LMFDB - Space of modular forms of level 6272, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 6272 = 2^{7} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6272.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 52 $
Sturm bound:			$1792$
Trace bound:			$29$
Distinguishing $T_p$:			$3$, $5$, $11$, $13$, $23$, $29$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(6272))$.

	Total	New	Old
Modular forms	960	164	796
Cusp forms	833	164	669
Eisenstein series	127	0	127

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

$2$	$7$	Fricke	Dim.
$+$	$+$	$+$	$36$
$+$	$-$	$-$	$45$
$-$	$+$	$-$	$44$
$-$	$-$	$+$	$39$
Plus space		$+$	$75$
Minus space		$-$	$89$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(6272))$ 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	7	$q$-expansion
6272.2.a.a	$1$	$50.082$	$\Q$	None	$0$	$-2$	$-2$	$0$	$-$	$-$	$q-2q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots$
6272.2.a.b	$1$	$50.082$	$\Q$	None	$0$	$-2$	$2$	$0$	$-$	$-$	$q-2q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots$
6272.2.a.c	$1$	$50.082$	$\Q$	None	$0$	$0$	$0$	$0$	$+$	$-$	$q-3q^{9}-2q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots$
6272.2.a.d	$1$	$50.082$	$\Q$	None	$0$	$0$	$0$	$0$	$-$	$-$	$q-3q^{9}-2q^{11}+4q^{13}+2q^{17}+4q^{19}+\cdots$
6272.2.a.e	$1$	$50.082$	$\Q$	None	$0$	$0$	$0$	$0$	$+$	$-$	$q-3q^{9}+2q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots$
6272.2.a.f	$1$	$50.082$	$\Q$	None	$0$	$0$	$0$	$0$	$+$	$-$	$q-3q^{9}+2q^{11}+4q^{13}+2q^{17}-4q^{19}+\cdots$
6272.2.a.g	$1$	$50.082$	$\Q$	None	$0$	$2$	$-2$	$0$	$-$	$-$	$q+2q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots$
6272.2.a.h	$1$	$50.082$	$\Q$	None	$0$	$2$	$2$	$0$	$+$	$-$	$q+2q^{3}+2q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots$
6272.2.a.i	$2$	$50.082$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$-2$	$0$	$+$	$-$	$q+(-1+\beta )q^{3}+(-1-\beta )q^{5}+(1-2\beta )q^{9}+\cdots$
6272.2.a.j	$2$	$50.082$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$2$	$0$	$-$	$-$	$q+(-1+\beta )q^{3}+(1+\beta )q^{5}+(1-2\beta )q^{9}+\cdots$
6272.2.a.k	$2$	$50.082$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$-$	$+$	$q+\beta q^{3}-2\beta q^{5}-q^{9}-4q^{11}-4q^{15}+\cdots$
6272.2.a.l	$2$	$50.082$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$+$	$+$	$q+\beta q^{3}+2\beta q^{5}-q^{9}-4q^{11}+4q^{15}+\cdots$
6272.2.a.m	$2$	$50.082$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$+$	$-$	$q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots$
6272.2.a.n	$2$	$50.082$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$-$	$-$	$q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots$
6272.2.a.o	$2$	$50.082$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$-$	$-$	$q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots$
6272.2.a.p	$2$	$50.082$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$-$	$-$	$q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots$
6272.2.a.q	$2$	$50.082$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$-$	$+$	$q+\beta q^{3}-2\beta q^{5}-q^{9}+4q^{11}-4q^{15}+\cdots$
6272.2.a.r	$2$	$50.082$	$\Q(\sqrt{2}) $	None	$0$	$0$	$0$	$0$	$-$	$+$	$q+\beta q^{3}+2\beta q^{5}-q^{9}+4q^{11}+4q^{15}+\cdots$
6272.2.a.s	$2$	$50.082$	$\Q(\sqrt{3}) $	None	$0$	$2$	$-2$	$0$	$-$	$-$	$q+(1+\beta )q^{3}+(-1+\beta )q^{5}+(1+2\beta )q^{9}+\cdots$
6272.2.a.t	$2$	$50.082$	$\Q(\sqrt{3}) $	None	$0$	$2$	$2$	$0$	$-$	$-$	$q+(1+\beta )q^{3}+(1-\beta )q^{5}+(1+2\beta )q^{9}+\cdots$
6272.2.a.u	$3$	$50.082$	3.3.316.1	None	$0$	$-2$	$-2$	$0$	$-$	$-$	$q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3+\cdots)q^{9}+\cdots$
6272.2.a.v	$3$	$50.082$	3.3.316.1	None	$0$	$-2$	$2$	$0$	$+$	$-$	$q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots$
