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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 184 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
81.2.a.a	$81$	$2$	81.a	1.a	$1$	$2$	$2$	$0.647$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	81.2.a.a	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}+2q^{7}-\beta q^{8}+\cdots$
81.2.c.a	$81$	$2$	81.c	9.c	$3$	$2$	$1$	$0.647$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $					27.2.a.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\cdots$
81.2.c.b	$81$	$2$	81.c	9.c	$3$	$4$	$2$	$0.647$	$\Q(\zeta_{12})$	None		✓	✓		81.2.a.a	$4$	$0$	$0$	$0$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}+(\beta_1-1)q^{4}+(\beta_{3}-\beta_{2})q^{5}+\cdots$
81.2.e.a	$81$	$2$	81.e	27.e	$9$	$12$	$2$	$0.647$	12.0.$\cdots$.1	None			✓	✓	27.2.e.a	$2$	$0$	$6$	$0$	$3$	$-6$		$3$	$\mathrm{SU}(2)[C_{9}]$	$q+(1+\beta _{3}-\beta _{8})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
81.2.g.a	$81$	$2$	81.g	81.g	$27$	$144$	$8$	$0.647$		None		✓	✓	✓	81.2.g.a	$2$	$0$	$-18$	$-18$	$-18$	$-18$			$\mathrm{SU}(2)[C_{27}]$
81.3.b.a	$81$	$3$	81.b	3.b	$2$	$2$	$2$	$2.207$	$\Q(\sqrt{-3}) $	None					9.3.d.a	$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}+q^{4}-2\beta q^{5}+2 q^{7}-5\beta q^{8}+\cdots$
81.3.b.b	$81$	$3$	81.b	3.b	$2$	$4$	$4$	$2.207$	$\Q(\sqrt{-2}, \sqrt{3})$	None		✓	✓		81.3.b.b	$2$	$0$	$0$	$0$	$0$	$-4$		$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
81.3.d.a	$81$	$3$	81.d	9.d	$6$	$2$	$1$	$2.207$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $					27.3.b.a	$4$	$0$	$0$	$0$	$0$	$13$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-4\zeta_{6}q^{4}+(13-13\zeta_{6})q^{7}+\zeta_{6}q^{13}+\cdots$
81.3.d.b	$81$	$3$	81.d	9.d	$6$	$4$	$2$	$2.207$	$\Q(\zeta_{12})$	None					27.3.b.b	$4$	$0$	$0$	$0$	$0$	$-10$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta_1 q^{2}+5\beta_{2} q^{4}+(-\beta_{3}+\beta_1)q^{5}+\cdots$
81.3.d.c	$81$	$3$	81.d	9.d	$6$	$8$	$4$	$2.207$	$\Q(\zeta_{24})$	None		✓	✓		81.3.b.b	$4$	$0$	$0$	$0$	$0$	$4$		$3^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta_{4} q^{2}+(-\beta_{3}+\beta_{2}-2\beta_1+2)q^{4}+\cdots$
81.3.f.a	$81$	$3$	81.f	27.f	$18$	$30$	$5$	$2.207$		None			✓	✓	27.3.f.a	$2$	$0$	$6$	$0$	$15$	$-6$			$\mathrm{SU}(2)[C_{18}]$
81.3.h.a	$81$	$3$	81.h	81.h	$54$	$306$	$17$	$2.207$		None		✓	✓	✓	81.3.h.a	$2$	$0$	$-18$	$-18$	$-18$	$-18$			$\mathrm{SU}(2)[C_{54}]$
81.4.a.a	$81$	$4$	81.a	1.a	$1$	$2$	$2$	$4.779$	$\Q(\sqrt{33}) $	None	✓				9.4.c.a	$1$	$1$	$-3$	$0$	$-15$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(1+3\beta )q^{4}+(-8+\beta )q^{5}+\cdots$
