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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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Results (1-50 of 162 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
60.2.d.a	$60$	$2$	60.d	5.b	$2$	$2$	$2$	$0.479$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	60.2.d.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(2 i+1)q^{5}-4 i q^{7}-q^{9}+\cdots$
60.2.e.a	$60$	$2$	60.e	12.b	$2$	$8$	$8$	$0.479$	8.0.342102016.5	None		✓	✓	✓	60.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-\beta _{4}-\beta _{7})q^{3}+(\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$
60.2.h.a	$60$	$2$	60.h	60.h	$2$	$4$	$4$	$0.479$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-5}) $		✓			60.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{6}+\cdots$
60.2.h.b	$60$	$2$	60.h	60.h	$2$	$4$	$4$	$0.479$	$\Q(\sqrt{-3}, \sqrt{5})$	$\Q(\sqrt{-15}) $		✓			60.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots$
60.2.i.a	$60$	$2$	60.i	15.e	$4$	$4$	$2$	$0.479$	$\Q(i, \sqrt{5})$	None		✓	✓	✓	60.2.i.a	$4$	$0$	$0$	$2$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots$
60.2.j.a	$60$	$2$	60.j	20.e	$4$	$12$	$6$	$0.479$	12.0.$\cdots$.1	None		✓	✓	✓	60.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{2}+\beta _{4}-\beta _{7})q^{4}+\cdots$
60.3.b.a	$60$	$3$	60.b	15.d	$2$	$4$	$4$	$1.635$	$\Q(i, \sqrt{5})$	None		✓	✓	✓	60.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots$
60.3.c.a	$60$	$3$	60.c	4.b	$2$	$8$	$8$	$1.635$	8.0.85100625.1	None		✓	✓	✓	60.3.c.a	$2$	$0$	$4$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{4}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
60.3.f.a	$60$	$3$	60.f	20.d	$2$	$4$	$4$	$1.635$	$\Q(\zeta_{12})$	None		✓			60.3.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{3}+\beta_1)q^{2}+\beta_{3} q^{3}+(2\beta_{2}+2)q^{4}+\cdots$
60.3.f.b	$60$	$3$	60.f	20.d	$2$	$8$	$8$	$1.635$	8.0.$\cdots$.4	None		✓	✓		60.3.f.b	$4$	$0$	$0$	$0$	$4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots$
60.3.g.a	$60$	$3$	60.g	3.b	$2$	$2$	$2$	$1.635$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	60.3.g.a	$2$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+\beta )q^{3}+\beta q^{5}+2q^{7}+(-1+4\beta )q^{9}+\cdots$
60.3.k.a	$60$	$3$	60.k	5.c	$4$	$4$	$2$	$1.635$	$\Q(i, \sqrt{6})$	None		✓	✓	✓	60.3.k.a	$2$	$0$	$0$	$0$	$12$	$20$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots$
60.3.l.a	$60$	$3$	60.l	60.l	$4$	$40$	$20$	$1.635$		None		✓	✓	✓	60.3.l.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
60.4.a.a	$60$	$4$	60.a	1.a	$1$	$1$	$1$	$3.540$	$\Q$	None	✓	✓	✓	✓	60.4.a.a	$1$	$1$	$0$	$-3$	$-5$	$-28$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-5q^{5}-28q^{7}+9q^{9}-24q^{11}+\cdots$
60.4.a.b	$60$	$4$	60.a	1.a	$1$	$1$	$1$	$3.540$	$\Q$	None	✓	✓	✓	✓	60.4.a.b	$1$	$0$	$0$	$-3$	$5$	$32$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+5q^{5}+2^{5}q^{7}+9q^{9}+6^{2}q^{11}+\cdots$
60.4.d.a	$60$	$4$	60.d	5.b	$2$	$2$	$2$	$3.540$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	60.4.d.a	$2$	$0$	$0$	$0$	$-20$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+(5 i-10)q^{5}+22 i q^{7}+\cdots$
60.4.e.a	$60$	$4$	60.e	12.b	$2$	$24$	$24$	$3.540$		None		✓	✓	✓	60.4.e.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
