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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 306 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
21.2.a.a	$21$	$2$	21.a	1.a	$1$	$1$	$1$	$0.168$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
21.2.e.a	$21$	$2$	21.e	7.c	$3$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-1$	$2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots$
21.2.g.a	$21$	$2$	21.g	21.g	$6$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$-3$	$0$	$1$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots$
21.3.b.a	$21$	$3$	21.b	3.b	$2$	$4$	$4$	$0.572$	4.0.65856.1	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots$
21.3.d.a	$21$	$3$	21.d	7.b	$2$	$2$	$2$	$0.572$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$
21.3.f.a	$21$	$3$	21.f	7.d	$6$	$2$	$1$	$0.572$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-3$	$-3$	$9$	$13$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-3\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots$
21.3.f.b	$21$	$3$	21.f	7.d	$6$	$2$	$1$	$0.572$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$3$	$-9$	$-7$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots$
21.3.f.c	$21$	$3$	21.f	7.d	$6$	$2$	$1$	$0.572$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-3$	$-6$	$-7$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots$
21.3.h.a	$21$	$3$	21.h	21.h	$6$	$2$	$1$	$0.572$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$3$	$0$	$-13$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-5-3\zeta_{6})q^{7}+\cdots$
21.3.h.b	$21$	$3$	21.h	21.h	$6$	$4$	$2$	$0.572$	$\Q(\sqrt{-3}, \sqrt{-5})$	None		$4$	$0$	$0$	$-4$	$0$	$14$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots$
21.4.a.a	$21$	$4$	21.a	1.a	$1$	$1$	$1$	$1.239$	$\Q$	None	✓	$1$	$1$	$-3$	$-3$	$-18$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}-3q^{3}+q^{4}-18q^{5}+9q^{6}+\cdots$
21.4.a.b	$21$	$4$	21.a	1.a	$1$	$1$	$1$	$1.239$	$\Q$	None	✓	$1$	$0$	$4$	$-3$	$-4$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-3q^{3}+8q^{4}-4q^{5}-12q^{6}+\cdots$
21.4.a.c	$21$	$4$	21.a	1.a	$1$	$2$	$2$	$1.239$	$\Q(\sqrt{57}) $	None	✓	$1$	$0$	$-3$	$6$	$6$	$14$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3q^{3}+(7+3\beta )q^{4}+\cdots$
21.4.c.a	$21$	$4$	21.c	21.c	$2$	$2$	$2$	$1.239$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$-20$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{6}q^{3}+8q^{4}+(-10+3\zeta_{6})q^{7}+\cdots$
21.4.c.b	$21$	$4$	21.c	21.c	$2$	$4$	$4$	$1.239$	$\Q(\sqrt{-6}, \sqrt{-17})$	None		$4$	$0$	$0$	$0$	$0$	$28$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{3}q^{3}-9q^{4}+(-\beta _{1}-2\beta _{3})q^{5}+\cdots$
21.4.e.a	$21$	$4$	21.e	7.c	$3$	$2$	$1$	$1.239$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$3$	$-3$	$3$	$-7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{2}-3\zeta_{6}q^{3}-\zeta_{6}q^{4}+(3+\cdots)q^{5}+\cdots$
21.4.e.b	$21$	$4$	21.e	7.c	$3$	$6$	$3$	$1.239$	6.0.9924270768.1	None		$2$	$0$	$-1$	$9$	$-11$	$-13$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(3-3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots$
21.4.g.a	$21$	$4$	21.g	21.g	$6$	$12$	$6$	$1.239$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$4$	$0$	$0$	$-3$	$0$	$-56$		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}-\beta _{6})q^{2}+(\beta _{7}+\beta _{8})q^{3}+(-2\beta _{4}+\cdots)q^{4}+\cdots$
