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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 73 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
3100.1.d.a	$3100$	$1$	3100.d	31.b	$2$	$2$	$2$	$1.547$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-155}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots$
3100.1.d.b	$3100$	$1$	3100.d	31.b	$2$	$2$	$2$	$1.547$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-155}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}+iq^{13}+iq^{17}+q^{19}+iq^{23}+\cdots$
3100.1.m.a	$3100$	$1$	3100.m	620.m	$4$	$2$	$1$	$1.547$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+iq^{2}-q^{4}+(1-i)q^{7}-iq^{8}+iq^{9}+\cdots$
3100.1.m.b	$3100$	$1$	3100.m	620.m	$4$	$2$	$1$	$1.547$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+q^{2}+q^{4}+(-1+i)q^{7}+q^{8}+iq^{9}+\cdots$
3100.1.m.c	$3100$	$1$	3100.m	620.m	$4$	$4$	$2$	$1.547$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(-\zeta_{12}^{4}+\zeta_{12}^{5}+\cdots)q^{7}+\cdots$
3100.1.m.d	$3100$	$1$	3100.m	620.m	$4$	$4$	$2$	$1.547$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}^{4}+\zeta_{12}^{5}+\cdots)q^{7}+\cdots$
3100.1.t.a	$3100$	$1$	3100.t	620.o	$6$	$4$	$2$	$1.547$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-4$	$2$	$0$	$2$		$1$		$q-q^{2}+\zeta_{12}^{2}q^{3}+q^{4}-\zeta_{12}^{2}q^{6}+\cdots$
3100.1.t.b	$3100$	$1$	3100.t	620.o	$6$	$4$	$2$	$1.547$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$4$	$-2$	$0$	$-2$		$1$		$q+q^{2}-\zeta_{12}^{2}q^{3}+q^{4}-\zeta_{12}^{2}q^{6}+\cdots$
3100.1.x.a	$3100$	$1$	3100.x	31.e	$6$	$2$	$1$	$1.547$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{9}+(-1-\zeta_{6})q^{11}-\zeta_{6}q^{19}+\cdots$
3100.1.z.a	$3100$	$1$	3100.z	124.i	$6$	$4$	$2$	$1.547$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}-\zeta_{12}^{2}q^{6}+\cdots$
3100.1.bc.a	$3100$	$1$	3100.bc	3100.ac	$10$	$8$	$2$	$1.547$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{20}^{7}q^{2}+(\zeta_{20}+\zeta_{20}^{9})q^{3}-\zeta_{20}^{4}q^{4}+\cdots$
3100.1.ch.a	$3100$	$1$	3100.ch	3100.bh	$10$	$8$	$2$	$1.547$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$2$	$0$	$2$	$0$		$1$		$q-\zeta_{20}^{4}q^{2}+(\zeta_{20}-\zeta_{20}^{3})q^{3}+\zeta_{20}^{8}q^{4}+\cdots$
3100.1.cj.a	$3100$	$1$	3100.cj	3100.bj	$10$	$8$	$2$	$1.547$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{20}^{7}q^{2}+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{3}-\zeta_{20}^{4}q^{4}+\cdots$
3100.1.ck.a	$3100$	$1$	3100.ck	3100.bk	$10$	$8$	$2$	$1.547$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$-8$	$0$	$2$	$0$		$1$		$q-q^{2}+(-\zeta_{20}-\zeta_{20}^{5})q^{3}+q^{4}-\zeta_{20}^{4}q^{5}+\cdots$
3100.1.cm.a	$3100$	$1$	3100.cm	775.w	$10$	$8$	$2$	$1.547$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$2$	$-8$		$1$		$q+\zeta_{20}^{6}q^{5}-q^{7}-\zeta_{20}^{6}q^{9}+(-\zeta_{20}^{3}+\cdots)q^{11}+\cdots$
3100.1.cr.a	$3100$	$1$	3100.cr	155.o	$12$	$4$	$1$	$1.547$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{7}-\zeta_{12}q^{9}-\zeta_{12}^{4}q^{11}+\cdots$
3100.1.cr.b	$3100$	$1$	3100.cr	155.o	$12$	$4$	$1$	$1.547$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{7}-\zeta_{12}q^{9}-\zeta_{12}^{4}q^{11}+\cdots$
3100.1.df.a	$3100$	$1$	3100.df	3100.cf	$20$	$8$	$1$	$1.547$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{20}^{5}q^{2}-q^{4}-\zeta_{20}^{7}q^{5}+(\zeta_{20}^{6}+\cdots)q^{7}+\cdots$
3100.1.df.b	$3100$	$1$	3100.df	3100.cf	$20$	$8$	$1$	$1.547$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+\zeta_{20}^{6}q^{2}-\zeta_{20}^{2}q^{4}-\zeta_{20}^{7}q^{5}+\cdots$
3100.1.df.c	$3100$	$1$	3100.df	3100.cf	$20$	$16$	$2$	$1.547$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q+\zeta_{60}^{2}q^{2}+\zeta_{60}^{4}q^{4}-\zeta_{60}^{19}q^{5}+\cdots$
3100.1.df.d	$3100$	$1$	3100.df	3100.cf	$20$	$16$	$2$	$1.547$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{60}^{5}q^{2}+\zeta_{60}^{10}q^{4}+\zeta_{60}^{29}q^{5}+\cdots$
3100.2.a.a	$3100$	$2$	3100.a	1.a	$1$	$1$	$1$	$24.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
3100.2.a.b	$3100$	$2$	3100.a	1.a	$1$	$1$	$1$	$24.754$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}-2q^{9}-2q^{13}+3q^{17}+\cdots$
3100.2.a.c	$3100$	$2$	3100.a	1.a	$1$	$1$	$1$	$24.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}-3q^{9}+6q^{11}+4q^{13}-5q^{19}+\cdots$
