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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 118 matches)

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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
972.1.c.a	$972$	$1$	972.c	3.b	$2$	$1$	$1$	$0.485$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.1.c.a	$2$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-q^{7}+2q^{13}+2q^{19}+q^{25}-q^{31}+\cdots$
972.1.c.b	$972$	$1$	972.c	3.b	$2$	$1$	$1$	$0.485$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.1.c.b	$2$	$0$	$0$	$0$	$0$	$2$		$1$		$q+2q^{7}-q^{13}-q^{19}+q^{25}-q^{31}+\cdots$
972.1.g.a	$972$	$1$	972.g	9.d	$6$	$2$	$1$	$0.485$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			972.1.c.b	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}-q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
972.1.g.b	$972$	$1$	972.g	9.d	$6$	$2$	$1$	$0.485$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			972.1.c.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
972.2.a.a	$972$	$2$	972.a	1.a	$1$	$1$	$1$	$7.761$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.2.a.a	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$N(\mathrm{U}(1))$	$q-4q^{7}+5q^{13}-7q^{19}-5q^{25}-7q^{31}+\cdots$
972.2.a.b	$972$	$2$	972.a	1.a	$1$	$1$	$1$	$7.761$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.2.a.b	$2$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$N(\mathrm{U}(1))$	$q-q^{7}-7q^{13}-q^{19}-5q^{25}-7q^{31}+\cdots$
972.2.a.c	$972$	$2$	972.a	1.a	$1$	$1$	$1$	$7.761$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.2.a.c	$2$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$N(\mathrm{U}(1))$	$q-q^{7}+2q^{13}+8q^{19}-5q^{25}+11q^{31}+\cdots$
972.2.a.d	$972$	$2$	972.a	1.a	$1$	$1$	$1$	$7.761$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.2.a.d	$2$	$0$	$0$	$0$	$0$	$5$	$-$	$1$	$N(\mathrm{U}(1))$	$q+5q^{7}+5q^{13}-7q^{19}-5q^{25}+11q^{31}+\cdots$
972.2.a.e	$972$	$2$	972.a	1.a	$1$	$2$	$2$	$7.761$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			972.2.a.e	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta q^{5}+2q^{7}+\beta q^{11}-q^{13}-\beta q^{17}+\cdots$
972.2.a.f	$972$	$2$	972.a	1.a	$1$	$3$	$3$	$7.761$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓	✓		972.2.a.f	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$3$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-1+\beta _{2})q^{7}+(-3+\beta _{1}+\cdots)q^{11}+\cdots$
972.2.a.g	$972$	$2$	972.a	1.a	$1$	$3$	$3$	$7.761$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓	✓		972.2.a.f	$1$	$0$	$0$	$0$	$0$	$-3$	$-$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-1-\beta _{1})q^{7}+(3+\beta _{1}-\beta _{2})q^{11}+\cdots$
972.2.b.a	$972$	$2$	972.b	12.b	$2$	$12$	$12$	$7.761$	12.0.$\cdots$.1	$_{}$	None	None		✓			972.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{10}q^{5}+\beta _{4}q^{7}+\cdots$
972.2.b.b	$972$	$2$	972.b	12.b	$2$	$12$	$12$	$7.761$	12.0.$\cdots$.1	$_{}$	None	None		✓			972.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{6}q^{4}+\beta _{11}q^{5}+(\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
972.2.b.c	$972$	$2$	972.b	12.b	$2$	$12$	$12$	$7.761$	12.0.$\cdots$.1	$_{}$	None	None		✓			972.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{7}q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
972.2.b.d	$972$	$2$	972.b	12.b	$2$	$36$	$36$	$7.761$		$_{}$	None	None		✓	✓		972.2.b.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
972.2.e.a	$972$	$2$	972.e	9.c	$3$	$2$	$1$	$7.761$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			972.2.a.d	$4$	$1$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(-5+5\zeta_{6})q^{7}-5\zeta_{6}q^{13}-7q^{19}+\cdots$