6272.2.a.w	$3$	$50.082$	3.3.316.1	None	$0$	$2$	$-2$	$0$	$+$	$-$	$q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots$
6272.2.a.x	$3$	$50.082$	3.3.316.1	None	$0$	$2$	$2$	$0$	$+$	$-$	$q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots$
6272.2.a.y	$4$	$50.082$	4.4.54864.1	None	$0$	$-2$	$-2$	$0$	$+$	$+$	$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.z	$4$	$50.082$	4.4.11344.1	None	$0$	$-2$	$-2$	$0$	$+$	$+$	$q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.ba	$4$	$50.082$	4.4.11344.1	None	$0$	$-2$	$-2$	$0$	$-$	$-$	$q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.bb	$4$	$50.082$	4.4.54864.1	None	$0$	$-2$	$-2$	$0$	$-$	$-$	$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.bc	$4$	$50.082$	4.4.54864.1	None	$0$	$-2$	$2$	$0$	$-$	$+$	$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.bd	$4$	$50.082$	4.4.11344.1	None	$0$	$-2$	$2$	$0$	$+$	$+$	$q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots$
6272.2.a.be	$4$	$50.082$	4.4.11344.1	None	$0$	$-2$	$2$	$0$	$+$	$-$	$q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots$
6272.2.a.bf	$4$	$50.082$	4.4.54864.1	None	$0$	$-2$	$2$	$0$	$-$	$-$	$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.bg	$4$	$50.082$	$\Q(\sqrt{2}, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$+$	$+$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots$
6272.2.a.bh	$4$	$50.082$	$\Q(\sqrt{2}, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$+$	$+$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(-1+\cdots)q^{11}+\cdots$
6272.2.a.bi	$4$	$50.082$	$\Q(\sqrt{2}, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$+$	$+$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots$
6272.2.a.bj	$4$	$50.082$	$\Q(\sqrt{2}, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$-$	$+$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(1+\cdots)q^{11}+\cdots$
6272.2.a.bk	$4$	$50.082$	4.4.9248.1	None	$0$	$0$	$0$	$0$	$-$	$-$	$q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots$
6272.2.a.bl	$4$	$50.082$	4.4.9248.1	None	$0$	$0$	$0$	$0$	$+$	$-$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots$
6272.2.a.bm	$4$	$50.082$	4.4.9248.1	None	$0$	$0$	$0$	$0$	$+$	$-$	$q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots$
6272.2.a.bn	$4$	$50.082$	4.4.9248.1	None	$0$	$0$	$0$	$0$	$+$	$-$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots$
6272.2.a.bo	$4$	$50.082$	4.4.54864.1	None	$0$	$2$	$-2$	$0$	$-$	$-$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.bp	$4$	$50.082$	4.4.11344.1	None	$0$	$2$	$-2$	$0$	$+$	$+$	$q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.bq	$4$	$50.082$	4.4.11344.1	None	$0$	$2$	$-2$	$0$	$+$	$-$	$q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.br	$4$	$50.082$	4.4.54864.1	None	$0$	$2$	$-2$	$0$	$-$	$+$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.bs	$4$	$50.082$	4.4.54864.1	None	$0$	$2$	$2$	$0$	$+$	$-$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.bt	$4$	$50.082$	4.4.11344.1	None	$0$	$2$	$2$	$0$	$-$	$+$	$q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots$
6272.2.a.bu	$4$	$50.082$	4.4.11344.1	None	$0$	$2$	$2$	$0$	$+$	$-$	$q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots$
6272.2.a.bv	$4$	$50.082$	4.4.54864.1	None	$0$	$2$	$2$	$0$	$-$	$+$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6272.2.a.bw	$6$	$50.082$	6.6.26849792.2	None	$0$	$0$	$0$	$0$	$-$	$+$	$q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots$
6272.2.a.bx	$6$	$50.082$	6.6.26849792.2	None	$0$	$0$	$0$	$0$	$-$	$+$	$q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots$
6272.2.a.by	$6$	$50.082$	6.6.26849792.2	None	$0$	$0$	$0$	$0$	$+$	$+$	$q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots$
6272.2.a.bz	$6$	$50.082$	6.6.26849792.2	None	$0$	$0$	$0$	$0$	$-$	$+$	$q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(6272))$ into lower level spaces