3100.2.a.d	$3100$	$2$	3100.a	1.a	$1$	$1$	$1$	$24.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-4q^{11}+4q^{13}+4q^{23}+\cdots$
3100.2.a.e	$3100$	$2$	3100.a	1.a	$1$	$1$	$1$	$24.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
3100.2.a.f	$3100$	$2$	3100.a	1.a	$1$	$1$	$1$	$24.754$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
3100.2.a.g	$3100$	$2$	3100.a	1.a	$1$	$1$	$1$	$24.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{7}+6q^{9}+2q^{11}-2q^{13}+\cdots$
3100.2.a.h	$3100$	$2$	3100.a	1.a	$1$	$3$	$3$	$24.754$	3.3.756.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+\beta _{2}q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots$
3100.2.a.i	$3100$	$2$	3100.a	1.a	$1$	$4$	$4$	$24.754$	4.4.25492.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots$
3100.2.a.j	$3100$	$2$	3100.a	1.a	$1$	$5$	$5$	$24.754$	5.5.3418929.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1-\beta _{2}+\beta _{4})q^{7}+\cdots$
3100.2.a.k	$3100$	$2$	3100.a	1.a	$1$	$5$	$5$	$24.754$	5.5.313905.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{4})q^{3}+(-1-\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
3100.2.a.l	$3100$	$2$	3100.a	1.a	$1$	$5$	$5$	$24.754$	5.5.313905.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{4})q^{3}+(1+\beta _{3})q^{7}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
3100.2.a.m	$3100$	$2$	3100.a	1.a	$1$	$5$	$5$	$24.754$	5.5.3418929.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{2}-\beta _{4})q^{7}+(2+\cdots)q^{9}+\cdots$
3100.2.a.n	$3100$	$2$	3100.a	1.a	$1$	$6$	$6$	$24.754$	6.6.337383424.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}+(\beta _{1}-\beta _{4})q^{7}+(2+\beta _{3})q^{9}+\cdots$
3100.2.a.o	$3100$	$2$	3100.a	1.a	$1$	$8$	$8$	$24.754$	8.8.$\cdots$.1	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{3}+(\beta _{3}+\beta _{5})q^{7}+(1+\beta _{4}+\beta _{6}+\cdots)q^{9}+\cdots$
3100.2.c.a	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}-2iq^{7}-6q^{9}+2q^{11}-2iq^{13}+\cdots$
3100.2.c.b	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{3}-iq^{7}-q^{9}-6q^{11}-2iq^{13}+\cdots$
3100.2.c.c	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+4iq^{7}+2q^{9}+2iq^{13}+3iq^{17}+\cdots$
3100.2.c.d	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{7}+3q^{9}-4q^{11}+2iq^{13}+2iq^{23}+\cdots$
3100.2.c.e	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3iq^{7}+3q^{9}+6q^{11}-4iq^{13}+\cdots$
3100.2.c.f	$3100$	$2$	3100.c	5.b	$2$	$6$	$6$	$24.754$	6.0.9144576.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{3})q^{3}+(\beta _{1}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots$
3100.2.c.g	$3100$	$2$	3100.c	5.b	$2$	$8$	$8$	$24.754$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{2}+\beta _{5}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots$
3100.2.c.h	$3100$	$2$	3100.c	5.b	$2$	$10$	$10$	$24.754$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{3}+(\beta _{2}-\beta _{6}+\beta _{8})q^{7}+\cdots$
3100.2.c.i	$3100$	$2$	3100.c	5.b	$2$	$10$	$10$	$24.754$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{8})q^{3}+(\beta _{6}+\beta _{7})q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots$
3100.2.i.a	$3100$	$2$	3100.i	31.c	$3$	$6$	$3$	$24.754$	6.0.954288.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{5})q^{3}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots$
3100.2.i.b	$3100$	$2$	3100.i	31.c	$3$	$10$	$5$	$24.754$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$-5$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{3}+(\beta _{1}-\beta _{2}+\beta _{5}-\beta _{9})q^{7}+\cdots$
3100.2.i.c	$3100$	$2$	3100.i	31.c	$3$	$10$	$5$	$24.754$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$-1$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{9}q^{3}+\beta _{7}q^{7}+(-\beta _{4}+\beta _{6}-\beta _{7}+\cdots)q^{9}+\cdots$
3100.2.i.d	$3100$	$2$	3100.i	31.c	$3$	$22$	$11$	$24.754$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$2$			$\mathrm{SU}(2)[C_{3}]$
3100.2.i.e	$3100$	$2$	3100.i	31.c	$3$	$22$	$11$	$24.754$		$_{}$	None	None		$2$	$0$	$0$	$1$	$0$	$-2$			$\mathrm{SU}(2)[C_{3}]$

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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.