60.4.h.a	$60$	$4$	60.h	60.h	$2$	$4$	$4$	$3.540$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-5}) $		✓			60.4.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2\beta _{2}q^{2}+(\beta _{1}-4\beta _{2})q^{3}-8q^{4}-5\beta _{3}q^{5}+\cdots$
60.4.h.b	$60$	$4$	60.h	60.h	$2$	$4$	$4$	$3.540$	$\Q(\sqrt{-3}, \sqrt{5})$	$\Q(\sqrt{-15}) $		✓			60.4.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots$
60.4.h.c	$60$	$4$	60.h	60.h	$2$	$24$	$24$	$3.540$		None		✓	✓		60.4.h.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
60.4.i.a	$60$	$4$	60.i	15.e	$4$	$4$	$2$	$3.540$	$\Q(\zeta_{8})$	None		✓			60.4.i.a	$4$	$0$	$0$	$-4$	$0$	$92$		$5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{2}-\beta_1-1)q^{3}+(2\beta_{3}+\beta_1)q^{5}+\cdots$
60.4.i.b	$60$	$4$	60.i	15.e	$4$	$8$	$4$	$3.540$	8.0.$\cdots$.7	None		✓	✓		60.4.i.b	$4$	$0$	$0$	$0$	$0$	$-80$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{3}+(\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6}+\beta _{7})q^{5}+\cdots$
60.4.j.a	$60$	$4$	60.j	20.e	$4$	$8$	$4$	$3.540$	8.0.157351936.1	None		✓			60.4.j.a	$4$	$0$	$0$	$0$	$-24$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{2}+\beta _{4})q^{2}+3\beta _{5}q^{3}+(6\beta _{3}+2\beta _{6}+\cdots)q^{4}+\cdots$
60.4.j.b	$60$	$4$	60.j	20.e	$4$	$28$	$14$	$3.540$		None		✓	✓		60.4.j.b	$4$	$0$	$0$	$0$	$24$	$0$			$\mathrm{SU}(2)[C_{4}]$
60.5.b.a	$60$	$5$	60.b	15.d	$2$	$8$	$8$	$6.202$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓	✓	60.5.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}\cdot 3^{2}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{6}q^{7}+(6+\beta _{2}+\cdots)q^{9}+\cdots$
60.5.c.a	$60$	$5$	60.c	4.b	$2$	$16$	$16$	$6.202$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	60.5.c.a	$2$	$0$	$-12$	$0$	$0$	$0$		$2^{32}\cdot 3^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{3})q^{2}+\beta _{2}q^{3}+(2+\beta _{3}+\beta _{7}+\cdots)q^{4}+\cdots$
60.5.f.a	$60$	$5$	60.f	20.d	$2$	$24$	$24$	$6.202$		None		✓	✓	✓	60.5.f.a	$4$	$0$	$0$	$0$	$-24$	$0$			$\mathrm{SU}(2)[C_{2}]$
60.5.g.a	$60$	$5$	60.g	3.b	$2$	$2$	$2$	$6.202$	$\Q(\sqrt{-5}) $	None		✓			60.5.g.a	$2$	$0$	$0$	$12$	$0$	$148$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(6+3\beta )q^{3}-5\beta q^{5}+74q^{7}+(-9+\cdots)q^{9}+\cdots$
60.5.g.b	$60$	$5$	60.g	3.b	$2$	$4$	$4$	$6.202$	$\Q(\sqrt{-5}, \sqrt{34})$	None		✓	✓		60.5.g.b	$2$	$0$	$0$	$-20$	$0$	$-40$		$3\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+(-5+\beta _{1})q^{3}-\beta _{3}q^{5}+(-10-\beta _{1}+\cdots)q^{7}+\cdots$
60.5.k.a	$60$	$5$	60.k	5.c	$4$	$8$	$4$	$6.202$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓	✓	60.5.k.a	$2$	$0$	$0$	$0$	$12$	$-140$		$2\cdot 3^{2}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+(2+2\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots$
60.5.l.a	$60$	$5$	60.l	60.l	$4$	$88$	$44$	$6.202$		None		✓	✓	✓	60.5.l.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
60.6.a.a	$60$	$6$	60.a	1.a	$1$	$1$	$1$	$9.623$	$\Q$	None	✓	✓	✓	✓	60.6.a.a	$1$	$0$	$0$	$-9$	$-25$	$44$	$-$	$1$	$\mathrm{SU}(2)$	$q-9q^{3}-5^{2}q^{5}+44q^{7}+3^{4}q^{9}+6^{3}q^{11}+\cdots$
60.6.a.b	$60$	$6$	60.a	1.a	$1$	$1$	$1$	$9.623$	$\Q$	None	✓	✓	✓	✓	60.6.a.b	$1$	$1$	$0$	$-9$	$25$	$-16$	$+$	$1$	$\mathrm{SU}(2)$	$q-9q^{3}+5^{2}q^{5}-2^{4}q^{7}+3^{4}q^{9}-564q^{11}+\cdots$
60.6.a.c	$60$	$6$	60.a	1.a	$1$	$1$	$1$	$9.623$	$\Q$	None	✓	✓	✓	✓	60.6.a.c	$1$	$1$	$0$	$9$	$-25$	$-244$	$+$	$1$	$\mathrm{SU}(2)$	$q+9q^{3}-5^{2}q^{5}-244q^{7}+3^{4}q^{9}+\cdots$
