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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 94 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
1116.1.b.a	$1116$	$1$	1116.b	372.b	$2$	$4$	$4$	$0.557$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
1116.1.b.b	$1116$	$1$	1116.b	372.b	$2$	$8$	$8$	$0.557$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
1116.1.t.a	$1116$	$1$	1116.t	31.e	$6$	$2$	$1$	$0.557$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{6}^{2}q^{7}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{19}+\cdots$
1116.1.x.a	$1116$	$1$	1116.x	124.i	$6$	$4$	$2$	$0.557$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}+\cdots$
1116.1.be.a	$1116$	$1$	1116.be	93.h	$6$	$4$	$2$	$0.557$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{5}+(1-\beta _{2})q^{13}-\beta _{2}q^{19}+\beta _{3}q^{23}+\cdots$
1116.1.ck.a	$1116$	$1$	1116.ck	31.h	$30$	$8$	$1$	$0.557$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(\zeta_{30}^{2}-\zeta_{30}^{11})q^{7}+(-\zeta_{30}^{12}+\zeta_{30}^{14}+\cdots)q^{13}+\cdots$
1116.2.a.a	$1116$	$2$	1116.a	1.a	$1$	$1$	$1$	$8.911$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-q^{7}+2q^{13}-q^{19}+6q^{23}+\cdots$
1116.2.a.b	$1116$	$2$	1116.a	1.a	$1$	$1$	$1$	$8.911$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}-6q^{11}-4q^{13}-5q^{19}+\cdots$
1116.2.a.c	$1116$	$2$	1116.a	1.a	$1$	$1$	$1$	$8.911$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-6q^{13}+8q^{17}+7q^{19}+\cdots$
1116.2.a.d	$1116$	$2$	1116.a	1.a	$1$	$1$	$1$	$8.911$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}+2q^{13}+4q^{19}-4q^{23}+\cdots$
1116.2.a.e	$1116$	$2$	1116.a	1.a	$1$	$1$	$1$	$8.911$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-5q^{7}-2q^{11}-4q^{13}+4q^{17}+\cdots$
1116.2.a.f	$1116$	$2$	1116.a	1.a	$1$	$1$	$1$	$8.911$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}+6q^{11}+2q^{13}-6q^{17}+\cdots$
1116.2.a.g	$1116$	$2$	1116.a	1.a	$1$	$2$	$2$	$8.911$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(-2+\cdots)q^{11}+\cdots$
1116.2.a.h	$1116$	$2$	1116.a	1.a	$1$	$2$	$2$	$8.911$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}-2\beta q^{11}-4q^{13}-4\beta q^{17}+\cdots$
1116.2.a.i	$1116$	$2$	1116.a	1.a	$1$	$2$	$2$	$8.911$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+3q^{7}+2q^{13}+q^{19}+2\beta q^{23}+\cdots$
1116.2.c.a	$1116$	$2$	1116.c	12.b	$2$	$60$	$60$	$8.911$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1116.2.e.a	$1116$	$2$	1116.e	93.c	$2$	$12$	$12$	$8.911$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$2^{9}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{5}+(1+\beta _{3})q^{7}+\beta _{6}q^{11}-\beta _{8}q^{13}+\cdots$
1116.2.g.a	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	$\Q(i, \sqrt{30})$	$_{}$	None	None		$4$	$0$	$-4$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+q^{5}-3\beta _{1}q^{7}+\cdots$
1116.2.g.b	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	$\Q(\sqrt{6}, \sqrt{-7})$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2-\beta _{1})q^{4}+2q^{5}+(2+\cdots)q^{8}+\cdots$
1116.2.g.c	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	$\Q(\sqrt{-2}, \sqrt{31})$	$_{}$	$\Q(\sqrt{-93}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+4q^{16}+\cdots$
1116.2.g.d	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$4$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}-q^{5}-3\beta _{1}q^{7}+\cdots$
1116.2.g.e	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	$\Q(i, \sqrt{30})$	$_{}$	None	None		$4$	$0$	$4$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}-q^{5}+3\beta _{1}q^{7}+\cdots$
1116.2.g.f	$1116$	$2$	1116.g	124.d	$2$	$6$	$6$	$8.911$	6.0.21717639.1	$_{}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}-\beta _{5})q^{5}+\cdots$
1116.2.g.g	$1116$	$2$	1116.g	124.d	$2$	$8$	$8$	$8.911$	8.0.49787136.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{5}+\beta _{7})q^{2}+(1-\beta _{3})q^{4}+(\beta _{5}+2\beta _{7})q^{5}+\cdots$
1116.2.g.h	$1116$	$2$	1116.g	124.d	$2$	$12$	$12$	$8.911$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{8}-\beta _{11})q^{5}+\cdots$
1116.2.g.i	$1116$	$2$	1116.g	124.d	$2$	$16$	$16$	$8.911$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{6}q^{5}+\beta _{4}q^{7}+\cdots$
