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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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1629.1.j.a	$1629$	$1$	1629.j	181.d	$4$	$2$	$1$	$0.813$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		✓			1629.1.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$1$		\(q-i q^{4}+(-i+1)q^{7}+2 q^{13}-q^{16}+\cdots\)
1629.1.j.b	$1629$	$1$	1629.j	181.d	$4$	$4$	$2$	$0.813$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		✓	✓		1629.1.j.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\zeta_{8}^{3}q^{2}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}q^{8}+\cdots\)
1629.1.o.a	$1629$	$1$	1629.o	1629.o	$6$	$2$	$1$	$0.813$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{181}) \)		✓	✓	✓	1629.1.o.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$1$		\(q+\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+(-1-\zeta_{6}+\cdots)q^{11}+\cdots\)
1629.1.bh.a	$1629$	$1$	1629.bh	1629.ah	$12$	$4$	$1$	$0.813$	\(\Q(\zeta_{12})\)	$S_{4}$	None	None		✓	✓	✓	1629.1.bh.a	$4$	$0$	\(2\)	\(2\)	\(0\)	\(-2\)		$1$		\(q+(\zeta_{12}-\zeta_{12}^{4})q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}^{5}q^{4}+\cdots\)
1629.1.bk.a	$1629$	$1$	1629.bk	181.i	$12$	$4$	$1$	$0.813$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	1629.1.bk.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$1$		\(q-\zeta_{12}q^{4}+(1+\zeta_{12}^{3})q^{7}+\zeta_{12}^{4}q^{13}+\cdots\)
1629.1.by.a	$1629$	$1$	1629.by	181.l	$20$	$8$	$1$	$0.813$	\(\Q(\zeta_{20})\)	$D_{20}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	1629.1.by.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$1$		\(q+\zeta_{20}q^{4}+(\zeta_{20}+\zeta_{20}^{4})q^{7}+(-\zeta_{20}^{6}+\cdots)q^{13}+\cdots\)
1629.1.cv.a	$1629$	$1$	1629.cv	181.p	$60$	$16$	$1$	$0.813$	\(\Q(\zeta_{60})\)	$D_{60}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	1629.1.cv.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$1$		\(q-\zeta_{60}^{19}q^{4}+(-\zeta_{60}^{6}+\zeta_{60}^{9})q^{7}+\cdots\)
1629.2.a.a	$1629$	$2$	1629.a	1.a	$1$	$3$	$3$	$13.008$	\(\Q(\zeta_{14})^+\)	$_{}$	None	None	✓				543.2.a.a	$1$	$1$	\(2\)	\(0\)	\(1\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
1629.2.a.b	$1629$	$2$	1629.a	1.a	$1$	$5$	$5$	$13.008$	5.5.170701.1	$_{}$	None	None	✓				543.2.a.b	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(9\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{4})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1629.2.a.c	$1629$	$2$	1629.a	1.a	$1$	$5$	$5$	$13.008$	5.5.24217.1	$_{}$	None	None	✓				181.2.a.a	$1$	$0$	\(3\)	\(0\)	\(5\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(1-\beta _{2}+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
1629.2.a.d	$1629$	$2$	1629.a	1.a	$1$	$7$	$7$	$13.008$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	$_{}$	None	None	✓				543.2.a.c	$1$	$0$	\(4\)	\(0\)	\(3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
1629.2.a.e	$1629$	$2$	1629.a	1.a	$1$	$8$	$8$	$13.008$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	$_{}$	None	None	✓				543.2.a.d	$1$	$1$	\(-3\)	\(0\)	\(-5\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1629.2.a.f	$1629$	$2$	1629.a	1.a	$1$	$8$	$8$	$13.008$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	$_{}$	None	None	✓		✓		543.2.a.e	$1$	$0$	\(-3\)	\(0\)	\(2\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{2}+(2+\beta _{1}+\beta _{5})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
