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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
140.1.h.a	$140$	$1$	140.h	35.c	$2$	$1$	$1$	$0.070$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	✓			140.1.h.a	$2$	$0$	$0$	$-1$	$1$	$1$		$1$		$q-q^{3}+q^{5}+q^{7}-q^{11}-q^{13}-q^{15}+\cdots$
140.1.h.b	$140$	$1$	140.h	35.c	$2$	$1$	$1$	$0.070$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	✓			140.1.h.a	$2$	$0$	$0$	$1$	$-1$	$-1$		$1$		$q+q^{3}-q^{5}-q^{7}-q^{11}+q^{13}-q^{15}+\cdots$
140.1.p.a	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			140.1.p.a	$4$	$0$	$-1$	$1$	$-1$	$-1$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
140.1.p.b	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		✓			140.1.p.a	$4$	$0$	$1$	$-1$	$-1$	$1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
140.2.a.a	$140$	$2$	140.a	1.a	$1$	$1$	$1$	$1.118$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	140.2.a.a	$1$	$0$	$0$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots$
140.2.a.b	$140$	$2$	140.a	1.a	$1$	$1$	$1$	$1.118$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	140.2.a.b	$1$	$0$	$0$	$3$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}-q^{7}+6q^{9}-5q^{11}+\cdots$
140.2.c.a	$140$	$2$	140.c	140.c	$2$	$4$	$4$	$1.118$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			140.2.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+2q^{4}+\cdots$
140.2.c.b	$140$	$2$	140.c	140.c	$2$	$16$	$16$	$1.118$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		140.2.c.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{9}q^{3}+(-1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
140.2.e.a	$140$	$2$	140.e	5.b	$2$	$2$	$2$	$1.118$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			140.2.e.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+(i-2)q^{5}-i q^{7}-6 q^{9}+\cdots$
140.2.e.b	$140$	$2$	140.e	5.b	$2$	$2$	$2$	$1.118$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			140.2.e.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2 i+1)q^{5}+i q^{7}+3 q^{9}-4 i q^{13}+\cdots$
140.2.g.a	$140$	$2$	140.g	28.d	$2$	$4$	$4$	$1.118$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			140.2.g.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}-\beta_1)q^{2}+(\beta_{3}-\beta_{2}+\beta_1)q^{3}+\cdots$
140.2.g.b	$140$	$2$	140.g	28.d	$2$	$4$	$4$	$1.118$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			140.2.g.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}-\beta_1)q^{2}+(-\beta_{3}+\beta_{2}-\beta_1)q^{3}+\cdots$
140.2.g.c	$140$	$2$	140.g	28.d	$2$	$8$	$8$	$1.118$	8.0.342102016.5	$_{}$	None	None		✓	✓		140.2.g.c	$4$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+(-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
140.2.i.a	$140$	$2$	140.i	7.c	$3$	$2$	$1$	$1.118$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			140.2.i.a	$2$	$0$	$0$	$-1$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots$
140.2.i.b	$140$	$2$	140.i	7.c	$3$	$2$	$1$	$1.118$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			140.2.i.b	$2$	$0$	$0$	$3$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$
140.2.k.a	$140$	$2$	140.k	20.e	$4$	$36$	$18$	$1.118$		$_{}$	None	None		✓	✓	✓	140.2.k.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
140.2.m.a	$140$	$2$	140.m	35.f	$4$	$8$	$4$	$1.118$	8.0.$\cdots$.3	$_{}$	None	None		✓	✓	✓	140.2.m.a	$4$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(-\beta _{2}+\beta _{6})q^{5}+(\beta _{4}-\beta _{7})q^{7}+\cdots$