1116.2.g.j	$1116$	$2$	1116.g	124.d	$2$	$16$	$16$	$8.911$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+\beta _{5}q^{4}-\beta _{6}q^{5}+\beta _{3}q^{7}+\cdots$
1116.2.i.a	$1116$	$2$	1116.i	31.c	$3$	$2$	$1$	$8.911$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+6\zeta_{6}q^{11}-5\zeta_{6}q^{13}+(5+\cdots)q^{19}+\cdots$
1116.2.i.b	$1116$	$2$	1116.i	31.c	$3$	$2$	$1$	$8.911$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(4-4\zeta_{6})q^{7}+7\zeta_{6}q^{13}+(1-\zeta_{6})q^{19}+\cdots$
1116.2.i.c	$1116$	$2$	1116.i	31.c	$3$	$2$	$1$	$8.911$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}-6\zeta_{6}q^{11}-5\zeta_{6}q^{13}+(5+\cdots)q^{19}+\cdots$
1116.2.i.d	$1116$	$2$	1116.i	31.c	$3$	$4$	$2$	$8.911$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}+(1+\cdots)q^{11}+\cdots$
1116.2.i.e	$1116$	$2$	1116.i	31.c	$3$	$4$	$2$	$8.911$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{5}+(-2+2\beta _{1})q^{7}-\beta _{2}q^{11}+\cdots$
1116.2.i.f	$1116$	$2$	1116.i	31.c	$3$	$6$	$3$	$8.911$	6.0.954288.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{5}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{7}+\cdots$
1116.2.i.g	$1116$	$2$	1116.i	31.c	$3$	$6$	$3$	$8.911$	6.0.65370672.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{4})q^{5}+(-2-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1116.2.j.a	$1116$	$2$	1116.j	9.c	$3$	$4$	$2$	$8.911$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$0$	$6$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{3}+\beta _{1}q^{5}+(1-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$
1116.2.j.b	$1116$	$2$	1116.j	9.c	$3$	$26$	$13$	$8.911$		$_{}$	None	None		$2$	$0$	$0$	$-5$	$5$	$3$			$\mathrm{SU}(2)[C_{3}]$
1116.2.j.c	$1116$	$2$	1116.j	9.c	$3$	$30$	$15$	$8.911$		$_{}$	None	None		$2$	$0$	$0$	$1$	$-2$	$0$			$\mathrm{SU}(2)[C_{3}]$
1116.2.k.a	$1116$	$2$	1116.k	279.e	$3$	$2$	$1$	$8.911$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots$
1116.2.k.b	$1116$	$2$	1116.k	279.e	$3$	$62$	$31$	$8.911$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
1116.2.l.a	$1116$	$2$	1116.l	279.g	$3$	$2$	$1$	$8.911$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-3$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+\zeta_{6})q^{3}-q^{5}+q^{7}+(3-3\zeta_{6})q^{9}+\cdots$
1116.2.l.b	$1116$	$2$	1116.l	279.g	$3$	$62$	$31$	$8.911$		$_{}$	None	None		$2$	$0$	$0$	$5$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
1116.2.m.a	$1116$	$2$	1116.m	31.d	$5$	$4$	$1$	$8.911$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2q^{5}+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{7}+\cdots$
1116.2.m.b	$1116$	$2$	1116.m	31.d	$5$	$4$	$1$	$8.911$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{5}+(3\zeta_{10}+\cdots)q^{7}+\cdots$
1116.2.m.c	$1116$	$2$	1116.m	31.d	$5$	$4$	$1$	$8.911$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{2}+\zeta_{10}^{3})q^{5}+(2\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1116.2.m.d	$1116$	$2$	1116.m	31.d	$5$	$8$	$2$	$8.911$	8.0.1903140625.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-9$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots$
1116.2.m.e	$1116$	$2$	1116.m	31.d	$5$	$8$	$2$	$8.911$	$\Q(\zeta_{15})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$8$		$2^{4}$	$\mathrm{U}(1)[D_{5}]$	$q+(2+2\zeta_{15}+2\zeta_{15}^{2}+\zeta_{15}^{6}+\zeta_{15}^{7})q^{7}+\cdots$
1116.2.m.f	$1116$	$2$	1116.m	31.d	$5$	$12$	$3$	$8.911$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-3$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{3}q^{5}+(\beta _{2}-\beta _{6}-\beta _{7})q^{7}+(-\beta _{4}+\cdots)q^{11}+\cdots$
1116.2.m.g	$1116$	$2$	1116.m	31.d	$5$	$16$	$4$	$8.911$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-14$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{3}-\beta _{6}-\beta _{10})q^{5}+(-2+\cdots)q^{7}+\cdots$
1116.2.p.a	$1116$	$2$	1116.p	279.o	$6$	$64$	$32$	$8.911$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{6}]$
1116.2.bb.a	$1116$	$2$	1116.bb	93.g	$6$	$4$	$2$	$8.911$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q-2\beta _{1}q^{7}+(\beta _{2}-\beta _{3})q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots$

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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.