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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2116.1.c.a	$2116$	$1$	2116.c	4.b	$2$	$1$	$1$	$1.056$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-23}) \)	\(\Q(\sqrt{23}) \)	✓	✓			2116.1.c.a	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$1$		\(q-q^{2}+q^{4}-q^{8}+q^{9}+2q^{13}+q^{16}+\cdots\)
2116.1.c.b	$2116$	$1$	2116.c	4.b	$2$	$1$	$1$	$1.056$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None	✓	✓			2116.1.c.b	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)		$1$		\(q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots\)
2116.1.c.c	$2116$	$1$	2116.c	4.b	$2$	$1$	$1$	$1.056$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None	✓	✓			2116.1.c.b	$2$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$1$		\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{9}+q^{10}+\cdots\)
2116.1.c.d	$2116$	$1$	2116.c	4.b	$2$	$2$	$2$	$1.056$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-1}) \)	None	✓	✓			2116.1.c.d	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$1$		\(q-q^{2}+q^{4}-\beta q^{5}-q^{8}+q^{9}+\beta q^{10}+\cdots\)
2116.1.c.e	$2116$	$1$	2116.c	4.b	$2$	$2$	$2$	$1.056$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-23}) \)	None		✓			2116.1.c.e	$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{6}^{2}q^{2}+(-\zeta_{6}-\zeta_{6}^{2})q^{3}-\zeta_{6}q^{4}+\cdots\)
2116.1.g.a	$2116$	$1$	2116.g	92.g	$22$	$10$	$1$	$1.056$	\(\Q(\zeta_{22})\)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None		✓			2116.1.c.b	$20$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)		$1$		\(q-\zeta_{22}^{5}q^{2}+\zeta_{22}^{10}q^{4}+\zeta_{22}^{8}q^{5}+\cdots\)
2116.1.g.b	$2116$	$1$	2116.g	92.g	$22$	$10$	$1$	$1.056$	\(\Q(\zeta_{22})\)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None		✓			2116.1.c.b	$20$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)		$1$		\(q-\zeta_{22}^{5}q^{2}+\zeta_{22}^{10}q^{4}-\zeta_{22}^{8}q^{5}+\cdots\)
2116.1.g.c	$2116$	$1$	2116.g	92.g	$22$	$10$	$1$	$1.056$	\(\Q(\zeta_{22})\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-23}) \)	\(\Q(\sqrt{23}) \)		✓			2116.1.c.a	$40$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$1$		\(q+\zeta_{22}^{5}q^{2}+\zeta_{22}^{10}q^{4}-\zeta_{22}^{4}q^{8}+\cdots\)
2116.1.g.d	$2116$	$1$	2116.g	92.g	$22$	$20$	$2$	$1.056$	\(\Q(\zeta_{33})\)	$D_{6}$	\(\Q(\sqrt{-23}) \)	None		✓			2116.1.c.e	$40$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$1$		\(q+\zeta_{66}^{19}q^{2}+(\zeta_{66}^{20}+\zeta_{66}^{31})q^{3}+\cdots\)
2116.1.g.e	$2116$	$1$	2116.g	92.g	$22$	$20$	$2$	$1.056$	20.0.\(\cdots\).3	$D_{6}$	\(\Q(\sqrt{-1}) \)	None		✓			2116.1.c.d	$40$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{18}q^{2}+\beta _{14}q^{4}-\beta _{9}q^{5}-\beta _{10}q^{8}+\cdots\)
2116.2.a.a	$2116$	$2$	2116.a	1.a	$1$	$1$	$1$	$16.896$	\(\Q\)	$_{}$	None	None	✓				92.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+4q^{7}+6q^{9}-2q^{11}+\cdots\)
2116.2.a.b	$2116$	$2$	2116.a	1.a	$1$	$1$	$1$	$16.896$	\(\Q\)	$_{}$	None	None	✓	✓			2116.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{9}+4q^{11}+q^{13}+\cdots\)
2116.2.a.c	$2116$	$2$	2116.a	1.a	$1$	$1$	$1$	$16.896$	\(\Q\)	$_{}$	None	None	✓	✓			2116.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}-4q^{11}+q^{13}+\cdots\)
2116.2.a.d	$2116$	$2$	2116.a	1.a	$1$	$1$	$1$	$16.896$	\(\Q\)	$_{}$	None	None	✓				92.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}-2q^{9}-q^{13}+6q^{17}+\cdots\)
2116.2.a.e	$2116$	$2$	2116.a	1.a	$1$	$2$	$2$	$16.896$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	✓			2116.2.a.e	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+q^{13}+\cdots\)
2116.2.a.f	$2116$	$2$	2116.a	1.a	$1$	$2$	$2$	$16.896$	\(\Q(\sqrt{3}) \)	$_{}$	None	None	✓	✓			2116.2.a.f	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+\beta q^{7}-2q^{9}+\beta q^{11}+\cdots\)
2116.2.a.g	$2116$	$2$	2116.a	1.a	$1$	$6$	$6$	$16.896$	6.6.197448192.1	$_{}$	None	None	✓	✓			2116.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
