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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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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
961.1.e.a	$961$	$1$	961.e	31.e	$6$	$2$	$1$	$0.480$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$1$	$1$		$1$		$q-q^{2}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
961.1.f.a	$961$	$1$	961.f	31.f	$10$	$4$	$1$	$0.480$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$1$	$0$	$-4$	$1$		$1$		$q+\zeta_{10}^{3}q^{2}-q^{5}+\zeta_{10}q^{7}+\zeta_{10}^{4}q^{8}+\cdots$
961.1.h.a	$961$	$1$	961.h	31.h	$30$	$8$	$1$	$0.480$	$\Q(\zeta_{15})$	$D_{3}$	$\Q(\sqrt{-31}) $	None		$16$	$0$	$2$	$0$	$4$	$-1$		$1$		$q+\zeta_{30}^{3}q^{2}-\zeta_{30}^{10}q^{5}+\zeta_{30}^{11}q^{7}+\cdots$
961.2.a.a	$961$	$2$	961.a	1.a	$1$	$2$	$2$	$7.674$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
961.2.a.b	$961$	$2$	961.a	1.a	$1$	$2$	$2$	$7.674$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$-2$	$0$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2\beta q^{3}-q^{4}+2\beta q^{6}+4q^{7}+\cdots$
961.2.a.c	$961$	$2$	961.a	1.a	$1$	$2$	$2$	$7.674$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
961.2.a.d	$961$	$2$	961.a	1.a	$1$	$2$	$2$	$7.674$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$-2$	$-3$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots$
961.2.a.e	$961$	$2$	961.a	1.a	$1$	$2$	$2$	$7.674$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$-3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots$
961.2.a.f	$961$	$2$	961.a	1.a	$1$	$2$	$2$	$7.674$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots$
961.2.a.g	$961$	$2$	961.a	1.a	$1$	$3$	$3$	$7.674$	3.3.837.1	$_{}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
961.2.a.h	$961$	$2$	961.a	1.a	$1$	$4$	$4$	$7.674$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓	$2$	$0$	$6$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{2})q^{2}-\beta _{1}q^{3}+(3-3\beta _{2})q^{4}+\cdots$
961.2.a.i	$961$	$2$	961.a	1.a	$1$	$8$	$8$	$7.674$	8.8.2051578125.1	$_{}$	None	None	✓	$1$	$1$	$2$	$-3$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{5}+\cdots)q^{3}+\cdots$
961.2.a.j	$961$	$2$	961.a	1.a	$1$	$8$	$8$	$7.674$	8.8.2051578125.1	$_{}$	None	None	✓	$1$	$0$	$2$	$3$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3}-\beta _{5})q^{2}+(1-\beta _{2}-\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots$
961.2.a.k	$961$	$2$	961.a	1.a	$1$	$12$	$12$	$7.674$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$8$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{8}q^{2}-\beta _{1}q^{3}+(1+\beta _{11})q^{4}+(1+\cdots)q^{5}+\cdots$
961.2.a.l	$961$	$2$	961.a	1.a	$1$	$16$	$16$	$7.674$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$2$	$1$	$-8$	$0$	$-16$	$-16$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{8})q^{2}+\beta _{1}q^{3}+(1-\beta _{15})q^{4}+\cdots$
961.2.c.a	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$-4$	$-2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots$
961.2.c.b	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-2\beta _{1}-2\beta _{3})q^{3}-q^{4}+(2\beta _{1}+\cdots)q^{6}+\cdots$
961.2.c.c	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$2$	$-2$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}-2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots$
961.2.c.d	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$2$	$-2$	$3$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(-1-\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
961.2.c.e	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$2$	$2$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots$
961.2.c.f	$961$	$2$	961.c	31.c	$3$	$4$	$2$	$7.674$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$2$	$2$	$3$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(1+\beta _{3})q^{3}+(-1-\beta _{2})q^{4}+\cdots$
961.2.c.g	$961$	$2$	961.c	31.c	$3$	$6$	$3$	$7.674$	6.0.2101707.2	$_{}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{3}]$	$q+\beta _{2}q^{2}+(2+\beta _{1})q^{4}+(-\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots$
961.2.c.h	$961$	$2$	961.c	31.c	$3$	$8$	$4$	$7.674$	8.0.207360000.1	$_{}$	None	None		$4$	$0$	$12$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\beta _{2})q^{2}-\beta _{1}q^{3}+(3-3\beta _{2})q^{4}+\cdots$
961.2.c.i	$961$	$2$	961.c	31.c	$3$	$16$	$8$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$-3$	$-3$	$2$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{2}+(-1-\beta _{6}-\beta _{9}+\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots$
961.2.c.j	$961$	$2$	961.c	31.c	$3$	$16$	$8$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$3$	$-3$	$2$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{2}+(1+\beta _{6}+\beta _{9}-\beta _{10}+\beta _{11}+\cdots)q^{3}+\cdots$
961.2.c.k	$961$	$2$	961.c	31.c	$3$	$24$	$12$	$7.674$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$-8$			$\mathrm{SU}(2)[C_{3}]$