Overview	Random
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:	\( N \)	\(=\)	\( 6272 = 2^{7} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6272.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 52 \)
Sturm bound:			\(1792\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(13\), \(23\), \(29\)

Introduction

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6272))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6272))\) 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	6272.2.a

Level	$6272$
Weight	$2$
Character orbit	6272.a
Rep. character	$\chi_{6272}(1,\cdot)$
Character field	$\Q$
Dimension	$164$
Newform subspaces	$52$
Sturm bound	$1792$
Trace bound	$29$

\(2\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(36\)
\(+\)	\(-\)	\(-\)	\(45\)
\(-\)	\(+\)	\(-\)	\(44\)
\(-\)	\(-\)	\(+\)	\(39\)
Plus space		\(+\)	\(75\)
Minus space		\(-\)	\(89\)

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	7	$q$-expansion
6272.2.a.a	\(1\)	\(50.082\)	\(\Q\)	None	\(0\)	\(-2\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(q-2q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
6272.2.a.b	\(1\)	\(50.082\)	\(\Q\)	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(-\)	\(-\)	\(q-2q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
6272.2.a.c	\(1\)	\(50.082\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(q-3q^{9}-2q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots\)
6272.2.a.d	\(1\)	\(50.082\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(q-3q^{9}-2q^{11}+4q^{13}+2q^{17}+4q^{19}+\cdots\)
6272.2.a.e	\(1\)	\(50.082\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(q-3q^{9}+2q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
6272.2.a.f	\(1\)	\(50.082\)	\(\Q\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(q-3q^{9}+2q^{11}+4q^{13}+2q^{17}-4q^{19}+\cdots\)
6272.2.a.g	\(1\)	\(50.082\)	\(\Q\)	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(q+2q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
6272.2.a.h	\(1\)	\(50.082\)	\(\Q\)	None	\(0\)	\(2\)	\(2\)	\(0\)	\(+\)	\(-\)	\(q+2q^{3}+2q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6272.2.a.i	\(2\)	\(50.082\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(q+(-1+\beta )q^{3}+(-1-\beta )q^{5}+(1-2\beta )q^{9}+\cdots\)
6272.2.a.j	\(2\)	\(50.082\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(-\)	\(-\)	\(q+(-1+\beta )q^{3}+(1+\beta )q^{5}+(1-2\beta )q^{9}+\cdots\)
6272.2.a.k	\(2\)	\(50.082\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(q+\beta q^{3}-2\beta q^{5}-q^{9}-4q^{11}-4q^{15}+\cdots\)
6272.2.a.l	\(2\)	\(50.082\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(q+\beta q^{3}+2\beta q^{5}-q^{9}-4q^{11}+4q^{15}+\cdots\)
6272.2.a.m	\(2\)	\(50.082\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots\)
6272.2.a.n	\(2\)	\(50.082\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(q+\beta q^{3}-\beta q^{5}-q^{9}+3\beta q^{13}-2q^{15}+\cdots\)
6272.2.a.o	\(2\)	\(50.082\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots\)
6272.2.a.p	\(2\)	\(50.082\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(q+\beta q^{3}+\beta q^{5}-q^{9}-3\beta q^{13}+2q^{15}+\cdots\)
6272.2.a.q	\(2\)	\(50.082\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(q+\beta q^{3}-2\beta q^{5}-q^{9}+4q^{11}-4q^{15}+\cdots\)
6272.2.a.r	\(2\)	\(50.082\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(q+\beta q^{3}+2\beta q^{5}-q^{9}+4q^{11}+4q^{15}+\cdots\)
6272.2.a.s	\(2\)	\(50.082\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+(1+2\beta )q^{9}+\cdots\)
6272.2.a.t	\(2\)	\(50.082\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(2\)	\(0\)	\(-\)	\(-\)	\(q+(1+\beta )q^{3}+(1-\beta )q^{5}+(1+2\beta )q^{9}+\cdots\)
6272.2.a.u	\(3\)	\(50.082\)	3.3.316.1	None	\(0\)	\(-2\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3+\cdots)q^{9}+\cdots\)
