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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 84 matches)

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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
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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3920.1.j.a	$3920$	$1$	3920.j	20.d	$2$	$1$	$1$	$1.956$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓				80.1.h.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}-q^{9}+q^{25}+2q^{29}+2q^{41}+\cdots$
3920.1.j.b	$3920$	$1$	3920.j	20.d	$2$	$2$	$2$	$1.956$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None	✓				560.1.bt.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{3}-q^{5}+2q^{9}+\beta q^{15}-\beta q^{23}+\cdots$
3920.1.j.c	$3920$	$1$	3920.j	20.d	$2$	$2$	$2$	$1.956$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{35}) $		✓			3920.1.j.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{5}-q^{9}+iq^{13}+iq^{17}-q^{25}+\cdots$
3920.1.j.d	$3920$	$1$	3920.j	20.d	$2$	$2$	$2$	$1.956$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None	✓				560.1.bt.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta q^{3}+q^{5}+2q^{9}-\beta q^{15}+\beta q^{23}+\cdots$
3920.1.j.e	$3920$	$1$	3920.j	20.d	$2$	$4$	$4$	$1.956$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		✓	✓		3920.1.j.e	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{12}+\zeta_{12}^{5})q^{3}-\zeta_{12}^{3}q^{5}+(1+\cdots)q^{9}+\cdots$
3920.1.v.a	$3920$	$1$	3920.v	140.j	$4$	$8$	$4$	$1.956$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	3920.1.v.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{5}-\zeta_{16}^{4}q^{9}+(\zeta_{16}^{5}+\zeta_{16}^{7}+\cdots)q^{13}+\cdots$
3920.1.bh.a	$3920$	$1$	3920.bh	5.c	$4$	$4$	$2$	$1.956$	$\Q(\zeta_{8})$	$S_{4}$	None	None					1960.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{3}-\zeta_{8}q^{5}-q^{11}+\zeta_{8}q^{13}+\cdots$
3920.1.bh.b	$3920$	$1$	3920.bh	5.c	$4$	$4$	$2$	$1.956$	$\Q(\zeta_{8})$	$S_{4}$	None	None					980.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}+q^{11}+\zeta_{8}q^{13}+\cdots$
3920.1.br.a	$3920$	$1$	3920.br	35.i	$6$	$2$	$1$	$1.956$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None					140.1.h.a	$4$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{11}-q^{13}+\cdots$
3920.1.br.b	$3920$	$1$	3920.br	35.i	$6$	$2$	$1$	$1.956$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None					140.1.h.a	$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{11}+q^{13}+\cdots$
3920.1.bt.a	$3920$	$1$	3920.bt	140.p	$6$	$2$	$1$	$1.956$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $					80.1.h.a	$8$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}q^{5}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{25}+q^{29}+\cdots$
3920.1.bt.b	$3920$	$1$	3920.bt	140.p	$6$	$2$	$1$	$1.956$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $					80.1.h.a	$8$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{6}q^{5}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{25}+q^{29}+\cdots$
3920.1.bt.c	$3920$	$1$	3920.bt	140.p	$6$	$4$	$2$	$1.956$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None					560.1.bt.a	$8$	$0$	$0$	$0$	$-2$	$0$		$3$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{4}q^{5}+(-1+\cdots)q^{9}+\cdots$
3920.1.bt.d	$3920$	$1$	3920.bt	140.p	$6$	$4$	$2$	$1.956$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		✓			3920.1.j.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(-1+\cdots)q^{9}+\cdots$
3920.1.bt.e	$3920$	$1$	3920.bt	140.p	$6$	$4$	$2$	$1.956$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		✓			3920.1.j.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(-1+\cdots)q^{9}+\cdots$
3920.1.bt.f	$3920$	$1$	3920.bt	140.p	$6$	$4$	$2$	$1.956$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{35}) $		✓			3920.1.j.c	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{5}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{3}q^{13}+\cdots$
3920.1.cl.a	$3920$	$1$	3920.cl	35.l	$12$	$8$	$2$	$1.956$	$\Q(\zeta_{24})$	$S_{4}$	None	None					980.1.l.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{7}q^{3}+\zeta_{24}^{5}q^{5}-\zeta_{24}^{4}q^{11}+\cdots$
3920.1.cl.b	$3920$	$1$	3920.cl	35.l	$12$	$8$	$2$	$1.956$	$\Q(\zeta_{24})$	$S_{4}$	None	None					1960.1.v.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{7}q^{3}+\zeta_{24}^{11}q^{5}+\zeta_{24}^{4}q^{11}+\cdots$
3920.1.cx.a	$3920$	$1$	3920.cx	140.x	$12$	$16$	$4$	$1.956$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	3920.1.v.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{48}^{5}q^{5}-\zeta_{48}^{20}q^{9}+(-\zeta_{48}^{15}+\cdots)q^{13}+\cdots$
3920.1.di.a	$3920$	$1$	3920.di	980.aa	$14$	$12$	$2$	$1.956$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	3920.1.di.a	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-\zeta_{28}^{7}+\zeta_{28}^{11})q^{3}+\zeta_{28}^{2}q^{5}+\cdots$