140.2.o.a	$140$	$2$	140.o	28.f	$6$	$32$	$16$	$1.118$		$_{}$	None	None		✓	✓	✓	140.2.o.a	$4$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
140.2.q.a	$140$	$2$	140.q	35.j	$6$	$4$	$2$	$1.118$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None		✓			140.2.q.a	$2$	$0$	$0$	$-6$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots$
140.2.q.b	$140$	$2$	140.q	35.j	$6$	$4$	$2$	$1.118$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None		✓			140.2.q.a	$2$	$0$	$0$	$6$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots$
140.2.s.a	$140$	$2$	140.s	140.s	$6$	$8$	$4$	$1.118$	$\Q(\sqrt{2}, \sqrt{-3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			140.2.s.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{5}q^{2}+(\beta _{1}-\beta _{5})q^{3}-2\beta _{4}q^{4}-\beta _{7}q^{5}+\cdots$
140.2.s.b	$140$	$2$	140.s	140.s	$6$	$32$	$16$	$1.118$		$_{}$	None	None		✓	✓		140.2.s.b	$8$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
140.2.u.a	$140$	$2$	140.u	35.k	$12$	$16$	$4$	$1.118$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	140.2.u.a	$4$	$0$	$0$	$0$	$6$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(2\beta _{1}+\beta _{2}+\beta _{10}-\beta _{11}+\beta _{13})q^{3}+\cdots$
140.2.w.a	$140$	$2$	140.w	140.w	$12$	$8$	$2$	$1.118$	$\Q(i, \sqrt{3}, \sqrt{14})$	$_{}$	None	None		✓			140.2.w.a	$8$	$0$	$-4$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2\beta _{2}+\cdots)q^{4}+\cdots$
140.2.w.b	$140$	$2$	140.w	140.w	$12$	$72$	$18$	$1.118$		$_{}$	None	None		✓	✓		140.2.w.b	$8$	$0$	$2$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{12}]$
140.3.b.a	$140$	$3$	140.b	4.b	$2$	$24$	$24$	$3.815$		$_{}$	None	None		✓	✓	✓	140.3.b.a	$2$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
140.3.d.a	$140$	$3$	140.d	7.b	$2$	$4$	$4$	$3.815$	$\Q(\sqrt{-5}, \sqrt{-13})$	$_{}$	None	None		✓	✓	✓	140.3.d.a	$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
140.3.f.a	$140$	$3$	140.f	20.d	$2$	$36$	$36$	$3.815$		$_{}$	None	None		✓	✓	✓	140.3.f.a	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{2}]$
140.3.h.a	$140$	$3$	140.h	35.c	$2$	$2$	$2$	$3.815$	$\Q(\sqrt{105}) $	$_{}$	$\Q(\sqrt{-35}) $	None	✓	✓			140.3.h.a	$2$	$0$	$0$	$-1$	$-10$	$14$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}-5q^{5}+7q^{7}+(17+\beta )q^{9}+\cdots$
140.3.h.b	$140$	$3$	140.h	35.c	$2$	$2$	$2$	$3.815$	$\Q(\sqrt{105}) $	$_{}$	$\Q(\sqrt{-35}) $	None	✓	✓			140.3.h.a	$2$	$0$	$0$	$1$	$10$	$-14$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}+5q^{5}-7q^{7}+(17+\beta )q^{9}+\cdots$
140.3.h.c	$140$	$3$	140.h	35.c	$2$	$4$	$4$	$3.815$	$\Q(\sqrt{2}, \sqrt{-41})$	$_{}$	None	None		✓	✓		140.3.h.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-2\beta _{2}+\beta _{3})q^{7}+\cdots$
140.3.j.a	$140$	$3$	140.j	140.j	$4$	$88$	$44$	$3.815$		$_{}$	None	None		✓	✓	✓	140.3.j.a	$8$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
140.3.l.a	$140$	$3$	140.l	5.c	$4$	$4$	$2$	$3.815$	$\Q(i, \sqrt{14})$	$_{}$	None	None		✓			140.3.l.a	$2$	$0$	$0$	$4$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1}+\beta _{2})q^{3}+(-3+\beta _{1}+3\beta _{2}+\cdots)q^{5}+\cdots$
140.3.l.b	$140$	$3$	140.l	5.c	$4$	$8$	$4$	$3.815$	8.0.$\cdots$.32	$_{}$	None	None		✓	✓		140.3.l.b	$2$	$0$	$0$	$-8$	$20$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2}-\beta _{3}-\beta _{5})q^{3}+(3-\beta _{1}+\cdots)q^{5}+\cdots$
