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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
2415.1.p.a	$2415$	$1$	2415.p	2415.p	$2$	$2$	$2$	$1.205$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2415}) $	None	✓	$2$	$0$	$-1$	$-2$	$-2$	$2$		$1$		$q+(-1+\beta )q^{2}-q^{3}+(1-\beta )q^{4}-q^{5}+\cdots$
2415.1.p.b	$2415$	$1$	2415.p	2415.p	$2$	$2$	$2$	$1.205$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2415}) $	None	✓	$2$	$0$	$-1$	$-2$	$2$	$-2$		$1$		$q+(-1+\beta )q^{2}-q^{3}+(1-\beta )q^{4}+q^{5}+\cdots$
2415.1.p.c	$2415$	$1$	2415.p	2415.p	$2$	$2$	$2$	$1.205$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2415}) $	None	✓	$2$	$0$	$-1$	$2$	$-2$	$-2$		$1$		$q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-q^{5}+\cdots$
2415.1.p.d	$2415$	$1$	2415.p	2415.p	$2$	$2$	$2$	$1.205$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2415}) $	None	✓	$2$	$0$	$-1$	$2$	$2$	$2$		$1$		$q-\beta q^{2}+q^{3}+\beta q^{4}+q^{5}-\beta q^{6}+q^{7}+\cdots$
2415.1.p.e	$2415$	$1$	2415.p	2415.p	$2$	$2$	$2$	$1.205$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2415}) $	None	✓	$2$	$0$	$1$	$-2$	$-2$	$-2$		$1$		$q+\beta q^{2}-q^{3}+\beta q^{4}-q^{5}-\beta q^{6}-q^{7}+\cdots$
2415.1.p.f	$2415$	$1$	2415.p	2415.p	$2$	$2$	$2$	$1.205$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2415}) $	None	✓	$2$	$0$	$1$	$-2$	$2$	$2$		$1$		$q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+q^{5}+\cdots$
2415.1.p.g	$2415$	$1$	2415.p	2415.p	$2$	$2$	$2$	$1.205$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2415}) $	None	✓	$2$	$0$	$1$	$2$	$-2$	$2$		$1$		$q+(1-\beta )q^{2}+q^{3}+(1-\beta )q^{4}-q^{5}+\cdots$
2415.1.p.h	$2415$	$1$	2415.p	2415.p	$2$	$2$	$2$	$1.205$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2415}) $	None	✓	$2$	$0$	$1$	$2$	$2$	$-2$		$1$		$q+\beta q^{2}+q^{3}+\beta q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots$
2415.1.bq.a	$2415$	$1$	2415.bq	2415.aq	$12$	$8$	$2$	$1.205$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q+(-\zeta_{24}^{4}-\zeta_{24}^{10})q^{2}-\zeta_{24}^{2}q^{3}+\cdots$
2415.1.bq.b	$2415$	$1$	2415.bq	2415.aq	$12$	$8$	$2$	$1.205$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$4$	$-4$	$0$	$0$		$1$		$q+(\zeta_{24}^{4}+\zeta_{24}^{10})q^{2}+\zeta_{24}^{8}q^{3}-\zeta_{24}^{2}q^{4}+\cdots$
2415.2.a.a	$2415$	$2$	2415.a	1.a	$1$	$1$	$1$	$19.284$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
2415.2.a.b	$2415$	$2$	2415.a	1.a	$1$	$1$	$1$	$19.284$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
2415.2.a.c	$2415$	$2$	2415.a	1.a	$1$	$1$	$1$	$19.284$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
2415.2.a.d	$2415$	$2$	2415.a	1.a	$1$	$1$	$1$	$19.284$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
2415.2.a.e	$2415$	$2$	2415.a	1.a	$1$	$1$	$1$	$19.284$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-3q^{11}+\cdots$
2415.2.a.f	$2415$	$2$	2415.a	1.a	$1$	$1$	$1$	$19.284$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+q^{11}+\cdots$
2415.2.a.g	$2415$	$2$	2415.a	1.a	$1$	$1$	$1$	$19.284$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+3q^{11}+\cdots$
2415.2.a.h	$2415$	$2$	2415.a	1.a	$1$	$1$	$1$	$19.284$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
2415.2.a.i	$2415$	$2$	2415.a	1.a	$1$	$1$	$1$	$19.284$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
2415.2.a.j	$2415$	$2$	2415.a	1.a	$1$	$2$	$2$	$19.284$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{7}+\cdots$
2415.2.a.k	$2415$	$2$	2415.a	1.a	$1$	$2$	$2$	$19.284$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}+q^{7}+\cdots$
2415.2.a.l	$2415$	$2$	2415.a	1.a	$1$	$3$	$3$	$19.284$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-3$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
2415.2.a.m	$2415$	$2$	2415.a	1.a	$1$	$3$	$3$	$19.284$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
2415.2.a.n	$2415$	$2$	2415.a	1.a	$1$	$3$	$3$	$19.284$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
2415.2.a.o	$2415$	$2$	2415.a	1.a	$1$	$5$	$5$	$19.284$	5.5.2508628.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-5$	$-5$	$-5$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
2415.2.a.p	$2415$	$2$	2415.a	1.a	$1$	$6$	$6$	$19.284$	6.6.42978136.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-6$	$-6$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
