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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 53 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2023.1.c.a	$2023$	$1$	2023.c	7.b	$2$	$1$	$1$	$1.010$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q-q^{2}-q^{7}+q^{8}+q^{9}-2q^{11}+q^{14}+\cdots$
2023.1.c.b	$2023$	$1$	2023.c	7.b	$2$	$1$	$1$	$1.010$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$1$		$1$		$q-q^{2}+q^{7}+q^{8}+q^{9}+2q^{11}-q^{14}+\cdots$
2023.1.c.c	$2023$	$1$	2023.c	7.b	$2$	$3$	$3$	$1.010$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-3$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots$
2023.1.c.d	$2023$	$1$	2023.c	7.b	$2$	$3$	$3$	$1.010$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots$
2023.1.c.e	$2023$	$1$	2023.c	7.b	$2$	$4$	$4$	$1.010$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
2023.1.d.a	$2023$	$1$	2023.d	119.d	$2$	$2$	$2$	$1.010$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}-iq^{7}-q^{8}-q^{9}-iq^{11}-iq^{14}+\cdots$
2023.1.d.b	$2023$	$1$	2023.d	119.d	$2$	$6$	$6$	$1.010$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\beta _{2}+\beta _{4})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{7}+\cdots$
2023.1.f.a	$2023$	$1$	2023.f	119.f	$4$	$4$	$2$	$1.010$	$\Q(\zeta_{8})$	$D_{3}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\zeta_{8}^{2}q^{9}+\cdots$
2023.1.f.b	$2023$	$1$	2023.f	119.f	$4$	$8$	$4$	$1.010$	8.0.40960000.1	$D_{5}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{4}-\beta _{5})q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots$
2023.1.f.c	$2023$	$1$	2023.f	119.f	$4$	$12$	$6$	$1.010$	12.0.$\cdots$.1	$D_{9}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{9}q^{2}+(-1+\beta _{6})q^{4}-\beta _{10}q^{7}+\cdots$
2023.1.l.a	$2023$	$1$	2023.l	119.l	$8$	$8$	$2$	$1.010$	$\Q(\zeta_{16})$	$D_{3}$	$\Q(\sqrt{-7}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{2}q^{2}-\zeta_{16}q^{7}-\zeta_{16}^{6}q^{8}+\zeta_{16}^{6}q^{9}+\cdots$
2023.1.l.b	$2023$	$1$	2023.l	119.l	$8$	$16$	$4$	$1.010$	16.0.$\cdots$.1	$D_{5}$	$\Q(\sqrt{-119}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{12}q^{2}-\beta _{1}q^{3}-\beta _{8}q^{4}+(-\beta _{10}+\cdots)q^{5}+\cdots$
2023.1.l.c	$2023$	$1$	2023.l	119.l	$8$	$24$	$6$	$1.010$	24.0.$\cdots$.1	$D_{9}$	$\Q(\sqrt{-7}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{21}q^{2}+(-\beta _{11}+\beta _{13}-\beta _{15})q^{4}+\cdots$
2023.2.a.a	$2023$	$2$	2023.a	1.a	$1$	$1$	$1$	$16.154$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$-1$	$-3$	$-4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-q^{4}-4q^{5}+3q^{6}+q^{7}+\cdots$
2023.2.a.b	$2023$	$2$	2023.a	1.a	$1$	$1$	$1$	$16.154$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}-q^{4}+4q^{5}-3q^{6}-q^{7}+\cdots$
2023.2.a.c	$2023$	$2$	2023.a	1.a	$1$	$3$	$3$	$16.154$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
2023.2.a.d	$2023$	$2$	2023.a	1.a	$1$	$3$	$3$	$16.154$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$2$	$3$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
2023.2.a.e	$2023$	$2$	2023.a	1.a	$1$	$4$	$4$	$16.154$	4.4.9301.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2023.2.a.f	$2023$	$2$	2023.a	1.a	$1$	$4$	$4$	$16.154$	4.4.2225.1	$_{}$	None	None	✓	$1$	$0$	$3$	$-2$	$-4$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2023.2.a.g	$2023$	$2$	2023.a	1.a	$1$	$4$	$4$	$16.154$	4.4.2225.1	$_{}$	None	None	✓	$1$	$0$	$3$	$2$	$4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2023.2.a.h	$2023$	$2$	2023.a	1.a	$1$	$5$	$5$	$16.154$	5.5.240133.1	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-4$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2023.2.a.i	$2023$	$2$	2023.a	1.a	$1$	$5$	$5$	$16.154$	5.5.240133.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{4})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
2023.2.a.j	$2023$	$2$	2023.a	1.a	$1$	$5$	$5$	$16.154$	5.5.453749.1	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(2-\beta _{3})q^{4}+\cdots$
2023.2.a.k	$2023$	$2$	2023.a	1.a	$1$	$9$	$9$	$16.154$	9.9.$\cdots$.1	$_{}$	None	None	✓	$1$	$1$	$-6$	$0$	$0$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{5})q^{2}-\beta _{4}q^{3}+(1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
2023.2.a.l	$2023$	$2$	2023.a	1.a	$1$	$9$	$9$	$16.154$	9.9.$\cdots$.1	$_{}$	None	None	✓	$1$	$1$	$-6$	$0$	$0$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{5})q^{2}+\beta _{4}q^{3}+(1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
2023.2.a.m	$2023$	$2$	2023.a	1.a	$1$	$10$	$10$	$16.154$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-8$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(2+\beta _{7}-\beta _{8})q^{4}+\cdots$
