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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 258 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
2304.1.b.a	$2304$	$1$	2304.b	8.d	$2$	$2$	$2$	$1.150$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-iq^{13}+q^{25}-iq^{37}+q^{49}+iq^{61}+\cdots$
2304.1.e.a	$2304$	$1$	2304.e	3.b	$2$	$2$	$2$	$1.150$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}-2q^{13}-\beta q^{17}-q^{25}-\beta q^{29}+\cdots$
2304.1.e.b	$2304$	$1$	2304.e	3.b	$2$	$2$	$2$	$1.150$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta q^{5}+2q^{13}-\beta q^{17}-q^{25}+\beta q^{29}+\cdots$
2304.1.g.a	$2304$	$1$	2304.g	4.b	$2$	$1$	$1$	$1.150$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-2q^{5}+3q^{25}+2q^{29}+q^{49}+2q^{53}+\cdots$
2304.1.g.b	$2304$	$1$	2304.g	4.b	$2$	$1$	$1$	$1.150$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+2q^{17}-q^{25}+2q^{41}+q^{49}+2q^{73}+\cdots$
2304.1.g.c	$2304$	$1$	2304.g	4.b	$2$	$1$	$1$	$1.150$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+2q^{5}+3q^{25}-2q^{29}+q^{49}-2q^{53}+\cdots$
2304.1.g.d	$2304$	$1$	2304.g	4.b	$2$	$2$	$2$	$1.150$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{2}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-iq^{7}-q^{25}-iq^{31}-3q^{49}+q^{73}+\cdots$
2304.1.h.a	$2304$	$1$	2304.h	24.h	$2$	$4$	$4$	$1.150$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{17}+\cdots$
2304.1.m.a	$2304$	$1$	2304.m	16.f	$4$	$4$	$2$	$1.150$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{7}+(-1+\zeta_{8}^{2})q^{13}+\cdots$
2304.1.m.b	$2304$	$1$	2304.m	16.f	$4$	$4$	$2$	$1.150$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{7}+(1-\zeta_{8}^{2})q^{13}-\zeta_{8}q^{19}+\cdots$
2304.1.o.a	$2304$	$1$	2304.o	36.f	$6$	$2$	$1$	$1.150$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(-1-\zeta_{6})q^{11}+\cdots$
2304.1.o.b	$2304$	$1$	2304.o	36.f	$6$	$2$	$1$	$1.150$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(1+\zeta_{6})q^{11}+q^{17}+\cdots$
2304.1.o.c	$2304$	$1$	2304.o	36.f	$6$	$4$	$2$	$1.150$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{5}q^{11}+\cdots$
2304.1.q.a	$2304$	$1$	2304.q	9.d	$6$	$2$	$1$	$1.150$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(1+\zeta_{6})q^{11}+(-\zeta_{6}+\cdots)q^{17}+\cdots$
2304.1.q.b	$2304$	$1$	2304.q	9.d	$6$	$2$	$1$	$1.150$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(-1-\zeta_{6})q^{11}+\cdots$
2304.1.q.c	$2304$	$1$	2304.q	9.d	$6$	$4$	$2$	$1.150$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{5}q^{11}+\cdots$
2304.1.t.a	$2304$	$1$	2304.t	72.p	$6$	$4$	$2$	$1.150$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}q^{7}+q^{9}-\zeta_{12}^{4}q^{11}+\cdots$
2304.1.t.b	$2304$	$1$	2304.t	72.p	$6$	$4$	$2$	$1.150$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}q^{7}+q^{9}+\zeta_{12}^{4}q^{11}+\cdots$
2304.1.z.a	$2304$	$1$	2304.z	144.v	$12$	$8$	$2$	$1.150$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{24}^{5}q^{3}+(-\zeta_{24}^{4}+\zeta_{24}^{10})q^{5}+\cdots$
2304.1.z.b	$2304$	$1$	2304.z	144.v	$12$	$8$	$2$	$1.150$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q+\zeta_{24}^{5}q^{3}+(\zeta_{24}^{4}-\zeta_{24}^{10})q^{5}+(\zeta_{24}^{5}+\cdots)q^{7}+\cdots$
2304.2.a.a	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-4q^{5}+4q^{13}+2q^{17}+11q^{25}+\cdots$
2304.2.a.b	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}+4q^{13}+2q^{17}+4q^{19}+\cdots$
2304.2.a.c	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{5}-4q^{13}+8q^{17}-q^{25}+10q^{29}+\cdots$
2304.2.a.d	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{5}+4q^{13}-8q^{17}-q^{25}+10q^{29}+\cdots$
