LMFDB - Space of modular forms of level 4719, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 4719 = 3 \cdot 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4719.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 44 $
Sturm bound:			$1232$
Trace bound:			$7$
Distinguishing $T_p$:			$2$, $5$, $7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(4719))$.

	Total	New	Old
Modular forms	640	218	422
Cusp forms	593	218	375
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.

$3$	$11$	$13$	Fricke	Dim.
$+$	$+$	$+$	$+$	$25$
$+$	$+$	$-$	$-$	$29$
$+$	$-$	$+$	$-$	$30$
$+$	$-$	$-$	$+$	$25$
$-$	$+$	$+$	$-$	$33$
$-$	$+$	$-$	$+$	$21$
$-$	$-$	$+$	$+$	$20$
$-$	$-$	$-$	$-$	$35$
Plus space			$+$	$91$
Minus space			$-$	$127$

Trace form

$ 218q + 4q^{2} + 218q^{4} + 4q^{5} - 2q^{6} + 12q^{7} + 218q^{9} + O(q^{10}) $

$ 218q + 4q^{2} + 218q^{4} + 4q^{5} - 2q^{6} + 12q^{7} + 218q^{9} - 8q^{10} + 4q^{12} + 2q^{13} - 4q^{14} + 222q^{16} + 4q^{17} + 4q^{18} - 4q^{19} + 4q^{20} + 4q^{21} + 16q^{23} - 6q^{24} + 238q^{25} + 12q^{28} + 4q^{29} - 4q^{30} - 20q^{31} + 4q^{32} - 24q^{34} - 32q^{35} + 218q^{36} + 28q^{37} - 4q^{38} + 4q^{39} - 20q^{41} + 12q^{42} + 4q^{45} + 32q^{46} - 4q^{47} - 8q^{48} + 250q^{49} + 44q^{50} + 10q^{52} + 20q^{53} - 2q^{54} - 4q^{56} + 20q^{57} + 8q^{58} - 28q^{59} + 20q^{61} - 36q^{62} + 12q^{63} + 250q^{64} - 4q^{65} - 20q^{67} + 44q^{68} - 8q^{69} + 32q^{70} - 20q^{71} + 12q^{73} + 56q^{74} + 8q^{75} - 36q^{76} - 2q^{78} - 16q^{79} + 116q^{80} + 218q^{81} + 88q^{82} - 28q^{83} + 44q^{84} + 48q^{85} + 64q^{86} + 36q^{89} - 8q^{90} - 4q^{91} + 88q^{92} + 20q^{93} + 52q^{94} - 64q^{95} - 34q^{96} + 20q^{97} + 20q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(4719))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	3	11	13	$q$-expansion
4719.2.a.a	$1$	$37.681$	$\Q$	None	$-2$	$-1$	$0$	$3$	$+$	$-$	$+$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots$
4719.2.a.b	$1$	$37.681$	$\Q$	None	$-2$	$1$	$-2$	$-3$	$-$	$-$	$+$	$q-2q^{2}+q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots$
4719.2.a.c	$1$	$37.681$	$\Q$	None	$-1$	$-1$	$2$	$4$	$+$	$-$	$+$	$q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots$
4719.2.a.d	$1$	$37.681$	$\Q$	None	$0$	$-1$	$2$	$-5$	$+$	$-$	$+$	$q-q^{3}-2q^{4}+2q^{5}-5q^{7}+q^{9}+2q^{12}+\cdots$
4719.2.a.e	$1$	$37.681$	$\Q$	None	$0$	$-1$	$2$	$-3$	$+$	$-$	$-$	$q-q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+2q^{12}+\cdots$
4719.2.a.f	$1$	$37.681$	$\Q$	None	$0$	$-1$	$2$	$3$	$+$	$-$	$+$	$q-q^{3}-2q^{4}+2q^{5}+3q^{7}+q^{9}+2q^{12}+\cdots$
4719.2.a.g	$1$	$37.681$	$\Q$	None	$0$	$-1$	$2$	$5$	$+$	$-$	$-$	$q-q^{3}-2q^{4}+2q^{5}+5q^{7}+q^{9}+2q^{12}+\cdots$
4719.2.a.h	$1$	$37.681$	$\Q$	None	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$q+q^{3}-2q^{4}-q^{7}+q^{9}-2q^{12}+q^{13}+\cdots$
4719.2.a.i	$1$	$37.681$	$\Q$	None	$0$	$1$	$0$	$1$	$-$	$-$	$+$	$q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{12}-q^{13}+\cdots$
4719.2.a.j	$1$	$37.681$	$\Q$	None	$1$	$-1$	$0$	$0$	$+$	$-$	$+$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots$
4719.2.a.k	$1$	$37.681$	$\Q$	None	$1$	$1$	$-2$	$0$	$-$	$-$	$+$	$q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots$
4719.2.a.l	$1$	$37.681$	$\Q$	None	$2$	$-1$	$0$	$-3$	$+$	$-$	$-$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots$
4719.2.a.m	$1$	$37.681$	$\Q$	None	$2$	$1$	$-2$	$3$	$-$	$-$	$-$	$q+2q^{2}+q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots$
4719.2.a.n	$2$	$37.681$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$-2$	$4$	$+$	$-$	$-$	$q+\beta q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots$
4719.2.a.o	$2$	$37.681$	$\Q(\sqrt{2}) $	None	$2$	$2$	$-4$	$4$	$-$	$-$	$-$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
4719.2.a.p	$2$	$37.681$	$\Q(\sqrt{2}) $	None	$2$	$2$	$0$	$0$	$-$	$-$	$-$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots$
4719.2.a.q	$3$	$37.681$	3.3.148.1	None	$-3$	$3$	$4$	$2$	$-$	$-$	$-$	$q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
4719.2.a.r	$3$	$37.681$	3.3.321.1	None	$-2$	$-3$	$-5$	$0$	$+$	$-$	$-$	$q+(-1-\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+\cdots$
4719.2.a.s	$3$	$37.681$	3.3.169.1	None	$-2$	$3$	$3$	$4$	$-$	$-$	$-$	$q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
4719.2.a.t	$3$	$37.681$	3.3.148.1	None	$-1$	$3$	$0$	$2$	$-$	$-$	$+$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots$