81.4.a.b	$81$	$4$	81.a	1.a	$1$	$2$	$2$	$4.779$	$\Q(\sqrt{57}) $	None	✓	✓			81.4.a.b	$1$	$0$	$-3$	$0$	$12$	$10$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(7+3\beta )q^{4}+(7-2\beta )q^{5}+\cdots$
81.4.a.c	$81$	$4$	81.a	1.a	$1$	$2$	$2$	$4.779$	$\Q(\sqrt{3}) $	None	✓	✓			81.4.a.c	$2$	$1$	$0$	$0$	$0$	$-44$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-5q^{4}-7\beta q^{5}-22q^{7}-13\beta q^{8}+\cdots$
81.4.a.d	$81$	$4$	81.a	1.a	$1$	$2$	$2$	$4.779$	$\Q(\sqrt{33}) $	None	✓				9.4.c.a	$1$	$0$	$3$	$0$	$15$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+3\beta )q^{4}+(8-\beta )q^{5}+\cdots$
81.4.a.e	$81$	$4$	81.a	1.a	$1$	$2$	$2$	$4.779$	$\Q(\sqrt{57}) $	None	✓	✓			81.4.a.b	$1$	$0$	$3$	$0$	$-12$	$10$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(7+3\beta )q^{4}+(-7+2\beta )q^{5}+\cdots$
81.4.c.a	$81$	$4$	81.c	9.c	$3$	$2$	$1$	$4.779$	$\Q(\sqrt{-3}) $	None					27.4.a.a	$2$	$0$	$-3$	$0$	$-15$	$25$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{2}-\zeta_{6}q^{4}-15\zeta_{6}q^{5}+\cdots$
81.4.c.b	$81$	$4$	81.c	9.c	$3$	$2$	$1$	$4.779$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $					9.4.a.a	$4$	$0$	$0$	$0$	$0$	$-20$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+8\zeta_{6}q^{4}+(-20+20\zeta_{6})q^{7}+70\zeta_{6}q^{13}+\cdots$
81.4.c.c	$81$	$4$	81.c	9.c	$3$	$2$	$1$	$4.779$	$\Q(\sqrt{-3}) $	None					27.4.a.a	$2$	$0$	$3$	$0$	$15$	$25$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{2}-\zeta_{6}q^{4}+15\zeta_{6}q^{5}+\cdots$
81.4.c.d	$81$	$4$	81.c	9.c	$3$	$4$	$2$	$4.779$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		✓			81.4.a.b	$2$	$0$	$-3$	$0$	$12$	$-10$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}-\beta _{3})q^{2}+(7\beta _{1}-3\beta _{2}+\cdots)q^{4}+\cdots$
81.4.c.e	$81$	$4$	81.c	9.c	$3$	$4$	$2$	$4.779$	$\Q(\sqrt{2}, \sqrt{-3})$	None					27.4.a.c	$4$	$0$	$0$	$0$	$0$	$-22$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+10\beta _{2}q^{4}+(4\beta _{1}+4\beta _{3})q^{5}+\cdots$
81.4.c.f	$81$	$4$	81.c	9.c	$3$	$4$	$2$	$4.779$	$\Q(\zeta_{12})$	None		✓			81.4.a.c	$4$	$0$	$0$	$0$	$0$	$44$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}+(-5\beta_1+5)q^{4}+(7\beta_{3}-7\beta_{2})q^{5}+\cdots$
81.4.c.g	$81$	$4$	81.c	9.c	$3$	$4$	$2$	$4.779$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		✓			81.4.a.b	$2$	$0$	$3$	$0$	$-12$	$-10$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{3})q^{2}+(7\beta _{1}-3\beta _{2}+3\beta _{3})q^{4}+\cdots$
81.4.e.a	$81$	$4$	81.e	27.e	$9$	$48$	$8$	$4.779$		None			✓	✓	27.4.e.a	$2$	$0$	$6$	$0$	$-6$	$-6$			$\mathrm{SU}(2)[C_{9}]$
81.4.g.a	$81$	$4$	81.g	81.g	$27$	$468$	$26$	$4.779$		None		✓	✓	✓	81.4.g.a	$2$	$0$	$-18$	$-18$	$-18$	$-18$			$\mathrm{SU}(2)[C_{27}]$