6272.2.a.v	\(3\)	\(50.082\)	3.3.316.1	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(+\)	\(-\)	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.w	\(3\)	\(50.082\)	3.3.316.1	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.x	\(3\)	\(50.082\)	3.3.316.1	None	\(0\)	\(2\)	\(2\)	\(0\)	\(+\)	\(-\)	\(q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
6272.2.a.y	\(4\)	\(50.082\)	4.4.54864.1	None	\(0\)	\(-2\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.z	\(4\)	\(50.082\)	4.4.11344.1	None	\(0\)	\(-2\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.ba	\(4\)	\(50.082\)	4.4.11344.1	None	\(0\)	\(-2\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bb	\(4\)	\(50.082\)	4.4.54864.1	None	\(0\)	\(-2\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bc	\(4\)	\(50.082\)	4.4.54864.1	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(-\)	\(+\)	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bd	\(4\)	\(50.082\)	4.4.11344.1	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(+\)	\(+\)	\(q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.be	\(4\)	\(50.082\)	4.4.11344.1	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(+\)	\(-\)	\(q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bf	\(4\)	\(50.082\)	4.4.54864.1	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(-\)	\(-\)	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bg	\(4\)	\(50.082\)	\(\Q(\sqrt{2}, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots\)
6272.2.a.bh	\(4\)	\(50.082\)	\(\Q(\sqrt{2}, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bi	\(4\)	\(50.082\)	\(\Q(\sqrt{2}, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{9}+\cdots\)
6272.2.a.bj	\(4\)	\(50.082\)	\(\Q(\sqrt{2}, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{9}+(1+\cdots)q^{11}+\cdots\)
6272.2.a.bk	\(4\)	\(50.082\)	4.4.9248.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(-\)	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bl	\(4\)	\(50.082\)	4.4.9248.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
6272.2.a.bm	\(4\)	\(50.082\)	4.4.9248.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots\)
6272.2.a.bn	\(4\)	\(50.082\)	4.4.9248.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(-\)	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(2-\beta _{3})q^{9}+(1+\beta _{3})q^{11}+\cdots\)
6272.2.a.bo	\(4\)	\(50.082\)	4.4.54864.1	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bp	\(4\)	\(50.082\)	4.4.11344.1	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bq	\(4\)	\(50.082\)	4.4.11344.1	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(q-\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.br	\(4\)	\(50.082\)	4.4.54864.1	None	\(0\)	\(2\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bs	\(4\)	\(50.082\)	4.4.54864.1	None	\(0\)	\(2\)	\(2\)	\(0\)	\(+\)	\(-\)	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bt	\(4\)	\(50.082\)	4.4.11344.1	None	\(0\)	\(2\)	\(2\)	\(0\)	\(-\)	\(+\)	\(q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bu	\(4\)	\(50.082\)	4.4.11344.1	None	\(0\)	\(2\)	\(2\)	\(0\)	\(+\)	\(-\)	\(q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}-\beta _{2})q^{9}+\cdots\)
6272.2.a.bv	\(4\)	\(50.082\)	4.4.54864.1	None	\(0\)	\(2\)	\(2\)	\(0\)	\(-\)	\(+\)	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6272.2.a.bw	\(6\)	\(50.082\)	6.6.26849792.2	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots\)
6272.2.a.bx	\(6\)	\(50.082\)	6.6.26849792.2	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots\)
6272.2.a.by	\(6\)	\(50.082\)	6.6.26849792.2	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(+\)	\(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{4}+\cdots)q^{9}+\cdots\)
6272.2.a.bz	\(6\)	\(50.082\)	6.6.26849792.2	None	\(0\)	\(0\)	\(0\)	\(0\)	\(-\)	\(+\)	\(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2-\beta _{4})q^{9}+\cdots\)