _{2}-\beta _{3})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots$
6864.2.a.bx	$4$	$54.809$	4.4.83476.1	None	$0$	$-4$	$2$	$2$	$+$	$+$	$-$	$+$	$q-q^{3}+\beta _{3}q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots$
6864.2.a.by	$4$	$54.809$	4.4.22676.1	None	$0$	$4$	$-3$	$-3$	$+$	$-$	$-$	$+$	$q+q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{3})q^{7}+\cdots$
6864.2.a.bz	$4$	$54.809$	4.4.8468.1	None	$0$	$4$	$0$	$-2$	$-$	$-$	$-$	$-$	$q+q^{3}+\beta _{3}q^{5}+(-1-\beta _{2}-\beta _{3})q^{7}+\cdots$
6864.2.a.ca	$4$	$54.809$	4.4.70164.1	None	$0$	$4$	$1$	$1$	$+$	$-$	$+$	$+$	$q+q^{3}+\beta _{1}q^{5}+(1+\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots$
6864.2.a.cb	$4$	$54.809$	4.4.90996.1	None	$0$	$4$	$2$	$-2$	$-$	$-$	$+$	$-$	$q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots$
6864.2.a.cc	$4$	$54.809$	4.4.23252.1	None	$0$	$4$	$4$	$-2$	$+$	$-$	$+$	$+$	$q+q^{3}+(1+\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}-q^{11}+\cdots$
6864.2.a.cd	$4$	$54.809$	4.4.29268.1	None	$0$	$4$	$4$	$2$	$+$	$-$	$-$	$-$	$q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2})q^{7}+q^{9}+\cdots$
6864.2.a.ce	$5$	$54.809$	5.5.46437524.1	None	$0$	$-5$	$1$	$3$	$+$	$+$	$+$	$-$	$q-q^{3}+\beta _{1}q^{5}+(1+\beta _{4})q^{7}+q^{9}-q^{11}+\cdots$
6864.2.a.cf	$5$	$54.809$	5.5.2172244.1	None	$0$	$5$	$1$	$5$	$+$	$-$	$-$	$-$	$q+q^{3}+\beta _{1}q^{5}+(1+\beta _{4})q^{7}+q^{9}+q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(6864))$ into lower level spaces

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Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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:	\( N \)	\(=\)	\( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6864.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(2688\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\), \(19\)

Introduction

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6864))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6864))\) 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	6864.2.a

Level	$6864$
Weight	$2$
Character orbit	6864.a
Rep. character	$\chi_{6864}(1,\cdot)$
Character field	$\Q$
Dimension	$120$
Newform subspaces	$58$
Sturm bound	$2688$
Trace bound	$17$

\(2\)	\(3\)	\(11\)	\(13\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(7\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(9\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(7\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(9\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(7\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(7\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(9\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(6\)
Plus space				\(+\)	\(52\)
Minus space				\(-\)	\(68\)