961.2.c.l	$961$	$2$	961.c	31.c	$3$	$32$	$16$	$7.674$		$_{}$	None	None		$4$	$0$	$-16$	$0$	$16$	$16$			$\mathrm{SU}(2)[C_{3}]$
961.2.d.a	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-3$	$-6$	$4$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}+(-2+2\zeta_{10}^{3})q^{3}+\cdots$
961.2.d.b	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-3$	$-1$	$-6$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
961.2.d.c	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-3$	$6$	$4$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}+(2-2\zeta_{10}^{3})q^{3}+\cdots$
961.2.d.d	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$-4$	$4$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-2\zeta_{10}+2\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
961.2.d.e	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$-1$	$-6$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\cdots)q^{3}+\cdots$
961.2.d.f	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$1$	$-6$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
961.2.d.g	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$4$	$4$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2})q^{2}+(2\zeta_{10}-2\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
961.2.d.h	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	$_{}$	None	None		$4$	$0$	$-8$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}+2\beta _{4}+\beta _{6})q^{2}+(\beta _{1}+\beta _{5}+\beta _{7})q^{3}+\cdots$
961.2.d.i	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	$_{}$	None	None		$4$	$0$	$2$	$-2$	$8$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}+\beta _{7})q^{2}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots$
961.2.d.j	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	$_{}$	None	None		$4$	$0$	$2$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+2\beta _{2}+\beta _{4})q^{2}+(\beta _{1}+\beta _{5})q^{3}+\cdots$
961.2.d.k	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	$_{}$	None	None		$8$	$0$	$2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+(2\beta _{1}+2\beta _{3}+2\beta _{5}+2\beta _{7})q^{3}+\cdots$
961.2.d.l	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	$_{}$	None	None		$4$	$0$	$2$	$2$	$8$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}+\beta _{7})q^{2}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
961.2.d.m	$961$	$2$	961.d	31.d	$5$	$12$	$3$	$7.674$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-31}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{5}]$	$q+\beta _{9}q^{2}+(2\beta _{4}+\beta _{5})q^{4}+(\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
961.2.d.n	$961$	$2$	961.d	31.d	$5$	$16$	$4$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$-6$	$-9$	$6$	$11$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{3}+\beta _{9}+\beta _{10}+\beta _{11}+\beta _{15})q^{2}+\cdots$
961.2.d.o	$961$	$2$	961.d	31.d	$5$	$16$	$4$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$-6$	$9$	$6$	$11$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{3}+\beta _{9}+\beta _{10}+\beta _{11}+\beta _{15})q^{2}+\cdots$
961.2.d.p	$961$	$2$	961.d	31.d	$5$	$16$	$4$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$-6$	$6$	$-9$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{11}+\beta _{12}+\beta _{14})q^{2}+(-1+\cdots)q^{3}+\cdots$
961.2.d.q	$961$	$2$	961.d	31.d	$5$	$16$	$4$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$6$	$6$	$-9$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{11}+\beta _{12}+\beta _{14})q^{2}+(1+\beta _{4}+\cdots)q^{3}+\cdots$
961.2.d.r	$961$	$2$	961.d	31.d	$5$	$48$	$12$	$7.674$		$_{}$	None	None		$8$	$0$	$0$	$0$	$32$	$-8$			$\mathrm{SU}(2)[C_{5}]$
961.2.d.s	$961$	$2$	961.d	31.d	$5$	$64$	$16$	$7.674$		$_{}$	None	None		$8$	$0$	$8$	$0$	$-64$	$16$			$\mathrm{SU}(2)[C_{5}]$
961.2.g.a	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	$\Q(\zeta_{15})$	$_{}$	None	None		$4$	$0$	$-6$	$-6$	$-4$	$-7$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-1-\zeta_{15}^{6})q^{2}+(-2+2\zeta_{15}^{4}+\cdots)q^{3}+\cdots$
961.2.g.b	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	$\Q(\zeta_{15})$	$_{}$	None	None		$4$	$0$	$-6$	$-1$	$6$	$3$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-1-\zeta_{15}^{6})q^{2}-\zeta_{15}^{7}q^{3}+(1-\zeta_{15}^{2}+\cdots)q^{4}+\cdots$
961.2.g.c	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	$\Q(\zeta_{15})$	$_{}$	None	None		$4$	$0$	$-6$	$1$	$6$	$3$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-1-\zeta_{15}^{6})q^{2}+\zeta_{15}^{7}q^{3}+(1-\zeta_{15}^{2}+\cdots)q^{4}+\cdots$
961.2.g.d	$961$	$2$	961.g	31.g	$15$	$8$	$1$	$7.674$	$\Q(\zeta_{15})$	$_{}$	None	None		$4$	$0$	$-6$	$6$	$-4$	$-7$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-1-\zeta_{15}^{6})q^{2}+(2-2\zeta_{15}^{4}+2\zeta_{15}^{5}+\cdots)q^{3}+\cdots$

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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.