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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 192 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
931.1.b.a	$931$	$1$	931.b	19.b	$2$	$1$	$1$	$0.465$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+2q^{17}+\cdots$
931.1.b.b	$931$	$1$	931.b	19.b	$2$	$1$	$1$	$0.465$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{4}+q^{5}+q^{9}-q^{11}+q^{16}-2q^{17}+\cdots$
931.1.k.a	$931$	$1$	931.k	133.k	$6$	$4$	$2$	$0.465$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}+\zeta_{12}q^{6}+\cdots$
931.1.r.a	$931$	$1$	931.r	133.r	$6$	$2$	$1$	$0.465$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
931.1.t.a	$931$	$1$	931.t	133.t	$6$	$4$	$2$	$0.465$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$
931.1.ba.a	$931$	$1$	931.ba	931.aa	$14$	$6$	$1$	$0.465$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-1$		$1$		$q-\zeta_{14}^{5}q^{4}+(\zeta_{14}^{2}+\zeta_{14}^{6})q^{5}+\zeta_{14}^{4}q^{7}+\cdots$
931.1.bq.a	$931$	$1$	931.bq	931.aq	$42$	$12$	$1$	$0.465$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$1$		$1$		$q-\zeta_{42}^{17}q^{4}+(-\zeta_{42}^{5}+\zeta_{42}^{18})q^{5}+\cdots$
931.2.a.a	$931$	$2$	931.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}-3q^{5}+q^{9}+3q^{11}+\cdots$
931.2.a.b	$931$	$2$	931.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}-3q^{5}-4q^{6}+\cdots$
931.2.a.c	$931$	$2$	931.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}+3q^{5}+4q^{6}+\cdots$
931.2.a.d	$931$	$2$	931.a	1.a	$1$	$2$	$2$	$7.434$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-3$	$3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots$
931.2.a.e	$931$	$2$	931.a	1.a	$1$	$2$	$2$	$7.434$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots$
931.2.a.f	$931$	$2$	931.a	1.a	$1$	$2$	$2$	$7.434$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots$
931.2.a.g	$931$	$2$	931.a	1.a	$1$	$2$	$2$	$7.434$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2-\beta )q^{3}+(1+\beta )q^{4}+3q^{5}+\cdots$
931.2.a.h	$931$	$2$	931.a	1.a	$1$	$2$	$2$	$7.434$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}+2\beta q^{5}-2q^{6}-2\beta q^{8}+\cdots$
931.2.a.i	$931$	$2$	931.a	1.a	$1$	$2$	$2$	$7.434$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{3}-2\beta q^{5}+2q^{6}-2\beta q^{8}+\cdots$
931.2.a.j	$931$	$2$	931.a	1.a	$1$	$2$	$2$	$7.434$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
931.2.a.k	$931$	$2$	931.a	1.a	$1$	$3$	$3$	$7.434$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-3$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$
931.2.a.l	$931$	$2$	931.a	1.a	$1$	$4$	$4$	$7.434$	4.4.5744.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
931.2.a.m	$931$	$2$	931.a	1.a	$1$	$4$	$4$	$7.434$	4.4.5744.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
931.2.a.n	$931$	$2$	931.a	1.a	$1$	$7$	$7$	$7.434$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-\beta _{2}q^{3}+(1+\beta _{3}-\beta _{5})q^{4}+\cdots$
931.2.a.o	$931$	$2$	931.a	1.a	$1$	$7$	$7$	$7.434$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+\beta _{2}q^{3}+(1+\beta _{3}-\beta _{5})q^{4}+\cdots$
931.2.a.p	$931$	$2$	931.a	1.a	$1$	$10$	$10$	$7.434$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-4$	$-16$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
931.2.a.q	$931$	$2$	931.a	1.a	$1$	$10$	$10$	$7.434$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$4$	$16$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(2+\beta _{9})q^{5}+\cdots$
931.2.c.a	$931$	$2$	931.c	133.c	$2$	$4$	$4$	$7.434$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1-\zeta_{12}^{3})q^{3}+\cdots$
931.2.c.b	$931$	$2$	931.c	133.c	$2$	$4$	$4$	$7.434$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}+(\beta _{1}+\beta _{3})q^{5}-3q^{9}+(-3+\cdots)q^{11}+\cdots$