2415.2.a.q	$2415$	$2$	2415.a	1.a	$1$	$6$	$6$	$19.284$	6.6.15751800.1	$_{}$	None	None	✓	$1$	$0$	$3$	$-6$	$-6$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\cdots$
2415.2.a.r	$2415$	$2$	2415.a	1.a	$1$	$7$	$7$	$19.284$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$7$	$-7$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
2415.2.a.s	$2415$	$2$	2415.a	1.a	$1$	$7$	$7$	$19.284$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-7$	$7$	$-7$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
2415.2.a.t	$2415$	$2$	2415.a	1.a	$1$	$7$	$7$	$19.284$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$7$	$-7$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
2415.2.a.u	$2415$	$2$	2415.a	1.a	$1$	$9$	$9$	$19.284$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$-9$	$9$	$9$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2415.2.a.v	$2415$	$2$	2415.a	1.a	$1$	$10$	$10$	$19.284$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$10$	$10$	$-10$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
2415.2.a.w	$2415$	$2$	2415.a	1.a	$1$	$10$	$10$	$19.284$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$10$	$10$	$10$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
2415.4.a.a	$2415$	$4$	2415.a	1.a	$1$	$1$	$1$	$142.490$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-8q^{4}-5q^{5}+7q^{7}+9q^{9}+\cdots$
2415.4.a.b	$2415$	$4$	2415.a	1.a	$1$	$1$	$1$	$142.490$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$-5$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots$
2415.4.a.c	$2415$	$4$	2415.a	1.a	$1$	$1$	$1$	$142.490$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-3$	$-5$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots$
2415.4.a.d	$2415$	$4$	2415.a	1.a	$1$	$1$	$1$	$142.490$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots$
2415.4.a.e	$2415$	$4$	2415.a	1.a	$1$	$12$	$12$	$142.490$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$36$	$60$	$-84$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots$
2415.4.a.f	$2415$	$4$	2415.a	1.a	$1$	$12$	$12$	$142.490$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$36$	$60$	$84$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots$
2415.4.a.g	$2415$	$4$	2415.a	1.a	$1$	$12$	$12$	$142.490$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$36$	$-60$	$84$	$-$	$2^{6}\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots$
2415.4.a.h	$2415$	$4$	2415.a	1.a	$1$	$12$	$12$	$142.490$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-36$	$60$	$84$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots$
2415.4.a.i	$2415$	$4$	2415.a	1.a	$1$	$15$	$15$	$142.490$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-45$	$-75$	$-105$	$-$	$2^{9}\cdot 3^{4}\cdot 7^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots$
2415.4.a.j	$2415$	$4$	2415.a	1.a	$1$	$15$	$15$	$142.490$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$-45$	$-75$	$-105$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots$
2415.4.a.k	$2415$	$4$	2415.a	1.a	$1$	$15$	$15$	$142.490$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$2$	$-45$	$75$	$-105$	$-$	$2^{10}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots$
2415.4.a.l	$2415$	$4$	2415.a	1.a	$1$	$15$	$15$	$142.490$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$4$	$45$	$-75$	$-105$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots$
2415.4.a.m	$2415$	$4$	2415.a	1.a	$1$	$16$	$16$	$142.490$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$-48$	$-80$	$112$	$-$	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots$
2415.4.a.n	$2415$	$4$	2415.a	1.a	$1$	$18$	$18$	$142.490$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$-54$	$-90$	$126$	$+$	$2^{8}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots$
2415.4.a.o	$2415$	$4$	2415.a	1.a	$1$	$19$	$19$	$142.490$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-57$	$95$	$-133$	$+$	$2^{7}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots$
2415.4.a.p	$2415$	$4$	2415.a	1.a	$1$	$19$	$19$	$142.490$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$57$	$-95$	$-133$	$+$	$2^{13}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots$
2415.4.a.q	$2415$	$4$	2415.a	1.a	$1$	$19$	$19$	$142.490$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$57$	$-95$	$133$	$+$	$2^{12}\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots$

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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.