81.5.b.a	$81$	$5$	81.b	3.b	$2$	$6$	$6$	$8.373$	6.0.39400128.1	None					9.5.d.a	$2$	$0$	$0$	$0$	$0$	$-24$		$2^{3}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-5+\beta _{2})q^{4}+\beta _{4}q^{5}+(-4+\cdots)q^{7}+\cdots$
81.5.b.b	$81$	$5$	81.b	3.b	$2$	$8$	$8$	$8.373$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓		81.5.b.b	$2$	$0$	$0$	$0$	$0$	$52$		$3^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-8+\beta _{5})q^{4}+(\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
81.5.d.a	$81$	$5$	81.d	9.d	$6$	$2$	$1$	$8.373$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $					27.5.b.a	$4$	$0$	$0$	$0$	$0$	$-71$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-2^{4}\zeta_{6}q^{4}+(-71+71\zeta_{6})q^{7}+337\zeta_{6}q^{13}+\cdots$
81.5.d.b	$81$	$5$	81.d	9.d	$6$	$4$	$2$	$8.373$	$\Q(\zeta_{12})$	None					27.5.b.c	$4$	$0$	$0$	$0$	$0$	$38$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta_1 q^{2}-7\beta_{2} q^{4}+(11\beta_{3}-11\beta_1)q^{5}+\cdots$
81.5.d.c	$81$	$5$	81.d	9.d	$6$	$4$	$2$	$8.373$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					9.5.b.a	$4$	$0$	$0$	$0$	$0$	$56$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(7\beta _{1}-7\beta _{3})q^{5}+\cdots$
81.5.d.d	$81$	$5$	81.d	9.d	$6$	$4$	$2$	$8.373$	$\Q(\sqrt{2}, \sqrt{-3})$	None					27.5.b.b	$4$	$0$	$0$	$0$	$0$	$-34$		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(38+38\beta _{1})q^{4}+(2\beta _{2}-2\beta _{3})q^{5}+\cdots$
81.5.d.e	$81$	$5$	81.d	9.d	$6$	$16$	$8$	$8.373$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		81.5.b.b	$4$	$0$	$0$	$0$	$0$	$-52$		$3^{40}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{7}q^{2}+(8-8\beta _{1}-\beta _{4}-\beta _{9})q^{4}+\cdots$
81.5.f.a	$81$	$5$	81.f	27.f	$18$	$66$	$11$	$8.373$		None			✓	✓	27.5.f.a	$2$	$0$	$6$	$0$	$-3$	$-6$			$\mathrm{SU}(2)[C_{18}]$
81.5.h.a	$81$	$5$	81.h	81.h	$54$	$630$	$35$	$8.373$		None		✓	✓	✓	81.5.h.a	$2$	$0$	$-18$	$-18$	$-18$	$-18$			$\mathrm{SU}(2)[C_{54}]$
81.6.a.a	$81$	$6$	81.a	1.a	$1$	$2$	$2$	$12.991$	$\Q(\sqrt{129}) $	None	✓	✓			81.6.a.a	$1$	$1$	$-3$	$0$	$30$	$-128$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(1+3\beta )q^{4}+(13+4\beta )q^{5}+\cdots$
81.6.a.b	$81$	$6$	81.a	1.a	$1$	$2$	$2$	$12.991$	$\Q(\sqrt{129}) $	None	✓	✓			81.6.a.a	$1$	$1$	$3$	$0$	$-30$	$-128$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+3\beta )q^{4}+(-13-4\beta )q^{5}+\cdots$
81.6.a.c	$81$	$6$	81.a	1.a	$1$	$4$	$4$	$12.991$	4.4.4875021.1	None	✓		✓		9.6.c.a	$1$	$1$	$-3$	$0$	$-78$	$-28$	$+$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(13-2\beta _{1}+\beta _{3})q^{4}+\cdots$
81.6.a.d	$81$	$6$	81.a	1.a	$1$	$4$	$4$	$12.991$	4.4.4875021.1	None	✓				9.6.c.a	$1$	$0$	$3$	$0$	$78$	$-28$	$-$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(13-2\beta _{1}+\beta _{3})q^{4}+\cdots$