2023.2.a.n	$2023$	$2$	2023.a	1.a	$1$	$10$	$10$	$16.154$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$8$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{7}-\beta _{8})q^{4}+\cdots$
2023.2.a.o	$2023$	$2$	2023.a	1.a	$1$	$15$	$15$	$16.154$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$0$	$0$	$15$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{13})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
2023.2.a.p	$2023$	$2$	2023.a	1.a	$1$	$15$	$15$	$16.154$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$0$	$0$	$-15$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{13})q^{3}+(1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
2023.2.a.q	$2023$	$2$	2023.a	1.a	$1$	$16$	$16$	$16.154$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$-8$	$-16$	$16$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2023.2.a.r	$2023$	$2$	2023.a	1.a	$1$	$16$	$16$	$16.154$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-4$	$8$	$16$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2023.4.a.a	$2023$	$4$	2023.a	1.a	$1$	$1$	$1$	$119.361$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$-16$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots$
2023.4.a.b	$2023$	$4$	2023.a	1.a	$1$	$1$	$1$	$119.361$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$6$	$20$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+6q^{3}-7q^{4}+20q^{5}-6q^{6}+\cdots$
2023.4.a.c	$2023$	$4$	2023.a	1.a	$1$	$1$	$1$	$119.361$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$3$	$-1$	$6$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-q^{3}+q^{4}+6q^{5}-3q^{6}-7q^{7}+\cdots$
2023.4.a.d	$2023$	$4$	2023.a	1.a	$1$	$1$	$1$	$119.361$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$3$	$1$	$-6$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+q^{3}+q^{4}-6q^{5}+3q^{6}+7q^{7}+\cdots$
2023.4.a.e	$2023$	$4$	2023.a	1.a	$1$	$3$	$3$	$119.361$	3.3.2429.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-5$	$19$	$21$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$
2023.4.a.f	$2023$	$4$	2023.a	1.a	$1$	$4$	$4$	$119.361$	4.4.68557.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$7$	$9$	$-28$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2+\beta _{1}+\beta _{3})q^{3}+\cdots$
2023.4.a.g	$2023$	$4$	2023.a	1.a	$1$	$7$	$7$	$119.361$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$4$	$-5$	$-35$	$49$	$-$	$3$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots$
2023.4.a.h	$2023$	$4$	2023.a	1.a	$1$	$9$	$9$	$119.361$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$-11$	$3$	$-63$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(4+\beta _{2})q^{4}+\cdots$
2023.4.a.i	$2023$	$4$	2023.a	1.a	$1$	$11$	$11$	$119.361$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-7$	$-2$	$2$	$-77$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2023.4.a.j	$2023$	$4$	2023.a	1.a	$1$	$11$	$11$	$119.361$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-7$	$2$	$-2$	$77$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2023.4.a.k	$2023$	$4$	2023.a	1.a	$1$	$12$	$12$	$119.361$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-3$	$12$	$84$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots$
2023.4.a.l	$2023$	$4$	2023.a	1.a	$1$	$12$	$12$	$119.361$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$3$	$-12$	$-84$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots$
2023.4.a.m	$2023$	$4$	2023.a	1.a	$1$	$13$	$13$	$119.361$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-14$	$-20$	$91$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots$
2023.4.a.n	$2023$	$4$	2023.a	1.a	$1$	$13$	$13$	$119.361$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$14$	$20$	$-91$	$+$	$2^{7}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots$
2023.4.a.o	$2023$	$4$	2023.a	1.a	$1$	$26$	$26$	$119.361$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-12$	$-40$	$182$	$-$		$\mathrm{SU}(2)$
2023.4.a.p	$2023$	$4$	2023.a	1.a	$1$	$26$	$26$	$119.361$		$_{}$	None	None	✓	$1$	$0$	$-8$	$12$	$40$	$-182$	$+$		$\mathrm{SU}(2)$
2023.4.a.q	$2023$	$4$	2023.a	1.a	$1$	$33$	$33$	$119.361$		$_{}$	None	None	✓	$1$	$1$	$-12$	$0$	$0$	$-231$	$-$		$\mathrm{SU}(2)$
2023.4.a.r	$2023$	$4$	2023.a	1.a	$1$	$33$	$33$	$119.361$		$_{}$	None	None	✓	$1$	$1$	$-12$	$0$	$0$	$231$	$-$		$\mathrm{SU}(2)$
2023.4.a.s	$2023$	$4$	2023.a	1.a	$1$	$39$	$39$	$119.361$		$_{}$	None	None	✓	$1$	$0$	$12$	$0$	$0$	$273$	$+$		$\mathrm{SU}(2)$

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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.