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	11	13	$q$-expansion
6864.2.a.a	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(-3\)	\(-5\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}-3q^{5}-5q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
6864.2.a.b	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(-3\)	\(-3\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}-3q^{5}-3q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6864.2.a.c	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(-4\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}-4q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.d	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-2q^{5}+q^{9}-q^{11}-q^{13}+2q^{15}+\cdots\)
6864.2.a.e	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}+q^{11}+q^{13}+2q^{15}+\cdots\)
6864.2.a.f	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(2\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+2q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.g	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.h	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}-2q^{7}+q^{9}+q^{11}+q^{13}+6q^{17}+\cdots\)
6864.2.a.i	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+q^{9}-q^{11}-q^{13}-4q^{17}+\cdots\)
6864.2.a.j	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(4\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+4q^{7}+q^{9}+q^{11}+q^{13}+4q^{19}+\cdots\)
6864.2.a.k	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(-4\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.l	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(-4\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.m	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(-4\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.n	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+2q^{5}+q^{9}+q^{11}+q^{13}-2q^{15}+\cdots\)
6864.2.a.o	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(3\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.p	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(-1\)	\(4\)	\(4\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+4q^{5}+4q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.q	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(-3\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-3q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
6864.2.a.r	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}-q^{11}+q^{13}-2q^{15}+\cdots\)
6864.2.a.s	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}-q^{11}+q^{13}-2q^{15}+\cdots\)
6864.2.a.t	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(-3\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6864.2.a.u	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(3\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}-q^{5}+3q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.v	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-4q^{7}+q^{9}+q^{11}-q^{13}+8q^{17}+\cdots\)
6864.2.a.w	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+q^{9}-q^{11}+q^{13}-4q^{17}+\cdots\)
6864.2.a.x	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+2q^{7}+q^{9}+q^{11}+q^{13}-2q^{17}+\cdots\)
6864.2.a.y	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(-4\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+2q^{5}-4q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6864.2.a.z	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}+2q^{5}+q^{9}-q^{11}-q^{13}+2q^{15}+\cdots\)
6864.2.a.ba	\(1\)	\(54.809\)	\(\Q\)	None	\(0\)	\(1\)	\(4\)	\(0\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+4q^{5}+q^{9}-q^{11}+q^{13}+4q^{15}+\cdots\)
6864.2.a.bb	\(2\)	\(54.809\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-4\)	\(0\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots\)
6864.2.a.bc	\(2\)	\(54.809\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-4\)	\(4\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-2+\beta )q^{5}+(2+2\beta )q^{7}+q^{9}+\cdots\)
6864.2.a.bd	\(2\)	\(54.809\)	\(\Q(\sqrt{41}) \)	None	\(0\)	\(-2\)	\(-1\)	\(-3\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+q^{11}+\cdots\)
6864.2.a.be	\(2\)	\(54.809\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(4\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+\beta q^{5}+2q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
6864.2.a.bf	\(2\)	\(54.809\)	\(\Q(\sqrt{41}) \)	None	\(0\)	\(-2\)	\(4\)	\(0\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+2q^{5}+q^{9}+q^{11}+q^{13}-2q^{15}+\cdots\)
6864.2.a.bg	\(2\)	\(54.809\)	\(\Q(\sqrt{6}) \)	None	\(0\)	\(2\)	\(-4\)	\(4\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+(-2+\beta )q^{5}+2q^{7}+q^{9}-q^{11}+\cdots\)
6864.2.a.bh	\(2\)	\(54.809\)	\(\Q(\sqrt{17}) \)	None	\(0\)	\(2\)	\(-3\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
6864.2.a.bi	\(2\)	\(54.809\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}+(-1+\beta )q^{5}+q^{9}-q^{11}-q^{13}+\cdots\)
6864.2.a.bj	\(2\)	\(54.809\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1-\beta )q^{5}+q^{9}+q^{11}-q^{13}+\cdots\)
6864.2.a.bk	\(2\)	\(54.809\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(-2\)	\(4\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1+\beta )q^{5}+2q^{7}+q^{9}+q^{11}+\cdots\)
6864.2.a.bl	\(2\)	\(54.809\)	\(\Q(\sqrt{33}) \)	None	\(0\)	\(2\)	\(1\)	\(1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6864.2.a.bm	\(2\)	\(54.809\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(2\)	\(0\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}+(1+\beta )q^{5}-2\beta q^{7}+q^{9}-q^{11}+\cdots\)
6864.2.a.bn	\(3\)	\(54.809\)	3.3.404.1	None	\(0\)	\(-3\)	\(-4\)	\(6\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+(-1-\beta _{2})q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6864.2.a.bo	\(3\)	\(54.809\)	3.3.892.1	None	\(0\)	\(-3\)	\(-1\)	\(-5\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}-\beta _{1}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6864.2.a.bp	\(3\)	\(54.809\)	3.3.148.1	None	\(0\)	\(-3\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
6864.2.a.bq	\(3\)	\(54.809\)	3.3.148.1	None	\(0\)	\(-3\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
6864.2.a.br	\(3\)	\(54.809\)	3.3.564.1	None	\(0\)	\(-3\)	\(2\)	\(-4\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
6864.2.a.bs	\(3\)	\(54.809\)	3.3.148.1	None	\(0\)	\(-3\)	\(4\)	\(2\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
6864.2.a.bt	\(3\)	\(54.809\)	3.3.404.1	None	\(0\)	\(-3\)	\(4\)	\(4\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}+(1+2\beta _{1}-\beta _{2})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
6864.2.a.bu	\(3\)	\(54.809\)	3.3.564.1	None	\(0\)	\(3\)	\(-2\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
6864.2.a.bv	\(3\)	\(54.809\)	3.3.1620.1	None	\(0\)	\(3\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+q^{9}+q^{11}+\cdots\)
6864.2.a.bw	\(4\)	\(54.809\)	4.4.70164.1	None	\(0\)	\(-4\)	\(1\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(1+\beta _{2}-\beta _{3})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots\)
6864.2.a.bx	\(4\)	\(54.809\)	4.4.83476.1	None	\(0\)	\(-4\)	\(2\)	\(2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}+\beta _{3}q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
6864.2.a.by	\(4\)	\(54.809\)	4.4.22676.1	None	\(0\)	\(4\)	\(-3\)	\(-3\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
6864.2.a.bz	\(4\)	\(54.809\)	4.4.8468.1	None	\(0\)	\(4\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+\beta _{3}q^{5}+(-1-\beta _{2}-\beta _{3})q^{7}+\cdots\)
6864.2.a.ca	\(4\)	\(54.809\)	4.4.70164.1	None	\(0\)	\(4\)	\(1\)	\(1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}+\beta _{1}q^{5}+(1+\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
6864.2.a.cb	\(4\)	\(54.809\)	4.4.90996.1	None	\(0\)	\(4\)	\(2\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots\)
6864.2.a.cc	\(4\)	\(54.809\)	4.4.23252.1	None	\(0\)	\(4\)	\(4\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q+q^{3}+(1+\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}-q^{11}+\cdots\)
6864.2.a.cd	\(4\)	\(54.809\)	4.4.29268.1	None	\(0\)	\(4\)	\(4\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2})q^{7}+q^{9}+\cdots\)
6864.2.a.ce	\(5\)	\(54.809\)	5.5.46437524.1	None	\(0\)	\(-5\)	\(1\)	\(3\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+\beta _{1}q^{5}+(1+\beta _{4})q^{7}+q^{9}-q^{11}+\cdots\)
6864.2.a.cf	\(5\)	\(54.809\)	5.5.2172244.1	None	\(0\)	\(5\)	\(1\)	\(5\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+\beta _{1}q^{5}+(1+\beta _{4})q^{7}+q^{9}+q^{11}+\cdots\)