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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 137 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1620.1.f.a	$1620$	$1$	1620.f	20.d	$2$	$1$	$1$	$0.808$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
1620.1.f.b	$1620$	$1$	1620.f	20.d	$2$	$1$	$1$	$0.808$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$1$		$1$		$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
1620.1.f.c	$1620$	$1$	1620.f	20.d	$2$	$1$	$1$	$0.808$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$1$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
1620.1.f.d	$1620$	$1$	1620.f	20.d	$2$	$1$	$1$	$0.808$	$\Q$	$D_{3}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-1$		$1$		$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
1620.1.f.e	$1620$	$1$	1620.f	20.d	$2$	$4$	$4$	$0.808$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
1620.1.l.a	$1620$	$1$	1620.l	5.c	$4$	$2$	$1$	$0.808$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+iq^{5}+(-1+i)q^{7}-q^{11}+(-1+\cdots)q^{17}+\cdots$
1620.1.l.b	$1620$	$1$	1620.l	5.c	$4$	$2$	$1$	$0.808$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-iq^{5}+(-1+i)q^{7}+q^{11}+(1-i+\cdots)q^{17}+\cdots$
1620.1.m.a	$1620$	$1$	1620.m	60.l	$4$	$8$	$4$	$0.808$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}q^{5}+\zeta_{24}^{3}q^{8}+\cdots$
1620.1.p.a	$1620$	$1$	1620.p	180.p	$6$	$4$	$2$	$0.808$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
1620.1.p.b	$1620$	$1$	1620.p	180.p	$6$	$4$	$2$	$0.808$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{15}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
1620.1.p.c	$1620$	$1$	1620.p	180.p	$6$	$4$	$2$	$0.808$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
1620.1.p.d	$1620$	$1$	1620.p	180.p	$6$	$4$	$2$	$0.808$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots$
1620.1.p.e	$1620$	$1$	1620.p	180.p	$6$	$4$	$2$	$0.808$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
1620.1.v.a	$1620$	$1$	1620.v	45.k	$12$	$4$	$1$	$0.808$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{4}q^{11}+\cdots$
1620.1.v.b	$1620$	$1$	1620.v	45.k	$12$	$4$	$1$	$0.808$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{12}^{5}q^{5}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}-\zeta_{12}^{4}q^{11}+\cdots$
1620.1.w.a	$1620$	$1$	1620.w	180.v	$12$	$8$	$2$	$0.808$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{9}q^{5}+\cdots$
1620.1.w.b	$1620$	$1$	1620.w	180.v	$12$	$8$	$2$	$0.808$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}q^{5}+\cdots$
1620.1.w.c	$1620$	$1$	1620.w	180.v	$12$	$8$	$2$	$0.808$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{5}q^{5}+\cdots$
1620.1.bf.a	$1620$	$1$	1620.bf	540.af	$18$	$6$	$1$	$0.808$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(\zeta_{18}^{4}+\cdots)q^{7}+\cdots$
1620.1.bf.b	$1620$	$1$	1620.bf	540.af	$18$	$6$	$1$	$0.808$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+(-\zeta_{18}^{4}+\cdots)q^{7}+\cdots$
1620.1.bp.a	$1620$	$1$	1620.bp	1620.ap	$54$	$18$	$1$	$0.808$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{54}^{25}q^{2}-\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots$
1620.1.bp.b	$1620$	$1$	1620.bp	1620.ap	$54$	$18$	$1$	$0.808$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{54}^{25}q^{2}+\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots$
1620.2.a.a	$1620$	$2$	1620.a	1.a	$1$	$1$	$1$	$12.936$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-3q^{11}-4q^{13}+5q^{19}+\cdots$
1620.2.a.b	$1620$	$2$	1620.a	1.a	$1$	$1$	$1$	$12.936$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-4q^{13}+6q^{17}+2q^{19}+\cdots$
1620.2.a.c	$1620$	$2$	1620.a	1.a	$1$	$1$	$1$	$12.936$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+3q^{11}-4q^{13}+6q^{17}+\cdots$
1620.2.a.d	$1620$	$2$	1620.a	1.a	$1$	$1$	$1$	$12.936$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}+3q^{11}-4q^{13}+5q^{19}+\cdots$
1620.2.a.e	$1620$	$2$	1620.a	1.a	$1$	$1$	$1$	$12.936$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-4q^{13}-6q^{17}+2q^{19}+\cdots$
1620.2.a.f	$1620$	$2$	1620.a	1.a	$1$	$1$	$1$	$12.936$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{11}-4q^{13}-6q^{17}+\cdots$
1620.2.a.g	$1620$	$2$	1620.a	1.a	$1$	$2$	$2$	$12.936$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta )q^{7}-\beta q^{11}+(2-2\beta )q^{13}+\cdots$
1620.2.a.h	$1620$	$2$	1620.a	1.a	$1$	$2$	$2$	$12.936$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta )q^{7}+\beta q^{11}+(2-2\beta )q^{13}+\cdots$
1620.2.a.i	$1620$	$2$	1620.a	1.a	$1$	$3$	$3$	$12.936$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$3$	$-$	$3$	$\mathrm{SU}(2)$	$q-q^{5}+(1-\beta _{1})q^{7}-\beta _{2}q^{11}+(2+\beta _{2})q^{13}+\cdots$
1620.2.a.j	$1620$	$2$	1620.a	1.a	$1$	$3$	$3$	$12.936$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{5}+(1-\beta _{1})q^{7}+\beta _{2}q^{11}+(2+\beta _{2})q^{13}+\cdots$
1620.2.d.a	$1620$	$2$	1620.d	5.b	$2$	$2$	$2$	$12.936$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-i)q^{5}+iq^{7}+q^{11}-iq^{17}+\cdots$
1620.2.d.b	$1620$	$2$	1620.d	5.b	$2$	$2$	$2$	$12.936$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{5}+iq^{7}-q^{11}+iq^{17}+\cdots$
1620.2.d.c	$1620$	$2$	1620.d	5.b	$2$	$6$	$6$	$12.936$	6.0.301925376.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}-\beta _{2}q^{11}+\cdots$
1620.2.d.d	$1620$	$2$	1620.d	5.b	$2$	$6$	$6$	$12.936$	6.0.301925376.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\beta _{2}q^{11}+\cdots$
1620.2.d.e	$1620$	$2$	1620.d	5.b	$2$	$8$	$8$	$12.936$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}+(-\beta _{1}+\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots$
1620.2.e.a	$1620$	$2$	1620.e	12.b	$2$	$48$	$48$	$12.936$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1620.2.e.b	$1620$	$2$	1620.e	12.b	$2$	$48$	$48$	$12.936$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1620.2.i.a	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots$
1620.2.i.b	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots$
1620.2.i.c	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots$
1620.2.i.d	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$
1620.2.i.e	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$
1620.2.i.f	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$
1620.2.i.g	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots$
1620.2.i.h	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots$
1620.2.i.i	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots$
1620.2.i.j	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$
1620.2.i.k	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$

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