140.3.n.a	$140$	$3$	140.n	35.i	$6$	$16$	$8$	$3.815$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	140.3.n.a	$4$	$0$	$0$	$0$	$3$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}-\beta _{11}q^{5}+\beta _{15}q^{7}+(-2+\cdots)q^{9}+\cdots$
140.3.p.a	$140$	$3$	140.p	140.p	$6$	$4$	$2$	$3.815$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			140.3.p.a	$4$	$0$	$-4$	$-4$	$10$	$-4$		$3$	$\mathrm{U}(1)[D_{6}]$	$q+(-2+2\beta _{1})q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+\cdots$
140.3.p.b	$140$	$3$	140.p	140.p	$6$	$4$	$2$	$3.815$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			140.3.p.a	$4$	$0$	$4$	$4$	$10$	$4$		$3$	$\mathrm{U}(1)[D_{6}]$	$q+(2-2\beta _{1})q^{2}+(2\beta _{1}-\beta _{2})q^{3}-4\beta _{1}q^{4}+\cdots$
140.3.p.c	$140$	$3$	140.p	140.p	$6$	$80$	$40$	$3.815$		$_{}$	None	None		✓	✓		140.3.p.c	$8$	$0$	$0$	$0$	$-22$	$0$			$\mathrm{SU}(2)[C_{6}]$
140.3.r.a	$140$	$3$	140.r	7.d	$6$	$12$	$6$	$3.815$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓	✓	140.3.r.a	$2$	$0$	$0$	$-6$	$0$	$14$		$7$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{3}+\beta _{7}q^{5}+(1-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
140.3.t.a	$140$	$3$	140.t	28.g	$6$	$64$	$32$	$3.815$		$_{}$	None	None		✓	✓	✓	140.3.t.a	$4$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
140.3.v.a	$140$	$3$	140.v	35.l	$12$	$32$	$8$	$3.815$		$_{}$	None	None		✓	✓	✓	140.3.v.a	$4$	$0$	$0$	$0$	$-2$	$14$			$\mathrm{SU}(2)[C_{12}]$
140.3.x.a	$140$	$3$	140.x	140.x	$12$	$176$	$44$	$3.815$		$_{}$	None	None		✓	✓	✓	140.3.x.a	$8$	$0$	$-2$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{12}]$
140.4.a.a	$140$	$4$	140.a	1.a	$1$	$1$	$1$	$8.260$	$\Q$	$_{}$	None	None	✓	✓			140.4.a.a	$1$	$0$	$0$	$-5$	$-5$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-5q^{3}-5q^{5}+7q^{7}-2q^{9}+15q^{11}+\cdots$
140.4.a.b	$140$	$4$	140.a	1.a	$1$	$1$	$1$	$8.260$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	140.4.a.b	$1$	$1$	$0$	$-5$	$5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{3}+5q^{5}+7q^{7}-2q^{9}-15q^{11}+\cdots$
140.4.a.c	$140$	$4$	140.a	1.a	$1$	$1$	$1$	$8.260$	$\Q$	$_{}$	None	None	✓	✓			140.4.a.c	$1$	$0$	$0$	$-4$	$5$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}+5q^{5}-7q^{7}-11q^{9}+68q^{11}+\cdots$
140.4.a.d	$140$	$4$	140.a	1.a	$1$	$1$	$1$	$8.260$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	140.4.a.d	$1$	$1$	$0$	$1$	$-5$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-5q^{5}-7q^{7}-26q^{9}-7q^{11}+\cdots$
140.4.a.e	$140$	$4$	140.a	1.a	$1$	$1$	$1$	$8.260$	$\Q$	$_{}$	None	None	✓	✓			140.4.a.e	$1$	$0$	$0$	$8$	$-5$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{3}-5q^{5}+7q^{7}+37q^{9}+28q^{11}+\cdots$
140.4.a.f	$140$	$4$	140.a	1.a	$1$	$1$	$1$	$8.260$	$\Q$	$_{}$	None	None	✓	✓			140.4.a.f	$1$	$0$	$0$	$9$	$5$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+9q^{3}+5q^{5}-7q^{7}+54q^{9}+55q^{11}+\cdots$
140.4.c.a	$140$	$4$	140.c	140.c	$2$	$4$	$4$	$8.260$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			140.4.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2\beta _{2}q^{2}+(2\beta _{1}+\beta _{2})q^{3}+8q^{4}-5\beta _{3}q^{5}+\cdots$
140.4.c.b	$140$	$4$	140.c	140.c	$2$	$64$	$64$	$8.260$		$_{}$	None	None		✓	✓		140.4.c.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.