972.2.e.b	$972$	$2$	972.e	9.c	$3$	$2$	$1$	$7.761$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			972.2.a.c	$4$	$0$	$0$	$0$	$0$	$1$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(1-\zeta_{6})q^{7}-2\zeta_{6}q^{13}+8q^{19}+(5+\cdots)q^{25}+\cdots$
972.2.e.c	$972$	$2$	972.e	9.c	$3$	$2$	$1$	$7.761$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			972.2.a.b	$4$	$0$	$0$	$0$	$0$	$1$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(1-\zeta_{6})q^{7}+7\zeta_{6}q^{13}-q^{19}+(5+\cdots)q^{25}+\cdots$
972.2.e.d	$972$	$2$	972.e	9.c	$3$	$2$	$1$	$7.761$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			972.2.a.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+(4-4\zeta_{6})q^{7}-5\zeta_{6}q^{13}-7q^{19}+\cdots$
972.2.e.e	$972$	$2$	972.e	9.c	$3$	$4$	$2$	$7.761$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			972.2.a.e	$4$	$0$	$0$	$0$	$0$	$-4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}+2\beta _{2}q^{7}+(-\beta _{1}-\beta _{3})q^{11}+\cdots$
972.2.e.f	$972$	$2$	972.e	9.c	$3$	$6$	$3$	$7.761$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			972.2.a.f	$2$	$0$	$0$	$0$	$0$	$3$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{4} q^{5}+(\beta_{5}-\beta_{2}+\beta_1)q^{7}+(-\beta_{5}-3\beta_1)q^{11}+\cdots$
972.2.e.g	$972$	$2$	972.e	9.c	$3$	$6$	$3$	$7.761$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			972.2.a.f	$2$	$0$	$0$	$0$	$0$	$3$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{5}+(\beta_{5}-\beta_{4}+\beta_{3}+\cdots+1)q^{7}+\cdots$
972.2.h.a	$972$	$2$	972.h	36.h	$6$	$12$	$6$	$7.761$	12.0.$\cdots$.1	$_{}$	None	None		✓			972.2.b.b	$4$	$0$	$0$	$0$	$0$	$6$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{7}q^{2}+(-1+\beta _{3}-\beta _{5}+\beta _{8})q^{4}+\cdots$
972.2.h.b	$972$	$2$	972.h	36.h	$6$	$12$	$6$	$7.761$	12.0.$\cdots$.1	$_{}$	None	None		✓			972.2.b.c	$4$	$0$	$0$	$0$	$0$	$6$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{2}+\beta _{5}q^{4}+(-\beta _{2}-\beta _{10})q^{5}+\cdots$
972.2.h.c	$972$	$2$	972.h	36.h	$6$	$12$	$6$	$7.761$	12.0.$\cdots$.1	$_{}$	None	None		✓			972.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{5}+\beta _{9}-\beta _{10}+\cdots)q^{5}+\cdots$
972.2.h.d	$972$	$2$	972.h	36.h	$6$	$12$	$6$	$7.761$	12.0.$\cdots$.1	$_{}$	None	None		✓			972.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+\beta _{7}q^{4}+(-\beta _{3}+\beta _{10})q^{5}+\cdots$
972.2.h.e	$972$	$2$	972.h	36.h	$6$	$12$	$6$	$7.761$	12.0.$\cdots$.1	$_{}$	None	None		✓			972.2.b.b	$4$	$0$	$0$	$0$	$0$	$-6$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{4})q^{2}+(1-\beta _{2}-\beta _{3}-\beta _{10}+\cdots)q^{4}+\cdots$
972.2.h.f	$972$	$2$	972.h	36.h	$6$	$12$	$6$	$7.761$	12.0.$\cdots$.1	$_{}$	None	None		✓			972.2.b.c	$4$	$0$	$0$	$0$	$0$	$-6$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{4}-\beta _{11})q^{5}+\cdots$
972.2.h.g	$972$	$2$	972.h	36.h	$6$	$72$	$36$	$7.761$		$_{}$	None	None		✓	✓		972.2.b.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
972.2.i.a	$972$	$2$	972.i	27.e	$9$	$18$	$3$	$7.761$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None					108.2.i.a	$2$	$0$	$0$	$0$	$-6$	$0$		$3^{5}$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(-\beta _{3}+\beta _{6}+\beta _{8}+\cdots)q^{7}+\cdots$
972.2.i.b	$972$	$2$	972.i	27.e	$9$	$18$	$3$	$7.761$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None					108.2.i.a	$2$	$0$	$0$	$0$	$-3$	$0$		$3^{5}$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{7}+\beta _{12})q^{5}+(-1+\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots$
972.2.i.c	$972$	$2$	972.i	27.e	$9$	$18$	$3$	$7.761$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None					108.2.i.a	$2$	$0$	$0$	$0$	$3$	$0$		$3^{5}$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{7}-\beta _{12})q^{5}+(-1+\beta _{1}+\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots$
