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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 58 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
3192.1.m.a	$3192$	$1$	3192.m	3192.m	$2$	$1$	$1$	$1.593$	$\Q$	$D_{2}$	$\Q(\sqrt{-14}) $, $\Q(\sqrt{-798}) $	$\Q(\sqrt{57}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
3192.1.m.b	$3192$	$1$	3192.m	3192.m	$2$	$1$	$1$	$1.593$	$\Q$	$D_{2}$	$\Q(\sqrt{-14}) $, $\Q(\sqrt{-798}) $	$\Q(\sqrt{57}) $	✓	$4$	$0$	$-1$	$1$	$0$	$-1$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
3192.1.m.c	$3192$	$1$	3192.m	3192.m	$2$	$1$	$1$	$1.593$	$\Q$	$D_{2}$	$\Q(\sqrt{-14}) $, $\Q(\sqrt{-798}) $	$\Q(\sqrt{57}) $	✓	$4$	$0$	$1$	$-1$	$0$	$-1$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
3192.1.m.d	$3192$	$1$	3192.m	3192.m	$2$	$1$	$1$	$1.593$	$\Q$	$D_{2}$	$\Q(\sqrt{-14}) $, $\Q(\sqrt{-798}) $	$\Q(\sqrt{57}) $	✓	$4$	$0$	$1$	$1$	$0$	$-1$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
3192.1.m.e	$3192$	$1$	3192.m	3192.m	$2$	$2$	$2$	$1.593$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-14}) $, $\Q(\sqrt{-399}) $	$\Q(\sqrt{114}) $		$8$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-q^{2}-iq^{3}+q^{4}-iq^{5}+iq^{6}+q^{7}+\cdots$
3192.1.m.f	$3192$	$1$	3192.m	3192.m	$2$	$2$	$2$	$1.593$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-38}) $, $\Q(\sqrt{-399}) $	$\Q(\sqrt{42}) $		$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+q^{7}+iq^{8}+\cdots$
3192.1.m.g	$3192$	$1$	3192.m	3192.m	$2$	$2$	$2$	$1.593$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-38}) $, $\Q(\sqrt{-399}) $	$\Q(\sqrt{42}) $		$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q+iq^{2}-iq^{3}-q^{4}+q^{6}+q^{7}-iq^{8}+\cdots$
3192.1.m.h	$3192$	$1$	3192.m	3192.m	$2$	$2$	$2$	$1.593$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-14}) $, $\Q(\sqrt{-399}) $	$\Q(\sqrt{114}) $		$8$	$0$	$2$	$0$	$0$	$2$		$1$		$q+q^{2}-iq^{3}+q^{4}+iq^{5}-iq^{6}+q^{7}+\cdots$
3192.1.m.i	$3192$	$1$	3192.m	3192.m	$2$	$4$	$4$	$1.593$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{4}q^{6}+\cdots$
3192.1.m.j	$3192$	$1$	3192.m	3192.m	$2$	$4$	$4$	$1.593$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots$
3192.1.m.k	$3192$	$1$	3192.m	3192.m	$2$	$4$	$4$	$1.593$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-399}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
3192.1.m.l	$3192$	$1$	3192.m	3192.m	$2$	$4$	$4$	$1.593$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-399}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+\zeta_{8}^{3}q^{2}+\zeta_{8}^{2}q^{3}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
3192.1.bu.a	$3192$	$1$	3192.bu	399.n	$6$	$4$	$2$	$1.593$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q+(1-\beta _{2})q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-\beta _{2}q^{9}+\cdots$
3192.1.eb.a	$3192$	$1$	3192.eb	3192.db	$6$	$12$	$6$	$1.593$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{15}q^{2}-\zeta_{36}q^{3}-\zeta_{36}^{12}q^{4}+\cdots$
3192.1.eb.b	$3192$	$1$	3192.eb	3192.db	$6$	$12$	$6$	$1.593$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{3}q^{2}-\zeta_{36}q^{3}+\zeta_{36}^{6}q^{4}+\zeta_{36}^{4}q^{6}+\cdots$
3192.1.ev.a	$3192$	$1$	3192.ev	399.ai	$6$	$4$	$2$	$1.593$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$2$		$1$		$q-q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{13}+\cdots$
3192.1.fm.a	$3192$	$1$	3192.fm	3192.em	$6$	$2$	$1$	$1.593$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$-1$	$-1$	$3$	$-2$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(1-\zeta_{6}^{2}+\cdots)q^{5}+\cdots$
3192.1.fm.b	$3192$	$1$	3192.fm	3192.em	$6$	$2$	$1$	$1.593$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$-1$	$1$	$-3$	$-2$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(-1+\zeta_{6}^{2}+\cdots)q^{5}+\cdots$
3192.1.fm.c	$3192$	$1$	3192.fm	3192.em	$6$	$2$	$1$	$1.593$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$1$	$-1$	$3$	$-2$		$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(1-\zeta_{6}^{2}+\cdots)q^{5}+\cdots$
