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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 69 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
3969.1.b.a	$3969$	$1$	3969.b	3.b	$2$	$4$	$4$	$1.981$	$\Q(\sqrt{-2}, \sqrt{3})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(2\beta _{1}-\beta _{3})q^{8}+\cdots$
3969.1.j.a	$3969$	$1$	3969.j	63.j	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-\zeta_{6}q^{13}+q^{16}+\zeta_{6}q^{19}-\zeta_{6}q^{25}+\cdots$
3969.1.j.b	$3969$	$1$	3969.j	63.j	$6$	$4$	$2$	$1.981$	$\Q(\sqrt{-2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{3}q^{2}-q^{4}+(-\beta _{1}+\beta _{3})q^{11}-q^{16}+\cdots$
3969.1.j.c	$3969$	$1$	3969.j	63.j	$6$	$8$	$4$	$1.981$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$		$q+(\zeta_{24}+\zeta_{24}^{11})q^{2}+(-1+\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
3969.1.k.a	$3969$	$1$	3969.k	63.k	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-q^{8}+q^{11}-\zeta_{6}^{2}q^{16}+\cdots$
3969.1.k.b	$3969$	$1$	3969.k	63.k	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{16}+q^{25}+\zeta_{6}q^{37}+\cdots$
3969.1.k.c	$3969$	$1$	3969.k	63.k	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}+(1+\zeta_{6})q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
3969.1.k.d	$3969$	$1$	3969.k	63.k	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+q^{8}-q^{11}-\zeta_{6}^{2}q^{16}+\cdots$
3969.1.k.e	$3969$	$1$	3969.k	63.k	$6$	$4$	$2$	$1.981$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots$
3969.1.l.a	$3969$	$1$	3969.l	63.l	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
3969.1.l.b	$3969$	$1$	3969.l	63.l	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
3969.1.m.a	$3969$	$1$	3969.m	7.d	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-q^{8}-\zeta_{6}q^{11}-\zeta_{6}^{2}q^{16}+\cdots$
3969.1.m.b	$3969$	$1$	3969.m	7.d	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+q^{8}+\zeta_{6}q^{11}-\zeta_{6}^{2}q^{16}+\cdots$
3969.1.m.c	$3969$	$1$	3969.m	7.d	$6$	$4$	$2$	$1.981$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots$
3969.1.n.a	$3969$	$1$	3969.n	63.n	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{13}-\zeta_{6}q^{16}-\zeta_{6}^{2}q^{19}+\cdots$
3969.1.n.b	$3969$	$1$	3969.n	63.n	$6$	$4$	$2$	$1.981$	$\Q(\sqrt{-2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{11}+\cdots$
3969.1.n.c	$3969$	$1$	3969.n	63.n	$6$	$8$	$4$	$1.981$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$		$q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots$
3969.1.q.a	$3969$	$1$	3969.q	21.h	$6$	$8$	$4$	$1.981$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$		$q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots$
3969.1.r.a	$3969$	$1$	3969.r	9.d	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}-q^{19}+\cdots$
3969.1.r.b	$3969$	$1$	3969.r	9.d	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+q^{19}+\cdots$
3969.1.r.c	$3969$	$1$	3969.r	9.d	$6$	$4$	$2$	$1.981$	$\Q(\sqrt{-2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{11}+\cdots$
3969.1.r.d	$3969$	$1$	3969.r	9.d	$6$	$8$	$4$	$1.981$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$		$q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots$
3969.1.t.a	$3969$	$1$	3969.t	63.t	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{8}-\zeta_{6}^{2}q^{11}-q^{16}+\zeta_{6}^{2}q^{22}+\cdots$
3969.1.t.b	$3969$	$1$	3969.t	63.t	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+(-1-\zeta_{6})q^{13}+q^{16}+\zeta_{6}^{2}q^{25}+\cdots$
3969.1.t.c	$3969$	$1$	3969.t	63.t	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+q^{16}+\zeta_{6}^{2}q^{25}-\zeta_{6}^{2}q^{37}+\cdots$
