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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 134 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
74.2.a.a	$74$	$2$	74.a	1.a	$1$	$2$	$2$	$0.591$	$\Q(\sqrt{13}) $	None	✓	✓	✓	✓	74.2.a.a	$1$	$0$	$-2$	$3$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
74.2.a.b	$74$	$2$	74.a	1.a	$1$	$2$	$2$	$0.591$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	74.2.a.b	$1$	$0$	$2$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots$
74.2.b.a	$74$	$2$	74.b	37.b	$2$	$4$	$4$	$0.591$	$\Q(i, \sqrt{21})$	None		✓	✓	✓	74.2.b.a	$2$	$0$	$0$	$-2$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
74.2.c.a	$74$	$2$	74.c	37.c	$3$	$2$	$1$	$0.591$	$\Q(\sqrt{-3}) $	None		✓			74.2.c.a	$2$	$0$	$1$	$-2$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
74.2.c.b	$74$	$2$	74.c	37.c	$3$	$2$	$1$	$0.591$	$\Q(\sqrt{-3}) $	None		✓			74.2.c.b	$2$	$0$	$1$	$2$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+2\zeta_{6}q^{3}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$
74.2.c.c	$74$	$2$	74.c	37.c	$3$	$6$	$3$	$0.591$	6.0.4406832.1	None		✓	✓		74.2.c.c	$2$	$0$	$-3$	$0$	$-1$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{3})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\beta _{3}q^{4}+\cdots$
74.2.e.a	$74$	$2$	74.e	37.e	$6$	$4$	$2$	$0.591$	$\Q(\zeta_{12})$	None		✓			74.2.e.a	$2$	$0$	$0$	$-2$	$-6$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
74.2.e.b	$74$	$2$	74.e	37.e	$6$	$4$	$2$	$0.591$	$\Q(\zeta_{12})$	None		✓			74.2.e.b	$2$	$0$	$0$	$-2$	$6$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$
74.2.f.a	$74$	$2$	74.f	37.f	$9$	$6$	$1$	$0.591$	$\Q(\zeta_{18})$	None		✓			74.2.f.a	$2$	$0$	$0$	$-3$	$3$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
74.2.f.b	$74$	$2$	74.f	37.f	$9$	$12$	$2$	$0.591$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		74.2.f.b	$2$	$0$	$0$	$-3$	$-6$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{4}-\beta _{7})q^{2}+(-1+\beta _{1}-\beta _{8})q^{3}+\cdots$
74.2.h.a	$74$	$2$	74.h	37.h	$18$	$12$	$2$	$0.591$	$\Q(\zeta_{36})$	None		✓	✓	✓	74.2.h.a	$2$	$0$	$0$	$6$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{18}]$	$q+\zeta_{36}q^{2}+(1-\zeta_{36}^{4}-\zeta_{36}^{6})q^{3}+\cdots$
74.3.d.a	$74$	$3$	74.d	37.d	$4$	$2$	$1$	$2.016$	$\Q(\sqrt{-1}) $	None		✓			74.3.d.a	$2$	$0$	$2$	$0$	$-12$	$10$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+i q^{3}+2 i q^{4}+(6 i-6)q^{5}+\cdots$
74.3.d.b	$74$	$3$	74.d	37.d	$4$	$2$	$1$	$2.016$	$\Q(\sqrt{-1}) $	None		✓			74.3.d.b	$2$	$0$	$2$	$0$	$6$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+4 i q^{3}+2 i q^{4}+(-3 i+3)q^{5}+\cdots$
74.3.d.c	$74$	$3$	74.d	37.d	$4$	$2$	$1$	$2.016$	$\Q(\sqrt{-1}) $	None		✓			74.3.d.c	$2$	$0$	$2$	$0$	$6$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}-3 i q^{3}+2 i q^{4}+(-3 i+3)q^{5}+\cdots$
74.3.d.d	$74$	$3$	74.d	37.d	$4$	$4$	$2$	$2.016$	$\Q(i, \sqrt{65})$	None		✓	✓		74.3.d.d	$2$	$0$	$-4$	$0$	$-6$	$-8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}-2\beta _{1}q^{4}+\cdots$
74.3.g.a	$74$	$3$	74.g	37.g	$12$	$8$	$2$	$2.016$	8.0.303595776.1	None		✓			74.3.g.a	$2$	$0$	$4$	$0$	$12$	$8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{4}+\beta _{5})q^{2}+(2\beta _{1}-\beta _{5}-\beta _{7})q^{3}+\cdots$
74.3.g.b	$74$	$3$	74.g	37.g	$12$	$12$	$3$	$2.016$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓		74.3.g.b	$2$	$0$	$-6$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(\beta _{4}-\beta _{7})q^{2}-\beta _{3}q^{3}+2\beta _{6}q^{4}+(1+\cdots)q^{5}+\cdots$
