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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	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
402.2.a.a	$402$	$2$	402.a	1.a	$1$	$1$	$1$	$3.210$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots$
402.2.a.b	$402$	$2$	402.a	1.a	$1$	$1$	$1$	$3.210$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots$
402.2.a.c	$402$	$2$	402.a	1.a	$1$	$1$	$1$	$3.210$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
402.2.a.d	$402$	$2$	402.a	1.a	$1$	$1$	$1$	$3.210$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+2q^{7}+\cdots$
402.2.a.e	$402$	$2$	402.a	1.a	$1$	$2$	$2$	$3.210$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$-2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2\beta q^{5}+q^{6}+(3+\cdots)q^{7}+\cdots$
402.2.a.f	$402$	$2$	402.a	1.a	$1$	$2$	$2$	$3.210$	$\Q(\sqrt{41}) $	None	✓	$1$	$0$	$2$	$-2$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-\beta q^{7}+\cdots$
402.2.a.g	$402$	$2$	402.a	1.a	$1$	$3$	$3$	$3.210$	3.3.316.1	None	✓	$1$	$0$	$3$	$3$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1-\beta _{2})q^{5}+q^{6}+\cdots$
402.2.d.a	$402$	$2$	402.d	201.d	$2$	$12$	$12$	$3.210$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-12$	$1$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{8}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{8}q^{6}+\cdots$
402.2.d.b	$402$	$2$	402.d	201.d	$2$	$12$	$12$	$3.210$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$12$	$-1$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{8}q^{3}+q^{4}+\beta _{7}q^{5}-\beta _{8}q^{6}+\cdots$
402.2.e.a	$402$	$2$	402.e	67.c	$3$	$6$	$3$	$3.210$	6.0.16638075.1	None		$2$	$0$	$-3$	$-6$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}-q^{3}+(-1-\beta _{4})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
402.2.e.b	$402$	$2$	402.e	67.c	$3$	$6$	$3$	$3.210$	6.0.48843675.1	None		$2$	$0$	$-3$	$6$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4})q^{2}+q^{3}-\beta _{4}q^{4}-\beta _{2}q^{5}+\cdots$
402.2.e.c	$402$	$2$	402.e	67.c	$3$	$6$	$3$	$3.210$	6.0.309123.1	None		$2$	$0$	$3$	$-6$	$-4$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}-q^{3}+(-1+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
402.2.e.d	$402$	$2$	402.e	67.c	$3$	$6$	$3$	$3.210$	6.0.18825075.4	None		$2$	$0$	$3$	$6$	$4$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+q^{3}+(-1-\beta _{1})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots$
402.2.h.a	$402$	$2$	402.h	201.f	$6$	$22$	$11$	$3.210$		None		$2$	$0$	$-11$	$1$	$0$	$-6$			$\mathrm{SU}(2)[C_{6}]$
402.2.h.b	$402$	$2$	402.h	201.f	$6$	$22$	$11$	$3.210$		None		$2$	$0$	$11$	$-1$	$0$	$-6$			$\mathrm{SU}(2)[C_{6}]$
402.2.i.a	$402$	$2$	402.i	67.e	$11$	$20$	$2$	$3.210$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-2$	$-2$	$3$	$7$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\beta _{12}q^{2}+\beta _{10}q^{3}-\beta _{16}q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots$
402.2.i.b	$402$	$2$	402.i	67.e	$11$	$20$	$2$	$3.210$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$2$	$-2$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\beta _{15}q^{2}-\beta _{18}q^{3}+(-1+\beta _{9}-\beta _{10}+\cdots)q^{4}+\cdots$
402.2.i.c	$402$	$2$	402.i	67.e	$11$	$30$	$3$	$3.210$		None		$2$	$0$	$-3$	$3$	$-3$	$-1$			$\mathrm{SU}(2)[C_{11}]$
402.2.i.d	$402$	$2$	402.i	67.e	$11$	$30$	$3$	$3.210$		None		$2$	$0$	$3$	$3$	$-1$	$-3$			$\mathrm{SU}(2)[C_{11}]$
402.2.j.a	$402$	$2$	402.j	201.j	$22$	$120$	$12$	$3.210$		None		$2$	$0$	$-12$	$1$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
402.2.j.b	$402$	$2$	402.j	201.j	$22$	$120$	$12$	$3.210$		None		$2$	$0$	$12$	$-1$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
402.2.m.a	$402$	$2$	402.m	67.g	$33$	$60$	$3$	$3.210$		None		$2$	$0$	$-3$	$-6$	$-4$	$1$			$\mathrm{SU}(2)[C_{33}]$
402.2.m.b	$402$	$2$	402.m	67.g	$33$	$60$	$3$	$3.210$		None		$2$	$0$	$-3$	$6$	$4$	$-3$			$\mathrm{SU}(2)[C_{33}]$
402.2.m.c	$402$	$2$	402.m	67.g	$33$	$60$	$3$	$3.210$		None		$2$	$0$	$3$	$-6$	$0$	$1$			$\mathrm{SU}(2)[C_{33}]$