3192.1.fm.d	$3192$	$1$	3192.fm	3192.em	$6$	$2$	$1$	$1.593$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$1$	$1$	$-3$	$-2$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(-1+\zeta_{6}^{2}+\cdots)q^{5}+\cdots$
3192.1.fm.e	$3192$	$1$	3192.fm	3192.em	$6$	$4$	$2$	$1.593$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$-2$	$0$	$0$	$4$		$1$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}+\cdots$
3192.1.fm.f	$3192$	$1$	3192.fm	3192.em	$6$	$4$	$2$	$1.593$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$2$	$0$	$0$	$4$		$1$		$q-\zeta_{12}^{4}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}+\cdots$
3192.1.hj.a	$3192$	$1$	3192.hj	3192.gj	$18$	$6$	$1$	$1.593$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$0$	$-3$	$3$		$1$		$q-\zeta_{18}^{7}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
3192.1.hj.b	$3192$	$1$	3192.hj	3192.gj	$18$	$6$	$1$	$1.593$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$0$	$-3$	$3$		$1$		$q+\zeta_{18}^{7}q^{2}-\zeta_{18}^{7}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
3192.1.hj.c	$3192$	$1$	3192.hj	3192.gj	$18$	$6$	$1$	$1.593$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$0$	$3$	$3$		$1$		$q-\zeta_{18}^{7}q^{2}-\zeta_{18}^{4}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
3192.1.hj.d	$3192$	$1$	3192.hj	3192.gj	$18$	$6$	$1$	$1.593$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$0$	$3$	$3$		$1$		$q+\zeta_{18}^{7}q^{2}+\zeta_{18}^{7}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
3192.1.hj.e	$3192$	$1$	3192.hj	3192.gj	$18$	$12$	$2$	$1.593$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$-6$		$1$		$q-\zeta_{36}^{14}q^{2}+\zeta_{36}^{5}q^{3}-\zeta_{36}^{10}q^{4}+\cdots$
3192.1.hj.f	$3192$	$1$	3192.hj	3192.gj	$18$	$12$	$2$	$1.593$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$-6$		$1$		$q+\zeta_{36}^{14}q^{2}-\zeta_{36}^{17}q^{3}-\zeta_{36}^{10}q^{4}+\cdots$
3192.2.a.a	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}-q^{7}+q^{9}-2q^{13}+4q^{15}+\cdots$
3192.2.a.b	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
3192.2.a.c	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots$
3192.2.a.d	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots$
3192.2.a.e	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{13}+q^{19}+q^{21}+\cdots$
3192.2.a.f	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
3192.2.a.g	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
3192.2.a.h	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
3192.2.a.i	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
3192.2.a.j	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots$
3192.2.a.k	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
3192.2.a.l	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
3192.2.a.m	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
3192.2.a.n	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots$
3192.2.a.o	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-2q^{13}-8q^{17}+\cdots$
3192.2.a.p	$3192$	$2$	3192.a	1.a	$1$	$1$	$1$	$25.488$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
3192.2.a.q	$3192$	$2$	3192.a	1.a	$1$	$2$	$2$	$25.488$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots$
3192.2.a.r	$3192$	$2$	3192.a	1.a	$1$	$2$	$2$	$25.488$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}-q^{7}+q^{9}+2\beta q^{11}+\cdots$
3192.2.a.s	$3192$	$2$	3192.a	1.a	$1$	$2$	$2$	$25.488$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}-4q^{11}+\cdots$
3192.2.a.t	$3192$	$2$	3192.a	1.a	$1$	$2$	$2$	$25.488$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{13}+\beta q^{15}+\cdots$
3192.2.a.u	$3192$	$2$	3192.a	1.a	$1$	$3$	$3$	$25.488$	3.3.568.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots$
3192.2.a.v	$3192$	$2$	3192.a	1.a	$1$	$3$	$3$	$25.488$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$0$	$-3$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+(-1+\beta _{1})q^{11}+\cdots$

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