60.6.a.d	$60$	$6$	60.a	1.a	$1$	$1$	$1$	$9.623$	$\Q$	None	✓	✓	✓	✓	60.6.a.d	$1$	$0$	$0$	$9$	$25$	$56$	$-$	$1$	$\mathrm{SU}(2)$	$q+9q^{3}+5^{2}q^{5}+56q^{7}+3^{4}q^{9}+156q^{11}+\cdots$
60.6.d.a	$60$	$6$	60.d	5.b	$2$	$6$	$6$	$9.623$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓	✓	60.6.d.a	$2$	$0$	$0$	$0$	$-38$	$0$		$2^{4}\cdot 3^{4}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-6-\beta _{1}-\beta _{2})q^{5}+(-3\beta _{1}+\cdots)q^{7}+\cdots$
60.6.e.a	$60$	$6$	60.e	12.b	$2$	$40$	$40$	$9.623$		None		✓	✓	✓	60.6.e.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
60.6.h.a	$60$	$6$	60.h	60.h	$2$	$4$	$4$	$9.623$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-5}) $		✓			60.6.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+4\beta _{1}q^{2}+(10\beta _{1}+\beta _{2})q^{3}-2^{5}q^{4}+\cdots$
60.6.h.b	$60$	$6$	60.h	60.h	$2$	$4$	$4$	$9.623$	$\Q(\sqrt{-3}, \sqrt{5})$	$\Q(\sqrt{-15}) $		✓			60.6.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+9\beta _{1}q^{3}+(31-\beta _{3})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots$
60.6.h.c	$60$	$6$	60.h	60.h	$2$	$48$	$48$	$9.623$		None		✓	✓		60.6.h.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
60.6.i.a	$60$	$6$	60.i	15.e	$4$	$20$	$10$	$9.623$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	60.6.i.a	$4$	$0$	$0$	$2$	$0$	$76$		$2^{23}\cdot 3^{14}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{3}-\beta _{5}q^{5}+(4+4\beta _{1}+\beta _{8})q^{7}+\cdots$
60.6.j.a	$60$	$6$	60.j	20.e	$4$	$60$	$30$	$9.623$		None		✓	✓	✓	60.6.j.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
60.7.b.a	$60$	$7$	60.b	15.d	$2$	$12$	$12$	$13.803$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	60.7.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{22}\cdot 3^{8}\cdot 5^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots$
60.7.c.a	$60$	$7$	60.c	4.b	$2$	$24$	$24$	$13.803$		None		✓	✓	✓	60.7.c.a	$2$	$0$	$20$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
60.7.f.a	$60$	$7$	60.f	20.d	$2$	$36$	$36$	$13.803$		None		✓	✓	✓	60.7.f.a	$4$	$0$	$0$	$0$	$44$	$0$			$\mathrm{SU}(2)[C_{2}]$
60.7.g.a	$60$	$7$	60.g	3.b	$2$	$8$	$8$	$13.803$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓	✓	60.7.g.a	$2$	$0$	$0$	$-20$	$0$	$-560$		$2^{7}\cdot 3^{7}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3-\beta _{1})q^{3}+\beta _{2}q^{5}+(-71-\beta _{4}+\cdots)q^{7}+\cdots$
60.7.k.a	$60$	$7$	60.k	5.c	$4$	$12$	$6$	$13.803$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓	✓	60.7.k.a	$2$	$0$	$0$	$0$	$312$	$120$		$2^{19}\cdot 3^{10}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+(26-4\beta _{1}+\beta _{2}+2\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$
60.7.l.a	$60$	$7$	60.l	60.l	$4$	$136$	$68$	$13.803$		None		✓	✓	✓	60.7.l.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
60.8.a.a	$60$	$8$	60.a	1.a	$1$	$1$	$1$	$18.743$	$\Q$	None	✓	✓	✓	✓	60.8.a.a	$1$	$1$	$0$	$-27$	$-125$	$1028$	$-$	$1$	$\mathrm{SU}(2)$	$q-3^{3}q^{3}-5^{3}q^{5}+1028q^{7}+3^{6}q^{9}+\cdots$
60.8.a.b	$60$	$8$	60.a	1.a	$1$	$1$	$1$	$18.743$	$\Q$	None	✓	✓	✓	✓	60.8.a.b	$1$	$0$	$0$	$-27$	$125$	$-832$	$+$	$1$	$\mathrm{SU}(2)$	$q-3^{3}q^{3}+5^{3}q^{5}-832q^{7}+3^{6}q^{9}+\cdots$

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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.