1629.2.a.g	$1629$	$2$	1629.a	1.a	$1$	$9$	$9$	$13.008$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	$_{}$	None	None	✓		✓		181.2.a.b	$1$	$1$	\(-3\)	\(0\)	\(-1\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1629.2.a.h	$1629$	$2$	1629.a	1.a	$1$	$10$	$10$	$13.008$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	1629.2.a.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-10\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots\)
1629.2.a.i	$1629$	$2$	1629.a	1.a	$1$	$20$	$20$	$13.008$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	1629.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(14\)	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{14}q^{5}+(1+\cdots)q^{7}+\cdots\)
1629.2.c.a	$1629$	$2$	1629.c	181.b	$2$	$12$	$12$	$13.008$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	\(\Q(\sqrt{-543}) \)	None		✓			1629.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3}+\cdots)q^{8}+\cdots\)
1629.2.c.b	$1629$	$2$	1629.c	181.b	$2$	$14$	$14$	$13.008$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	$_{}$	None	None					181.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots\)
1629.2.c.c	$1629$	$2$	1629.c	181.b	$2$	$14$	$14$	$13.008$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	$_{}$	None	None					543.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}-\beta _{13}q^{7}+\cdots\)
1629.2.c.d	$1629$	$2$	1629.c	181.b	$2$	$16$	$16$	$13.008$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None					543.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$2\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}-\beta _{5}q^{7}+\cdots\)
1629.2.c.e	$1629$	$2$	1629.c	181.b	$2$	$20$	$20$	$13.008$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		✓	✓		1629.2.c.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{2}-\beta _{3}q^{4}-\beta _{12}q^{5}+\beta _{8}q^{7}+\cdots\)
1629.4.a.a	$1629$	$4$	1629.a	1.a	$1$	$1$	$1$	$96.114$	\(\Q\)	$_{}$	None	None	✓				181.4.a.a	$1$	$0$	\(3\)	\(0\)	\(18\)	\(20\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+q^{4}+18q^{5}+20q^{7}-21q^{8}+\cdots\)
1629.4.a.b	$1629$	$4$	1629.a	1.a	$1$	$17$	$17$	$96.114$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	$_{}$	None	None	✓				543.4.a.a	$1$	$1$	\(5\)	\(0\)	\(21\)	\(-62\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
1629.4.a.c	$1629$	$4$	1629.a	1.a	$1$	$19$	$19$	$96.114$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	$_{}$	None	None	✓				181.4.a.b	$1$	$0$	\(8\)	\(0\)	\(16\)	\(-73\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
1629.4.a.d	$1629$	$4$	1629.a	1.a	$1$	$22$	$22$	$96.114$		$_{}$	None	None	✓				543.4.a.b	$1$	$0$	\(7\)	\(0\)	\(11\)	\(8\)	$+$		$\mathrm{SU}(2)$
1629.4.a.e	$1629$	$4$	1629.a	1.a	$1$	$23$	$23$	$96.114$		$_{}$	None	None	✓				543.4.a.c	$1$	$1$	\(-7\)	\(0\)	\(-29\)	\(-6\)	$-$		$\mathrm{SU}(2)$
1629.4.a.f	$1629$	$4$	1629.a	1.a	$1$	$25$	$25$	$96.114$		$_{}$	None	None	✓		✓		181.4.a.c	$1$	$1$	\(-7\)	\(0\)	\(-26\)	\(31\)	$-$		$\mathrm{SU}(2)$
1629.4.a.g	$1629$	$4$	1629.a	1.a	$1$	$28$	$28$	$96.114$		$_{}$	None	None	✓		✓		543.4.a.d	$1$	$0$	\(-9\)	\(0\)	\(-19\)	\(92\)	$+$		$\mathrm{SU}(2)$
1629.4.a.h	$1629$	$4$	1629.a	1.a	$1$	$40$	$40$	$96.114$		$_{}$	None	None	✓	✓	✓	✓	1629.4.a.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-88\)	$-$		$\mathrm{SU}(2)$
1629.4.a.i	$1629$	$4$	1629.a	1.a	$1$	$50$	$50$	$96.114$		$_{}$	None	None	✓	✓	✓	✓	1629.4.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(80\)	$+$		$\mathrm{SU}(2)$

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