4719.2.a.u	$3$	$37.681$	3.3.564.1	None	$1$	$-3$	$-2$	$-2$	$+$	$-$	$-$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
4719.2.a.v	$3$	$37.681$	3.3.321.1	None	$2$	$-3$	$-5$	$0$	$+$	$-$	$+$	$q+(1+\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots$
4719.2.a.w	$3$	$37.681$	3.3.169.1	None	$2$	$3$	$3$	$-4$	$-$	$-$	$+$	$q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
4719.2.a.x	$4$	$37.681$	4.4.2777.1	None	$-2$	$-4$	$-3$	$5$	$+$	$-$	$-$	$q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots$
4719.2.a.y	$4$	$37.681$	4.4.2777.1	None	$2$	$-4$	$-3$	$-5$	$+$	$-$	$+$	$q+(1-\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots$
4719.2.a.z	$4$	$37.681$	4.4.8468.1	None	$2$	$-4$	$0$	$-2$	$+$	$-$	$+$	$q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots$
4719.2.a.ba	$5$	$37.681$	5.5.210557.1	None	$-2$	$5$	$3$	$-6$	$-$	$-$	$+$	$q+\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
4719.2.a.bb	$5$	$37.681$	5.5.394064.1	None	$-1$	$-5$	$2$	$2$	$+$	$+$	$+$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
4719.2.a.bc	$5$	$37.681$	5.5.303952.1	None	$-1$	$5$	$-2$	$-6$	$-$	$+$	$-$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
4719.2.a.bd	$5$	$37.681$	5.5.394064.1	None	$1$	$-5$	$2$	$-2$	$+$	$+$	$-$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
4719.2.a.be	$5$	$37.681$	5.5.303952.1	None	$1$	$5$	$-2$	$6$	$-$	$+$	$+$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
4719.2.a.bf	$5$	$37.681$	5.5.210557.1	None	$2$	$5$	$3$	$6$	$-$	$-$	$-$	$q-\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
4719.2.a.bg	$6$	$37.681$	6.6.966125.1	None	$-1$	$6$	$-6$	$-5$	$-$	$+$	$-$	$q-\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
4719.2.a.bh	$6$	$37.681$	6.6.966125.1	None	$1$	$6$	$-6$	$5$	$-$	$-$	$+$	$q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
4719.2.a.bi	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-3$	$-10$	$-8$	$-1$	$+$	$-$	$-$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
4719.2.a.bj	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-2$	$-10$	$4$	$4$	$+$	$+$	$+$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
4719.2.a.bk	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-2$	$10$	$-4$	$-12$	$-$	$+$	$-$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
4719.2.a.bl	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$2$	$-10$	$4$	$-4$	$+$	$+$	$-$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
4719.2.a.bm	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$2$	$10$	$-4$	$12$	$-$	$+$	$+$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
4719.2.a.bn	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$3$	$-10$	$-8$	$1$	$+$	$+$	$+$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
4719.2.a.bo	$14$	$37.681$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$-3$	$-14$	$8$	$-3$	$+$	$-$	$+$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots$
4719.2.a.bp	$14$	$37.681$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$3$	$-14$	$8$	$3$	$+$	$+$	$-$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots$
4719.2.a.bq	$18$	$37.681$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$-1$	$18$	$10$	$-7$	$-$	$+$	$+$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots$
4719.2.a.br	$18$	$37.681$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$1$	$18$	$10$	$7$	$-$	$-$	$-$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(4719))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(4719)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(11))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(33))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(39))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(121))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(143))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(363))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(429))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(1573))$$^{\oplus 2}$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4719 = 3 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4719.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 44 \)
Sturm bound:			\(1232\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4719))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4719))\) 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	4719.2.a