2304.2.a.e	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}+4q^{13}+2q^{17}-4q^{19}+\cdots$
2304.2.a.f	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-4q^{11}+4q^{13}+2q^{17}-4q^{19}+\cdots$
2304.2.a.g	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}+4q^{11}-4q^{13}+2q^{17}+4q^{19}+\cdots$
2304.2.a.h	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-6q^{11}+6q^{17}+2q^{19}-5q^{25}+\cdots$
2304.2.a.i	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+6q^{11}+6q^{17}-2q^{19}-5q^{25}+\cdots$
2304.2.a.j	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-4q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots$
2304.2.a.k	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}+4q^{11}+4q^{13}+2q^{17}+4q^{19}+\cdots$
2304.2.a.l	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-4q^{13}+2q^{17}-4q^{19}+\cdots$
2304.2.a.m	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+2q^{5}-4q^{13}-8q^{17}-q^{25}-10q^{29}+\cdots$
2304.2.a.n	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+2q^{5}+4q^{13}+8q^{17}-q^{25}-10q^{29}+\cdots$
2304.2.a.o	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}-4q^{13}+2q^{17}+4q^{19}+\cdots$
2304.2.a.p	$2304$	$2$	2304.a	1.a	$1$	$1$	$1$	$18.398$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{5}-4q^{13}+2q^{17}+11q^{25}+\cdots$
2304.2.a.q	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-6}) $	None	✓	$4$	$1$	$0$	$0$	$0$	$-4$	$+$	$2$	$N(\mathrm{U}(1))$	$q+\beta q^{5}-2q^{7}-2\beta q^{11}+3q^{25}-\beta q^{29}+\cdots$
2304.2.a.r	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-\beta q^{7}-4q^{11}+2\beta q^{13}+2q^{17}+\cdots$
2304.2.a.s	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-\beta q^{7}-6q^{17}-4q^{19}-2\beta q^{23}+\cdots$
2304.2.a.t	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-2}) $	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$N(\mathrm{U}(1))$	$q+\beta q^{11}-6q^{17}-3\beta q^{19}-5q^{25}+\cdots$
2304.2.a.u	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+\beta q^{7}-6q^{17}+4q^{19}+2\beta q^{23}+\cdots$
2304.2.a.v	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$N(\mathrm{U}(1))$	$q+\beta q^{7}-2\beta q^{13}-8q^{19}-5q^{25}+\cdots$
2304.2.a.w	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$N(\mathrm{U}(1))$	$q-\beta q^{7}-2\beta q^{13}+8q^{19}-5q^{25}+\cdots$
2304.2.a.x	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+\beta q^{7}+4q^{11}+2\beta q^{13}+2q^{17}+\cdots$
2304.2.a.y	$2304$	$2$	2304.a	1.a	$1$	$2$	$2$	$18.398$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-6}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$4$	$-$	$2$	$N(\mathrm{U}(1))$	$q+\beta q^{5}+2q^{7}+2\beta q^{11}+3q^{25}-\beta q^{29}+\cdots$
2304.2.a.z	$2304$	$2$	2304.a	1.a	$1$	$4$	$4$	$18.398$	$\Q(\zeta_{24})^+$	$_{}$	$\Q(\sqrt{-6}) $	None	✓	$8$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{5}$	$N(\mathrm{U}(1))$	$q+\beta _{2}q^{5}+\beta _{1}q^{7}+\beta _{3}q^{11}+7q^{25}+\cdots$
2304.2.c.a	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-2\beta q^{7}-4q^{11}-2q^{13}+\beta q^{17}+\cdots$
2304.2.c.b	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-2\beta q^{7}-4q^{11}+2q^{13}-\beta q^{17}+\cdots$
2304.2.c.c	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3\beta q^{5}-6q^{13}-5\beta q^{17}-13q^{25}+\cdots$
2304.2.c.d	$2304$	$2$	2304.c	12.b	$2$	$2$	$2$	$18.398$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}-6q^{13}-3\beta q^{17}+3q^{25}+\cdots$

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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.