21.5.b.a	$21$	$5$	21.b	3.b	$2$	$8$	$8$	$2.171$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-5+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
21.5.d.a	$21$	$5$	21.d	7.b	$2$	$6$	$6$	$2.171$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$-6$	$0$	$0$	$-22$		$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(10-\beta _{4}+\cdots)q^{4}+\cdots$
21.5.f.a	$21$	$5$	21.f	7.d	$6$	$2$	$1$	$2.171$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$9$	$18$	$77$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2\zeta_{6}q^{2}+(3+3\zeta_{6})q^{3}+(12-12\zeta_{6})q^{4}+\cdots$
21.5.f.b	$21$	$5$	21.f	7.d	$6$	$2$	$1$	$2.171$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$5$	$9$	$-3$	$-91$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+5\zeta_{6}q^{2}+(3+3\zeta_{6})q^{3}+(-9+9\zeta_{6})q^{4}+\cdots$
21.5.f.c	$21$	$5$	21.f	7.d	$6$	$6$	$3$	$2.171$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$3$	$-27$	$39$	$23$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(-3-3\beta _{2})q^{3}+\cdots$
21.5.h.a	$21$	$5$	21.h	21.h	$6$	$2$	$1$	$2.171$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$-9$	$0$	$71$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-9\zeta_{6}q^{3}-2^{4}\zeta_{6}q^{4}+(55-39\zeta_{6})q^{7}+\cdots$
21.5.h.b	$21$	$5$	21.h	21.h	$6$	$16$	$8$	$2.171$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$8$	$0$	$-168$		$3^{7}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(-10\beta _{2}+\cdots)q^{4}+\cdots$
21.6.a.a	$21$	$6$	21.a	1.a	$1$	$1$	$1$	$3.368$	$\Q$	None	✓	$1$	$0$	$-6$	$-9$	$78$	$49$	$-$	$1$	$\mathrm{SU}(2)$	$q-6q^{2}-9q^{3}+4q^{4}+78q^{5}+54q^{6}+\cdots$
21.6.a.b	$21$	$6$	21.a	1.a	$1$	$1$	$1$	$3.368$	$\Q$	None	✓	$1$	$1$	$1$	$-9$	$-34$	$-49$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-9q^{3}-31q^{4}-34q^{5}-9q^{6}+\cdots$
21.6.a.c	$21$	$6$	21.a	1.a	$1$	$1$	$1$	$3.368$	$\Q$	None	✓	$1$	$0$	$5$	$9$	$94$	$-49$	$-$	$1$	$\mathrm{SU}(2)$	$q+5q^{2}+9q^{3}-7q^{4}+94q^{5}+45q^{6}+\cdots$
21.6.a.d	$21$	$6$	21.a	1.a	$1$	$1$	$1$	$3.368$	$\Q$	None	✓	$1$	$0$	$10$	$9$	$-106$	$-49$	$-$	$1$	$\mathrm{SU}(2)$	$q+10q^{2}+9q^{3}+68q^{4}-106q^{5}+\cdots$
21.6.c.a	$21$	$6$	21.c	21.c	$2$	$12$	$12$	$3.368$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$112$		$2^{7}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2^{4}-\beta _{1})q^{4}+\cdots$
21.6.e.a	$21$	$6$	21.e	7.c	$3$	$2$	$1$	$3.368$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$9$	$-11$	$259$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+9\zeta_{6}q^{3}+28\zeta_{6}q^{4}+\cdots$
21.6.e.b	$21$	$6$	21.e	7.c	$3$	$4$	$2$	$3.368$	$\Q(\sqrt{-3}, \sqrt{-83})$	None		$2$	$0$	$3$	$18$	$33$	$-350$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}-\beta _{3})q^{2}-9\beta _{1}q^{3}+(31\beta _{1}+\cdots)q^{4}+\cdots$
21.6.e.c	$21$	$6$	21.e	7.c	$3$	$8$	$4$	$3.368$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-3$	$-36$	$0$	$258$		$3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+9\beta _{2}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
21.6.g.a	$21$	$6$	21.g	21.g	$6$	$2$	$1$	$3.368$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$27$	$0$	$211$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(9+9\zeta_{6})q^{3}+(-2^{5}+2^{5}\zeta_{6})q^{4}+\cdots$
21.6.g.b	$21$	$6$	21.g	21.g	$6$	$4$	$2$	$3.368$	$\Q(\sqrt{-3}, \sqrt{-17})$	None		$4$	$0$	$0$	$-48$	$0$	$490$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\beta _{1}q^{2}+(-2^{4}+\beta _{1}+8\beta _{2}+\beta _{3})q^{3}+\cdots$