2116.2.a.h	$2116$	$2$	2116.a	1.a	$1$	$8$	$8$	$16.896$	8.8.5780865024.1	$_{}$	None	None	✓	✓			2116.2.a.h	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{5})q^{3}-\beta _{7}q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
2116.2.a.i	$2116$	$2$	2116.a	1.a	$1$	$10$	$10$	$16.896$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None	✓		✓		92.2.e.a	$1$	$1$	\(0\)	\(1\)	\(-12\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{4})q^{3}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
2116.2.a.j	$2116$	$2$	2116.a	1.a	$1$	$10$	$10$	$16.896$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None	✓		✓		92.2.e.a	$1$	$0$	\(0\)	\(1\)	\(12\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{4})q^{3}+(1+\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{5}+\cdots\)
2116.3.d.a	$2116$	$3$	2116.d	23.b	$2$	$12$	$12$	$57.657$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None		✓			2116.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{3})q^{3}+(\beta _{8}+\beta _{9})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2116.3.d.b	$2116$	$3$	2116.d	23.b	$2$	$32$	$32$	$57.657$		$_{}$	None	None		✓			2116.3.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
2116.3.d.c	$2116$	$3$	2116.d	23.b	$2$	$40$	$40$	$57.657$		$_{}$	None	None			✓		92.3.f.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
2116.4.a.a	$2116$	$4$	2116.a	1.a	$1$	$3$	$3$	$124.848$	3.3.1229.1	$_{}$	None	None	✓				92.4.a.a	$1$	$0$	\(0\)	\(-4\)	\(10\)	\(46\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(4+\beta _{1}-3\beta _{2})q^{5}+\cdots\)
2116.4.a.b	$2116$	$4$	2116.a	1.a	$1$	$3$	$3$	$124.848$	3.3.28669.1	$_{}$	None	None	✓				92.4.a.b	$1$	$0$	\(0\)	\(8\)	\(0\)	\(-42\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(3+\beta _{2})q^{3}-\beta _{1}q^{5}+(-14+\beta _{1}+\cdots)q^{7}+\cdots\)
2116.4.a.c	$2116$	$4$	2116.a	1.a	$1$	$6$	$6$	$124.848$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	$_{}$	None	None	✓	✓			2116.4.a.c	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(-20\)	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{1}+\beta _{3})q^{5}+(-3+\cdots)q^{7}+\cdots\)
2116.4.a.d	$2116$	$4$	2116.a	1.a	$1$	$6$	$6$	$124.848$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	$_{}$	None	None	✓	✓			2116.4.a.c	$1$	$0$	\(0\)	\(1\)	\(5\)	\(20\)	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{3})q^{5}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
2116.4.a.e	$2116$	$4$	2116.a	1.a	$1$	$6$	$6$	$124.848$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	$_{}$	None	None	✓	✓			2116.4.a.e	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$+$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{3}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2116.4.a.f	$2116$	$4$	2116.a	1.a	$1$	$10$	$10$	$124.848$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None	✓	✓			2116.4.a.f	$2$	$1$	\(0\)	\(-12\)	\(0\)	\(0\)	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)
2116.4.a.g	$2116$	$4$	2116.a	1.a	$1$	$12$	$12$	$124.848$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	$_{}$	None	None	✓	✓			2116.4.a.g	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$+$	$2^{14}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{6}q^{3}+(\beta _{1}+\beta _{8})q^{5}+(-\beta _{1}+\beta _{7}+\cdots)q^{7}+\cdots\)
2116.4.a.h	$2116$	$4$	2116.a	1.a	$1$	$20$	$20$	$124.848$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None	✓	✓			2116.4.a.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$-$	$2^{23}\cdot 3^{2}\cdot 23^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{3}+\beta _{11}q^{5}+(\beta _{12}+\beta _{15})q^{7}+\cdots\)
2116.4.a.i	$2116$	$4$	2116.a	1.a	$1$	$30$	$30$	$124.848$		$_{}$	None	None	✓		✓		92.4.e.a	$1$	$1$	\(0\)	\(-2\)	\(-50\)	\(2\)	$-$		$\mathrm{SU}(2)$
2116.4.a.j	$2116$	$4$	2116.a	1.a	$1$	$30$	$30$	$124.848$		$_{}$	None	None	✓		✓		92.4.e.a	$1$	$0$	\(0\)	\(-2\)	\(50\)	\(-2\)	$+$		$\mathrm{SU}(2)$

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