74.3.i.a	$74$	$3$	74.i	37.i	$36$	$36$	$3$	$2.016$		None		✓			74.3.i.a	$2$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{36}]$
74.3.i.b	$74$	$3$	74.i	37.i	$36$	$48$	$4$	$2.016$		None		✓	✓		74.3.i.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{36}]$
74.4.a.a	$74$	$4$	74.a	1.a	$1$	$1$	$1$	$4.366$	$\Q$	None	✓	✓	✓	✓	74.4.a.a	$1$	$1$	$-2$	$-5$	$12$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-5q^{3}+4q^{4}+12q^{5}+10q^{6}+\cdots$
74.4.a.b	$74$	$4$	74.a	1.a	$1$	$1$	$1$	$4.366$	$\Q$	None	✓	✓	✓	✓	74.4.a.b	$1$	$1$	$2$	$-5$	$-14$	$-19$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-5q^{3}+4q^{4}-14q^{5}-10q^{6}+\cdots$
74.4.a.c	$74$	$4$	74.a	1.a	$1$	$3$	$3$	$4.366$	3.3.15629.1	None	✓	✓	✓	✓	74.4.a.c	$1$	$0$	$-6$	$4$	$7$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+4q^{4}+(2+\cdots)q^{5}+\cdots$
74.4.a.d	$74$	$4$	74.a	1.a	$1$	$4$	$4$	$4.366$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	74.4.a.d	$1$	$0$	$8$	$4$	$21$	$23$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(5+\beta _{2}+\cdots)q^{5}+\cdots$
74.4.b.a	$74$	$4$	74.b	37.b	$2$	$10$	$10$	$4.366$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓	✓	✓	74.4.b.a	$2$	$0$	$0$	$14$	$0$	$-4$		$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(1-\beta _{2})q^{3}-4q^{4}+(2\beta _{5}+\cdots)q^{5}+\cdots$
74.4.c.a	$74$	$4$	74.c	37.c	$3$	$8$	$4$	$4.366$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			74.4.c.a	$2$	$0$	$8$	$-5$	$-10$	$3$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\beta _{2})q^{2}+(-\beta _{1}-\beta _{2})q^{3}-4\beta _{2}q^{4}+\cdots$
74.4.c.b	$74$	$4$	74.c	37.c	$3$	$10$	$5$	$4.366$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓	✓		74.4.c.b	$2$	$0$	$-10$	$-5$	$-1$	$-1$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+2\beta _{3}q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots$
74.4.e.a	$74$	$4$	74.e	37.e	$6$	$20$	$10$	$4.366$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	74.4.e.a	$2$	$0$	$0$	$-2$	$-18$	$-2$		$2^{18}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{11}q^{2}+\beta _{14}q^{3}+4\beta _{6}q^{4}+(-1+\cdots)q^{5}+\cdots$
74.4.f.a	$74$	$4$	74.f	37.f	$9$	$24$	$4$	$4.366$		None		✓			74.4.f.a	$2$	$0$	$0$	$6$	$-9$	$-75$			$\mathrm{SU}(2)[C_{9}]$
74.4.f.b	$74$	$4$	74.f	37.f	$9$	$30$	$5$	$4.366$		None		✓	✓		74.4.f.b	$2$	$0$	$0$	$6$	$-6$	$-75$			$\mathrm{SU}(2)[C_{9}]$
74.4.h.a	$74$	$4$	74.h	37.h	$18$	$60$	$10$	$4.366$		None		✓	✓	✓	74.4.h.a	$2$	$0$	$0$	$-12$	$18$	$150$			$\mathrm{SU}(2)[C_{18}]$
74.5.d.a	$74$	$5$	74.d	37.d	$4$	$14$	$7$	$7.649$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓			74.5.d.a	$2$	$0$	$-28$	$0$	$-12$	$48$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2+2\beta _{5})q^{2}+(\beta _{1}+\beta _{5})q^{3}-8\beta _{5}q^{4}+\cdots$
74.5.d.b	$74$	$5$	74.d	37.d	$4$	$14$	$7$	$7.649$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓			74.5.d.b	$2$	$0$	$28$	$0$	$36$	$-48$		$2\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2+2\beta _{5})q^{2}+(\beta _{1}-\beta _{5})q^{3}+8\beta _{5}q^{4}+\cdots$
74.5.g.a	$74$	$5$	74.g	37.g	$12$	$28$	$7$	$7.649$		None		✓			74.5.g.a	$2$	$0$	$-28$	$0$	$42$	$48$			$\mathrm{SU}(2)[C_{12}]$
74.5.g.b	$74$	$5$	74.g	37.g	$12$	$28$	$7$	$7.649$		None		✓			74.5.g.b	$2$	$0$	$28$	$0$	$-102$	$-48$			$\mathrm{SU}(2)[C_{12}]$