931.2.c.c	$931$	$2$	931.c	133.c	$2$	$4$	$4$	$7.434$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(1+\zeta_{12}^{3})q^{3}+\cdots$
931.2.c.d	$931$	$2$	931.c	133.c	$2$	$6$	$6$	$7.434$	6.0.6967728.1	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+\beta _{4}q^{5}+\cdots$
931.2.c.e	$931$	$2$	931.c	133.c	$2$	$6$	$6$	$7.434$	6.0.6967728.1	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(1+\beta _{1})q^{3}-q^{4}-\beta _{4}q^{5}+\cdots$
931.2.c.f	$931$	$2$	931.c	133.c	$2$	$40$	$40$	$7.434$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
931.2.e.a	$931$	$2$	931.e	19.c	$3$	$4$	$2$	$7.434$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-1$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
931.2.e.b	$931$	$2$	931.e	19.c	$3$	$6$	$3$	$7.434$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$-2$	$1$	$-3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}+\beta _{5})q^{3}+\cdots$
931.2.e.c	$931$	$2$	931.e	19.c	$3$	$10$	$5$	$7.434$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$-3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots$
931.2.e.d	$931$	$2$	931.e	19.c	$3$	$20$	$10$	$7.434$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{5}-\beta _{8})q^{2}+\beta _{3}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
931.2.e.e	$931$	$2$	931.e	19.c	$3$	$24$	$12$	$7.434$		$_{}$	None	None		$2$	$0$	$1$	$-3$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
931.2.e.f	$931$	$2$	931.e	19.c	$3$	$24$	$12$	$7.434$		$_{}$	None	None		$2$	$0$	$1$	$3$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
931.2.e.g	$931$	$2$	931.e	19.c	$3$	$40$	$20$	$7.434$		$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
931.2.f.a	$931$	$2$	931.f	7.c	$3$	$2$	$1$	$7.434$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$2$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
931.2.f.b	$931$	$2$	931.f	7.c	$3$	$2$	$1$	$7.434$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots$
931.2.f.c	$931$	$2$	931.f	7.c	$3$	$2$	$1$	$7.434$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots$
931.2.f.d	$931$	$2$	931.f	7.c	$3$	$4$	$2$	$7.434$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-1$	$-3$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
931.2.f.e	$931$	$2$	931.f	7.c	$3$	$4$	$2$	$7.434$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-1$	$3$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
931.2.f.f	$931$	$2$	931.f	7.c	$3$	$4$	$2$	$7.434$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+2\beta _{1}q^{5}-2q^{6}+\cdots$
931.2.f.g	$931$	$2$	931.f	7.c	$3$	$4$	$2$	$7.434$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$1$	$-3$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(1-\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots$
931.2.f.h	$931$	$2$	931.f	7.c	$3$	$4$	$2$	$7.434$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$1$	$3$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots$
931.2.f.i	$931$	$2$	931.f	7.c	$3$	$4$	$2$	$7.434$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\cdots$
931.2.f.j	$931$	$2$	931.f	7.c	$3$	$4$	$2$	$7.434$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$3$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots$
931.2.f.k	$931$	$2$	931.f	7.c	$3$	$4$	$2$	$7.434$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$3$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$
931.2.f.l	$931$	$2$	931.f	7.c	$3$	$6$	$3$	$7.434$	6.0.1415907.1	$_{}$	None	None		$2$	$0$	$-2$	$-3$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}+\beta _{5})q^{2}+(-1-\beta _{1}-\beta _{4})q^{3}+\cdots$
931.2.f.m	$931$	$2$	931.f	7.c	$3$	$6$	$3$	$7.434$	6.0.1415907.1	$_{}$	None	None		$2$	$0$	$-2$	$3$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}+\beta _{5})q^{2}+(1+\beta _{1}+\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots$

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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.