Level	$4719$
Weight	$2$
Character orbit	4719.a
Rep. character	$\chi_{4719}(1,\cdot)$
Character field	$\Q$
Dimension	$218$
Newform subspaces	$44$
Sturm bound	$1232$
Trace bound	$7$

\(3\)	\(11\)	\(13\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(25\)
\(+\)	\(+\)	\(-\)	\(-\)	\(29\)
\(+\)	\(-\)	\(+\)	\(-\)	\(30\)
\(+\)	\(-\)	\(-\)	\(+\)	\(25\)
\(-\)	\(+\)	\(+\)	\(-\)	\(33\)
\(-\)	\(+\)	\(-\)	\(+\)	\(21\)
\(-\)	\(-\)	\(+\)	\(+\)	\(20\)
\(-\)	\(-\)	\(-\)	\(-\)	\(35\)
Plus space			\(+\)	\(91\)
Minus space			\(-\)	\(127\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	3	11	13	$q$-expansion
4719.2.a.a	\(1\)	\(37.681\)	\(\Q\)	None	\(-2\)	\(-1\)	\(0\)	\(3\)	\(+\)	\(-\)	\(+\)	\(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
4719.2.a.b	\(1\)	\(37.681\)	\(\Q\)	None	\(-2\)	\(1\)	\(-2\)	\(-3\)	\(-\)	\(-\)	\(+\)	\(q-2q^{2}+q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots\)
4719.2.a.c	\(1\)	\(37.681\)	\(\Q\)	None	\(-1\)	\(-1\)	\(2\)	\(4\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
4719.2.a.d	\(1\)	\(37.681\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(-5\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}-2q^{4}+2q^{5}-5q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.e	\(1\)	\(37.681\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(-3\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.f	\(1\)	\(37.681\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(3\)	\(+\)	\(-\)	\(+\)	\(q-q^{3}-2q^{4}+2q^{5}+3q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.g	\(1\)	\(37.681\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(5\)	\(+\)	\(-\)	\(-\)	\(q-q^{3}-2q^{4}+2q^{5}+5q^{7}+q^{9}+2q^{12}+\cdots\)
4719.2.a.h	\(1\)	\(37.681\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-2q^{4}-q^{7}+q^{9}-2q^{12}+q^{13}+\cdots\)
4719.2.a.i	\(1\)	\(37.681\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{12}-q^{13}+\cdots\)
4719.2.a.j	\(1\)	\(37.681\)	\(\Q\)	None	\(1\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
4719.2.a.k	\(1\)	\(37.681\)	\(\Q\)	None	\(1\)	\(1\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
4719.2.a.l	\(1\)	\(37.681\)	\(\Q\)	None	\(2\)	\(-1\)	\(0\)	\(-3\)	\(+\)	\(-\)	\(-\)	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
4719.2.a.m	\(1\)	\(37.681\)	\(\Q\)	None	\(2\)	\(1\)	\(-2\)	\(3\)	\(-\)	\(-\)	\(-\)	\(q+2q^{2}+q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots\)
4719.2.a.n	\(2\)	\(37.681\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(-2\)	\(4\)	\(+\)	\(-\)	\(-\)	\(q+\beta q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
4719.2.a.o	\(2\)	\(37.681\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(2\)	\(-4\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
4719.2.a.p	\(2\)	\(37.681\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots\)
4719.2.a.q	\(3\)	\(37.681\)	3.3.148.1	None	\(-3\)	\(3\)	\(4\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.r	\(3\)	\(37.681\)	3.3.321.1	None	\(-2\)	\(-3\)	\(-5\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+(-1-\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+\cdots\)
4719.2.a.s	\(3\)	\(37.681\)	3.3.169.1	None	\(-2\)	\(3\)	\(3\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.t	\(3\)	\(37.681\)	3.3.148.1	None	\(-1\)	\(3\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