3969.1.t.d	$3969$	$1$	3969.t	63.t	$6$	$2$	$1$	$1.981$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}-q^{8}+\zeta_{6}^{2}q^{11}-q^{16}+\zeta_{6}^{2}q^{22}+\cdots$
3969.1.t.e	$3969$	$1$	3969.t	63.t	$6$	$4$	$2$	$1.981$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(\zeta_{12}-\zeta_{12}^{5})q^{2}+(1+\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{4}+\cdots$
3969.1.br.a	$3969$	$1$	3969.br	441.ac	$42$	$12$	$1$	$1.981$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{42}^{18}q^{4}-\zeta_{42}^{2}q^{7}+(-\zeta_{42}^{3}+\cdots)q^{13}+\cdots$
3969.1.bt.a	$3969$	$1$	3969.bt	441.ae	$42$	$12$	$1$	$1.981$	$\Q(\zeta_{21})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{42}^{11}q^{4}+\zeta_{42}^{16}q^{7}+(\zeta_{42}^{8}-\zeta_{42}^{17}+\cdots)q^{13}+\cdots$
3969.1.bx.a	$3969$	$1$	3969.bx	441.ai	$42$	$12$	$1$	$1.981$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{42}q^{4}+\zeta_{42}^{4}q^{7}+(-\zeta_{42}^{9}-\zeta_{42}^{13}+\cdots)q^{13}+\cdots$
3969.1.bz.a	$3969$	$1$	3969.bz	441.ak	$42$	$12$	$1$	$1.981$	$\Q(\zeta_{21})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{42}^{16}q^{4}-\zeta_{42}^{8}q^{7}+(-\zeta_{42}^{4}+\cdots)q^{13}+\cdots$
3969.1.ca.a	$3969$	$1$	3969.ca	441.al	$42$	$12$	$1$	$1.981$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{42}^{10}q^{4}+\zeta_{42}^{19}q^{7}+(\zeta_{42}^{4}-\zeta_{42}^{6}+\cdots)q^{13}+\cdots$
3969.1.cb.a	$3969$	$1$	3969.cb	441.am	$42$	$12$	$1$	$1.981$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{42}^{18}q^{4}+\zeta_{42}^{16}q^{7}+(-\zeta_{42}+\cdots)q^{13}+\cdots$
3969.2.a.a	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}-5q^{11}+\cdots$
3969.2.a.b	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}-2q^{11}+\cdots$
3969.2.a.c	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-5q^{11}+\cdots$
3969.2.a.d	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+5q^{11}+\cdots$
3969.2.a.e	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+2q^{11}+\cdots$
3969.2.a.f	$3969$	$2$	3969.a	1.a	$1$	$1$	$1$	$31.693$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+5q^{11}+\cdots$
3969.2.a.g	$3969$	$2$	3969.a	1.a	$1$	$2$	$2$	$31.693$	$\Q(\sqrt{15}) $	$_{}$	None	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+\beta q^{5}+3q^{8}-\beta q^{10}+\cdots$
3969.2.a.h	$3969$	$2$	3969.a	1.a	$1$	$2$	$2$	$31.693$	$\Q(\sqrt{21}) $	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-\beta q^{2}+(3+\beta )q^{4}+(-5-2\beta )q^{8}+\cdots$
3969.2.a.i	$3969$	$2$	3969.a	1.a	$1$	$2$	$2$	$31.693$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+\beta q^{5}-\beta q^{8}+3q^{10}+\cdots$
3969.2.a.j	$3969$	$2$	3969.a	1.a	$1$	$2$	$2$	$31.693$	$\Q(\sqrt{21}) $	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{2}+(3+\beta )q^{4}+(5+2\beta )q^{8}+(1+\cdots)q^{11}+\cdots$
3969.2.a.k	$3969$	$2$	3969.a	1.a	$1$	$2$	$2$	$31.693$	$\Q(\sqrt{15}) $	$_{}$	None	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+\beta q^{10}+\cdots$
3969.2.a.l	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
3969.2.a.m	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	3.3.321.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2})q^{5}+\cdots$
3969.2.a.n	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	3.3.621.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots$
3969.2.a.o	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	3.3.621.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
3969.2.a.p	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	3.3.321.1	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2})q^{5}+\cdots$
3969.2.a.q	$3969$	$2$	3969.a	1.a	$1$	$3$	$3$	$31.693$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$

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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.