972.2.i.d	$972$	$2$	972.i	27.e	$9$	$18$	$3$	$7.761$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None					108.2.i.a	$2$	$0$	$0$	$0$	$6$	$0$		$3^{5}$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{2}-\beta _{4}-\beta _{6})q^{5}+(-\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots$
972.2.l.a	$972$	$2$	972.l	108.l	$18$	$96$	$16$	$7.761$		$_{}$	None	None					108.2.l.a	$4$	$0$	$-3$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{18}]$
972.2.l.b	$972$	$2$	972.l	108.l	$18$	$96$	$16$	$7.761$		$_{}$	None	None					108.2.l.a	$4$	$0$	$-3$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{18}]$
972.2.l.c	$972$	$2$	972.l	108.l	$18$	$96$	$16$	$7.761$		$_{}$	None	None					108.2.l.a	$4$	$0$	$3$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{18}]$
972.2.l.d	$972$	$2$	972.l	108.l	$18$	$96$	$16$	$7.761$		$_{}$	None	None					108.2.l.a	$4$	$0$	$3$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{18}]$
972.2.m.a	$972$	$2$	972.m	81.g	$27$	$162$	$9$	$7.761$		$_{}$	None	None			✓	✓	324.2.m.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{27}]$
972.2.p.a	$972$	$2$	972.p	324.p	$54$	$936$	$52$	$7.761$		$_{}$	None	None			✓	✓	324.2.p.a	$4$	$0$	$18$	$0$	$36$	$0$			$\mathrm{SU}(2)[C_{54}]$
972.2.q.a	$972$	$2$	972.q	243.i	$81$	$1458$	$27$	$7.761$		$_{}$	None	None		✓	✓	✓	972.2.q.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{81}]$
972.2.t.a	$972$	$2$	972.t	972.t	$162$	$8640$	$160$	$7.761$		$_{}$	None	None		✓	✓	✓	972.2.t.a	$4$	$0$	$-54$	$0$	$-108$	$0$			$\mathrm{SU}(2)[C_{162}]$
972.3.c.a	$972$	$3$	972.c	3.b	$2$	$1$	$1$	$26.485$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.3.c.a	$2$	$0$	$0$	$0$	$0$	$-13$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-13q^{7}-22q^{13}+26q^{19}+5^{2}q^{25}+\cdots$
972.3.c.b	$972$	$3$	972.c	3.b	$2$	$1$	$1$	$26.485$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.3.c.b	$2$	$0$	$0$	$0$	$0$	$-13$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-13q^{7}+23q^{13}-37q^{19}+5^{2}q^{25}+\cdots$
972.3.c.c	$972$	$3$	972.c	3.b	$2$	$1$	$1$	$26.485$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.3.c.c	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{7}-q^{13}+11q^{19}+5^{2}q^{25}+\cdots$
972.3.c.d	$972$	$3$	972.c	3.b	$2$	$1$	$1$	$26.485$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	✓			972.3.c.d	$2$	$0$	$0$	$0$	$0$	$11$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+11q^{7}-q^{13}+11q^{19}+5^{2}q^{25}+\cdots$
972.3.c.e	$972$	$3$	972.c	3.b	$2$	$2$	$2$	$26.485$	$\Q(\sqrt{-6}) $	$_{}$	None	None		✓			972.3.c.e	$2$	$0$	$0$	$0$	$0$	$-8$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-4q^{7}+\beta q^{11}+5q^{13}-\beta q^{17}+\cdots$
972.3.c.f	$972$	$3$	972.c	3.b	$2$	$2$	$2$	$26.485$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			972.3.c.f	$2$	$0$	$0$	$0$	$0$	$-2$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-q^{7}-2\beta q^{11}-7 q^{13}+5\beta q^{17}+\cdots$
972.3.c.g	$972$	$3$	972.c	3.b	$2$	$2$	$2$	$26.485$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			972.3.c.g	$2$	$0$	$0$	$0$	$0$	$4$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}+2 q^{7}-4\beta q^{11}-10 q^{13}+\cdots$
972.3.c.h	$972$	$3$	972.c	3.b	$2$	$2$	$2$	$26.485$	$\Q(\sqrt{-7}) $	$_{}$	None	None		✓			972.3.c.h	$2$	$0$	$0$	$0$	$0$	$16$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}+8q^{7}+2\beta q^{11}+20q^{13}+\cdots$
972.3.c.i	$972$	$3$	972.c	3.b	$2$	$12$	$12$	$26.485$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		972.3.c.i	$2$	$0$	$0$	$0$	$0$	$6$		$3^{20}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{5}+(1+\beta _{4})q^{7}+\beta _{9}q^{11}+(-3+\cdots)q^{13}+\cdots$

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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.