4719.2.a.u	\(3\)	\(37.681\)	3.3.564.1	None	\(1\)	\(-3\)	\(-2\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4719.2.a.v	\(3\)	\(37.681\)	3.3.321.1	None	\(2\)	\(-3\)	\(-5\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+(1+\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.w	\(3\)	\(37.681\)	3.3.169.1	None	\(2\)	\(3\)	\(3\)	\(-4\)	\(-\)	\(-\)	\(+\)	\(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4719.2.a.x	\(4\)	\(37.681\)	4.4.2777.1	None	\(-2\)	\(-4\)	\(-3\)	\(5\)	\(+\)	\(-\)	\(-\)	\(q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)
4719.2.a.y	\(4\)	\(37.681\)	4.4.2777.1	None	\(2\)	\(-4\)	\(-3\)	\(-5\)	\(+\)	\(-\)	\(+\)	\(q+(1-\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots\)
4719.2.a.z	\(4\)	\(37.681\)	4.4.8468.1	None	\(2\)	\(-4\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.ba	\(5\)	\(37.681\)	5.5.210557.1	None	\(-2\)	\(5\)	\(3\)	\(-6\)	\(-\)	\(-\)	\(+\)	\(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
4719.2.a.bb	\(5\)	\(37.681\)	5.5.394064.1	None	\(-1\)	\(-5\)	\(2\)	\(2\)	\(+\)	\(+\)	\(+\)	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.bc	\(5\)	\(37.681\)	5.5.303952.1	None	\(-1\)	\(5\)	\(-2\)	\(-6\)	\(-\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bd	\(5\)	\(37.681\)	5.5.394064.1	None	\(1\)	\(-5\)	\(2\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
4719.2.a.be	\(5\)	\(37.681\)	5.5.303952.1	None	\(1\)	\(5\)	\(-2\)	\(6\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bf	\(5\)	\(37.681\)	5.5.210557.1	None	\(2\)	\(5\)	\(3\)	\(6\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
4719.2.a.bg	\(6\)	\(37.681\)	6.6.966125.1	None	\(-1\)	\(6\)	\(-6\)	\(-5\)	\(-\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
4719.2.a.bh	\(6\)	\(37.681\)	6.6.966125.1	None	\(1\)	\(6\)	\(-6\)	\(5\)	\(-\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
4719.2.a.bi	\(10\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-3\)	\(-10\)	\(-8\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bj	\(10\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-2\)	\(-10\)	\(4\)	\(4\)	\(+\)	\(+\)	\(+\)	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
4719.2.a.bk	\(10\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-2\)	\(10\)	\(-4\)	\(-12\)	\(-\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
4719.2.a.bl	\(10\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(2\)	\(-10\)	\(4\)	\(-4\)	\(+\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
4719.2.a.bm	\(10\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(2\)	\(10\)	\(-4\)	\(12\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
4719.2.a.bn	\(10\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(3\)	\(-10\)	\(-8\)	\(1\)	\(+\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4719.2.a.bo	\(14\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(-3\)	\(-14\)	\(8\)	\(-3\)	\(+\)	\(-\)	\(+\)	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
4719.2.a.bp	\(14\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(3\)	\(-14\)	\(8\)	\(3\)	\(+\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
4719.2.a.bq	\(18\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(-1\)	\(18\)	\(10\)	\(-7\)	\(-\)	\(+\)	\(+\)	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)
4719.2.a.br	\(18\)	\(37.681\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(1\)	\(18\)	\(10\)	\(7\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)