402.2.m.d	$402$	$2$	402.m	67.g	$33$	$60$	$3$	$3.210$		None		$2$	$0$	$3$	$6$	$0$	$1$			$\mathrm{SU}(2)[C_{33}]$
402.2.n.a	$402$	$2$	402.n	201.p	$66$	$220$	$11$	$3.210$		None		$2$	$0$	$-11$	$1$	$0$	$6$			$\mathrm{SU}(2)[C_{66}]$
402.2.n.b	$402$	$2$	402.n	201.p	$66$	$220$	$11$	$3.210$		None		$2$	$0$	$11$	$-1$	$0$	$6$			$\mathrm{SU}(2)[C_{66}]$
402.3.b.a	$402$	$3$	402.b	67.b	$2$	$24$	$24$	$10.954$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
402.3.c.a	$402$	$3$	402.c	3.b	$2$	$4$	$4$	$10.954$	$\Q(\sqrt{-2}, \sqrt{67})$	None		$2$	$0$	$0$	$4$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(1+2\beta _{2})q^{3}-2q^{4}+\beta _{1}q^{5}+\cdots$
402.3.c.b	$402$	$3$	402.c	3.b	$2$	$40$	$40$	$10.954$		None		$2$	$0$	$0$	$-4$	$0$	$-20$			$\mathrm{SU}(2)[C_{2}]$
402.3.f.a	$402$	$3$	402.f	201.g	$6$	$92$	$46$	$10.954$		None		$4$	$0$	$0$	$12$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
402.3.g.a	$402$	$3$	402.g	67.d	$6$	$4$	$2$	$10.954$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(1-2\beta _{2})q^{3}+2\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots$
402.3.g.b	$402$	$3$	402.g	67.d	$6$	$16$	$8$	$10.954$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{11}q^{2}+(-1+2\beta _{4})q^{3}+(2-2\beta _{4}+\cdots)q^{4}+\cdots$
402.3.g.c	$402$	$3$	402.g	67.d	$6$	$24$	$12$	$10.954$		None		$2$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{6}]$
402.3.k.a	$402$	$3$	402.k	201.k	$22$	$440$	$44$	$10.954$		None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{22}]$
402.3.l.a	$402$	$3$	402.l	67.f	$22$	$240$	$24$	$10.954$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
402.3.o.a	$402$	$3$	402.o	67.h	$66$	$200$	$10$	$10.954$		None		$2$	$0$	$0$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{66}]$
402.3.o.b	$402$	$3$	402.o	67.h	$66$	$240$	$12$	$10.954$		None		$2$	$0$	$0$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{66}]$
402.3.p.a	$402$	$3$	402.p	201.o	$66$	$920$	$46$	$10.954$		None		$4$	$0$	$0$	$-12$	$0$	$-4$			$\mathrm{SU}(2)[C_{66}]$
402.4.a.a	$402$	$4$	402.a	1.a	$1$	$1$	$1$	$23.719$	$\Q$	None	✓	$1$	$0$	$-2$	$-3$	$14$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+14q^{5}+6q^{6}+\cdots$
402.4.a.b	$402$	$4$	402.a	1.a	$1$	$2$	$2$	$23.719$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$4$	$6$	$-18$	$-26$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(-9+\beta )q^{5}+\cdots$
402.4.a.c	$402$	$4$	402.a	1.a	$1$	$3$	$3$	$23.719$	3.3.868440.1	None	✓	$1$	$0$	$-6$	$-9$	$-22$	$22$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(-7-\beta _{1})q^{5}+\cdots$
402.4.a.d	$402$	$4$	402.a	1.a	$1$	$3$	$3$	$23.719$	3.3.44852.1	None	✓	$1$	$1$	$-6$	$-9$	$-3$	$-21$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(-2+\beta _{1}-2\beta _{2})q^{5}+\cdots$
402.4.a.e	$402$	$4$	402.a	1.a	$1$	$3$	$3$	$23.719$	3.3.3132.1	None	✓	$1$	$1$	$6$	$-9$	$-12$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(-4+\beta _{1}-\beta _{2})q^{5}+\cdots$
402.4.a.f	$402$	$4$	402.a	1.a	$1$	$4$	$4$	$23.719$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$-8$	$12$	$-13$	$-15$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+(-3+\beta _{2})q^{5}+\cdots$
402.4.a.g	$402$	$4$	402.a	1.a	$1$	$4$	$4$	$23.719$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$-8$	$12$	$12$	$-8$	$+$	$3$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots$
402.4.a.h	$402$	$4$	402.a	1.a	$1$	$6$	$6$	$23.719$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$12$	$-18$	$3$	$1$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(1-\beta _{1})q^{5}+\cdots$
402.4.a.i	$402$	$4$	402.a	1.a	$1$	$6$	$6$	$23.719$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$12$	$18$	$27$	$37$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(4-\beta _{2})q^{5}+\cdots$
402.4.d.a	$402$	$4$	402.d	201.d	$2$	$34$	$34$	$23.719$		None		$2$	$0$	$-68$	$-7$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
402.4.d.b	$402$	$4$	402.d	201.d	$2$	$34$	$34$	$23.719$		None		$2$	$0$	$68$	$7$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.