3920.1.fc.a	$3920$	$1$	3920.fc	980.aq	$42$	$24$	$2$	$1.956$	$\Q(\zeta_{84})$	$D_{42}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	3920.1.fc.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-\zeta_{84}^{15}+\zeta_{84}^{35})q^{3}-\zeta_{84}^{32}q^{5}+\cdots$
3920.2.a.a	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				245.2.a.a	$1$	$1$	$0$	$-3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}-q^{11}+3q^{13}+\cdots$
3920.2.a.b	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				70.2.e.a	$1$	$0$	$0$	$-3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}+2q^{11}+3q^{15}+\cdots$
3920.2.a.c	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				280.2.a.a	$1$	$0$	$0$	$-3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}+5q^{11}+5q^{13}+\cdots$
3920.2.a.d	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				140.2.i.b	$1$	$0$	$0$	$-3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+6q^{9}+2q^{11}+6q^{13}+\cdots$
3920.2.a.e	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				70.2.e.d	$1$	$1$	$0$	$-2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}-3q^{11}+q^{13}+\cdots$
3920.2.a.f	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				1960.2.a.b	$1$	$1$	$0$	$-2$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots$
3920.2.a.g	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				70.2.e.b	$1$	$0$	$0$	$-2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-3q^{11}-5q^{13}+\cdots$
3920.2.a.h	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				20.2.a.a	$1$	$0$	$0$	$-2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots$
3920.2.a.i	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				280.2.q.c	$1$	$1$	$0$	$-2$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}+q^{11}+3q^{13}+\cdots$
3920.2.a.j	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				490.2.a.f	$1$	$0$	$0$	$-2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
3920.2.a.k	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				140.2.i.a	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-6q^{11}+2q^{13}+\cdots$
3920.2.a.l	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				1960.2.a.f	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-3q^{11}-q^{13}+\cdots$
3920.2.a.m	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				280.2.q.a	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-2q^{11}+q^{15}+\cdots$
3920.2.a.n	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				980.2.a.d	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}+q^{11}-5q^{13}+\cdots$
3920.2.a.o	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				1960.2.a.d	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}+5q^{11}+7q^{13}+\cdots$
3920.2.a.p	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				70.2.e.c	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}+6q^{11}-4q^{13}+\cdots$
3920.2.a.q	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				280.2.q.b	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}+2q^{11}-4q^{13}+\cdots$
3920.2.a.r	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				280.2.a.b	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}+5q^{11}-q^{13}+\cdots$
3920.2.a.s	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				40.2.a.a	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots$
3920.2.a.t	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				70.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}-4q^{11}+6q^{13}-2q^{17}+\cdots$
3920.2.a.u	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				140.2.a.a	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}-3q^{11}+q^{13}+\cdots$
3920.2.a.v	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				280.2.q.b	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}+2q^{11}+4q^{13}+\cdots$
3920.2.a.w	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				140.2.i.a	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-6q^{11}-2q^{13}+\cdots$
3920.2.a.x	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				1960.2.a.f	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-3q^{11}+q^{13}+\cdots$
3920.2.a.y	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				280.2.q.a	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-2q^{11}+q^{15}+\cdots$
3920.2.a.z	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				980.2.a.d	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+q^{11}+5q^{13}+\cdots$
3920.2.a.ba	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				35.2.a.a	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+3q^{11}-5q^{13}+\cdots$
3920.2.a.bb	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				1960.2.a.d	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+5q^{11}-7q^{13}+\cdots$
3920.2.a.bc	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	$_{}$	None	None	✓				70.2.e.c	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+6q^{11}+4q^{13}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.