74.5.i.a	$74$	$5$	74.i	37.i	$36$	$72$	$6$	$7.649$		None		✓			74.5.i.a	$2$	$0$	$0$	$0$	$-78$	$0$			$\mathrm{SU}(2)[C_{36}]$
74.5.i.b	$74$	$5$	74.i	37.i	$36$	$72$	$6$	$7.649$		None		✓			74.5.i.b	$2$	$0$	$0$	$0$	$114$	$0$			$\mathrm{SU}(2)[C_{36}]$
74.6.a.a	$74$	$6$	74.a	1.a	$1$	$1$	$1$	$11.868$	$\Q$	None	✓	✓			74.6.a.a	$1$	$1$	$4$	$-15$	$4$	$15$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-15q^{3}+2^{4}q^{4}+4q^{5}-60q^{6}+\cdots$
74.6.a.b	$74$	$6$	74.a	1.a	$1$	$1$	$1$	$11.868$	$\Q$	None	✓	✓			74.6.a.b	$1$	$1$	$4$	$7$	$-84$	$-139$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+7q^{3}+2^{4}q^{4}-84q^{5}+28q^{6}+\cdots$
74.6.a.c	$74$	$6$	74.a	1.a	$1$	$3$	$3$	$11.868$	3.3.324233.1	None	✓	✓	✓	✓	74.6.a.c	$1$	$1$	$-12$	$-8$	$-42$	$84$	$+$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(-3+\beta _{1}-\beta _{2})q^{3}+2^{4}q^{4}+\cdots$
74.6.a.d	$74$	$6$	74.a	1.a	$1$	$5$	$5$	$11.868$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	74.6.a.d	$1$	$0$	$-20$	$19$	$-67$	$182$	$-$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(4+\beta _{2})q^{3}+2^{4}q^{4}+(-14+\cdots)q^{5}+\cdots$
74.6.a.e	$74$	$6$	74.a	1.a	$1$	$5$	$5$	$11.868$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	74.6.a.e	$1$	$0$	$20$	$19$	$95$	$170$	$-$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+(4-\beta _{1})q^{3}+2^{4}q^{4}+(19+\beta _{2}+\cdots)q^{5}+\cdots$
74.6.b.a	$74$	$6$	74.b	37.b	$2$	$14$	$14$	$11.868$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓	✓	✓	74.6.b.a	$2$	$0$	$0$	$14$	$0$	$-312$		$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{2}+(1+\beta _{2})q^{3}-2^{4}q^{4}+(\beta _{9}+\cdots)q^{5}+\cdots$
74.6.c.a	$74$	$6$	74.c	37.c	$3$	$14$	$7$	$11.868$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			74.6.c.a	$2$	$0$	$-28$	$-8$	$57$	$188$		$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-4+4\beta _{3})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\cdots$
74.6.c.b	$74$	$6$	74.c	37.c	$3$	$16$	$8$	$11.868$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		74.6.c.b	$2$	$0$	$32$	$-8$	$70$	$-32$		$2^{10}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(4+4\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2^{4}\beta _{3}q^{4}+\cdots$
74.6.e.a	$74$	$6$	74.e	37.e	$6$	$28$	$14$	$11.868$		None		✓	✓	✓	74.6.e.a	$2$	$0$	$0$	$-20$	$-90$	$-156$			$\mathrm{SU}(2)[C_{6}]$
74.6.f.a	$74$	$6$	74.f	37.f	$9$	$48$	$8$	$11.868$		None		✓			74.6.f.a	$2$	$0$	$0$	$-3$	$-72$	$114$			$\mathrm{SU}(2)[C_{9}]$
74.6.f.b	$74$	$6$	74.f	37.f	$9$	$54$	$9$	$11.868$		None		✓	✓		74.6.f.b	$2$	$0$	$0$	$-3$	$39$	$114$			$\mathrm{SU}(2)[C_{9}]$
74.6.h.a	$74$	$6$	74.h	37.h	$18$	$96$	$16$	$11.868$		None		✓	✓	✓	74.6.h.a	$2$	$0$	$0$	$6$	$90$	$-228$			$\mathrm{SU}(2)[C_{18}]$
74.7.d.a	$74$	$7$	74.d	37.d	$4$	$18$	$9$	$17.024$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓			74.7.d.a	$2$	$0$	$72$	$0$	$294$	$-104$		$2^{10}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(4-4\beta _{6})q^{2}+(\beta _{1}-4\beta _{6})q^{3}-2^{5}\beta _{6}q^{4}+\cdots$
74.7.d.b	$74$	$7$	74.d	37.d	$4$	$20$	$10$	$17.024$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓		74.7.d.b	$2$	$0$	$-80$	$0$	$60$	$104$		$2^{9}\cdot 3^{2}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-4-4\beta _{6})q^{2}+(-\beta _{1}+3\beta _{6})q^{3}+\cdots$

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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.