81.6.a.e	$81$	$6$	81.a	1.a	$1$	$6$	$6$	$12.991$	6.6.6100947648.1	None	✓	✓	✓		81.6.a.e	$2$	$0$	$0$	$0$	$0$	$372$	$-$	$2^{4}\cdot 3^{9}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(5^{2}-\beta _{3})q^{4}+(2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
81.6.c.a	$81$	$6$	81.c	9.c	$3$	$2$	$1$	$12.991$	$\Q(\sqrt{-3}) $	None					3.6.a.a	$2$	$1$	$-6$	$0$	$6$	$40$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-6+6\zeta_{6})q^{2}-4\zeta_{6}q^{4}+6\zeta_{6}q^{5}+\cdots$
81.6.c.b	$81$	$6$	81.c	9.c	$3$	$2$	$1$	$12.991$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $					27.6.a.a	$4$	$0$	$0$	$0$	$0$	$211$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2^{5}\zeta_{6}q^{4}+(211-211\zeta_{6})q^{7}+775\zeta_{6}q^{13}+\cdots$
81.6.c.c	$81$	$6$	81.c	9.c	$3$	$2$	$1$	$12.991$	$\Q(\sqrt{-3}) $	None					3.6.a.a	$2$	$0$	$6$	$0$	$-6$	$40$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(6-6\zeta_{6})q^{2}-4\zeta_{6}q^{4}-6\zeta_{6}q^{5}+\cdots$
81.6.c.d	$81$	$6$	81.c	9.c	$3$	$4$	$2$	$12.991$	$\Q(\sqrt{-3}, \sqrt{17})$	None					27.6.a.b	$2$	$0$	$-9$	$0$	$-72$	$8$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-4\beta _{1}-\beta _{2})q^{2}+(-31+22\beta _{1}+\cdots)q^{4}+\cdots$
81.6.c.e	$81$	$6$	81.c	9.c	$3$	$4$	$2$	$12.991$	$\Q(\sqrt{-3}, \sqrt{-43})$	None		✓			81.6.a.a	$2$	$0$	$-3$	$0$	$30$	$128$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2-2\beta _{1}-\beta _{3})q^{2}+(4\beta _{1}-3\beta _{2}+\cdots)q^{4}+\cdots$
81.6.c.f	$81$	$6$	81.c	9.c	$3$	$4$	$2$	$12.991$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					27.6.a.c	$4$	$0$	$0$	$0$	$0$	$-334$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(-22+22\beta _{1})q^{4}+(8\beta _{2}+\cdots)q^{5}+\cdots$
81.6.c.g	$81$	$6$	81.c	9.c	$3$	$4$	$2$	$12.991$	$\Q(\sqrt{-3}, \sqrt{-43})$	None		✓			81.6.a.a	$2$	$0$	$3$	$0$	$-30$	$128$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}-\beta _{3})q^{2}+(\beta _{1}+3\beta _{2}-3\beta _{3})q^{4}+\cdots$
81.6.c.h	$81$	$6$	81.c	9.c	$3$	$4$	$2$	$12.991$	$\Q(\sqrt{-3}, \sqrt{17})$	None					27.6.a.b	$2$	$0$	$9$	$0$	$72$	$8$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(4\beta _{1}+\beta _{2})q^{2}+(-31+22\beta _{1}+9\beta _{2}+\cdots)q^{4}+\cdots$
81.6.c.i	$81$	$6$	81.c	9.c	$3$	$12$	$6$	$12.991$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		81.6.a.e	$4$	$0$	$0$	$0$	$0$	$-372$		$2^{8}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{5}q^{2}+(\beta _{1}-5^{2}\beta _{2}-\beta _{8})q^{4}+(2\beta _{4}+\cdots)q^{5}+\cdots$
81.6.e.a	$81$	$6$	81.e	27.e	$9$	$84$	$14$	$12.991$		None			✓	✓	27.6.e.a	$2$	$0$	$6$	$0$	$93$	$-6$			$\mathrm{SU}(2)[C_{9}]$

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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.