21.6.g.c	$21$	$6$	21.g	21.g	$6$	$16$	$8$	$3.368$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$18$	$0$	$-616$		$2^{4}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{6})q^{3}+(12+\cdots)q^{4}+\cdots$
21.7.b.a	$21$	$7$	21.b	3.b	$2$	$12$	$12$	$4.831$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$52$	$0$	$0$		$2^{2}\cdot 3^{8}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(4-\beta _{3})q^{3}+(-43+\beta _{2}+\cdots)q^{4}+\cdots$
21.7.d.a	$21$	$7$	21.d	7.b	$2$	$8$	$8$	$4.831$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$10$	$0$	$0$	$28$		$2^{5}\cdot 3^{7}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(44+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
21.7.f.a	$21$	$7$	21.f	7.d	$6$	$8$	$4$	$4.831$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-5$	$-108$	$-294$	$-656$		$2^{2}\cdot 3\cdot 7$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{1}+\beta _{2})q^{2}+(-18+9\beta _{2}+\cdots)q^{3}+\cdots$
21.7.f.b	$21$	$7$	21.f	7.d	$6$	$8$	$4$	$4.831$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-5$	$108$	$-42$	$748$		$3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{2})q^{2}+(9+9\beta _{2})q^{3}+(-43+\cdots)q^{4}+\cdots$
21.7.h.a	$21$	$7$	21.h	21.h	$6$	$28$	$14$	$4.831$		None		$4$	$0$	$0$	$-1$	$0$	$1120$			$\mathrm{SU}(2)[C_{6}]$
21.8.a.a	$21$	$8$	21.a	1.a	$1$	$1$	$1$	$6.560$	$\Q$	None	✓	$1$	$1$	$2$	$27$	$-278$	$-343$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3^{3}q^{3}-124q^{4}-278q^{5}+\cdots$
21.8.a.b	$21$	$8$	21.a	1.a	$1$	$2$	$2$	$6.560$	$\Q(\sqrt{1065}) $	None	✓	$1$	$1$	$-9$	$-54$	$-360$	$686$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-4-\beta )q^{2}-3^{3}q^{3}+(154+9\beta )q^{4}+\cdots$
21.8.a.c	$21$	$8$	21.a	1.a	$1$	$2$	$2$	$6.560$	$\Q(\sqrt{67}) $	None	✓	$1$	$0$	$12$	$-54$	$-24$	$-686$	$+$	$2$	$\mathrm{SU}(2)$	$q+(6+\beta )q^{2}-3^{3}q^{3}+(176+12\beta )q^{4}+\cdots$
21.8.a.d	$21$	$8$	21.a	1.a	$1$	$3$	$3$	$6.560$	3.3.2910828.1	None	✓	$1$	$0$	$-3$	$81$	$-114$	$1029$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+3^{3}q^{3}+(75+\beta _{2})q^{4}+\cdots$
21.8.c.a	$21$	$8$	21.c	21.c	$2$	$16$	$16$	$6.560$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$-1288$		$2^{13}\cdot 3^{19}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-48+\beta _{3})q^{4}+\cdots$
21.8.e.a	$21$	$8$	21.e	7.c	$3$	$8$	$4$	$6.560$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$1$	$-108$	$-196$	$154$		$2^{2}\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{2}+3^{3}\beta _{4}q^{3}+(-2\beta _{1}+5^{2}\beta _{4}+\cdots)q^{4}+\cdots$
21.8.e.b	$21$	$8$	21.e	7.c	$3$	$10$	$5$	$6.560$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-15$	$135$	$198$	$-859$		$2^{2}\cdot 3^{3}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3-\beta _{1}+3\beta _{4})q^{2}+3^{3}\beta _{4}q^{3}+\cdots$
21.8.g.a	$21$	$8$	21.g	21.g	$6$	$2$	$1$	$6.560$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$81$	$0$	$-1763$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(3^{3}+3^{3}\zeta_{6})q^{3}+(-2^{7}+2^{7}\zeta_{6})q^{4}+\cdots$
21.8.g.b	$21$	$8$	21.g	21.g	$6$	$32$	$16$	$6.560$		None		$4$	$0$	$0$	$-84$	$0$	$2464$			$\mathrm{SU}(2)[C_{6}]$

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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.