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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 (41 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	7	41	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6027.2.a.a	$6027$	$2$	6027.a	1.a	$1$	$1$	$1$	$48.126$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots$
6027.2.a.b	$6027$	$2$	6027.a	1.a	$1$	$1$	$1$	$48.126$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}+3q^{8}+\cdots$
6027.2.a.c	$6027$	$2$	6027.a	1.a	$1$	$1$	$1$	$48.126$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+3q^{5}+q^{6}+3q^{8}+\cdots$
6027.2.a.d	$6027$	$2$	6027.a	1.a	$1$	$1$	$1$	$48.126$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}+3q^{8}+\cdots$
6027.2.a.e	$6027$	$2$	6027.a	1.a	$1$	$1$	$1$	$48.126$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+2q^{5}+q^{9}+5q^{11}+\cdots$
6027.2.a.f	$6027$	$2$	6027.a	1.a	$1$	$1$	$1$	$48.126$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots$
6027.2.a.g	$6027$	$2$	6027.a	1.a	$1$	$1$	$1$	$48.126$	$\Q$	None	✓	$1$	$1$	$2$	$-1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{9}+4q^{11}+\cdots$
6027.2.a.h	$6027$	$2$	6027.a	1.a	$1$	$1$	$1$	$48.126$	$\Q$	None	✓	$1$	$0$	$2$	$1$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{9}+4q^{11}+\cdots$
6027.2.a.i	$6027$	$2$	6027.a	1.a	$1$	$2$	$2$	$48.126$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$-2$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+q^{5}+\cdots$
6027.2.a.j	$6027$	$2$	6027.a	1.a	$1$	$2$	$2$	$48.126$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-1$	$-2$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(2-\beta )q^{5}+\cdots$
6027.2.a.k	$6027$	$2$	6027.a	1.a	$1$	$2$	$2$	$48.126$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-1$	$2$	$-4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-2q^{5}-\beta q^{6}+\cdots$
6027.2.a.l	$6027$	$2$	6027.a	1.a	$1$	$2$	$2$	$48.126$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-2\beta q^{5}+q^{9}+(4+\beta )q^{11}+\cdots$
6027.2.a.m	$6027$	$2$	6027.a	1.a	$1$	$2$	$2$	$48.126$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-2+\beta )q^{5}-\beta q^{6}+\cdots$
6027.2.a.n	$6027$	$2$	6027.a	1.a	$1$	$2$	$2$	$48.126$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-2\beta q^{5}+q^{9}+(4-\beta )q^{11}+\cdots$
6027.2.a.o	$6027$	$2$	6027.a	1.a	$1$	$3$	$3$	$48.126$	3.3.148.1	None	✓	$1$	$1$	$-1$	$3$	$-1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
6027.2.a.p	$6027$	$2$	6027.a	1.a	$1$	$3$	$3$	$48.126$	3.3.1620.1	None	✓	$1$	$1$	$0$	$-3$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-\beta _{1}q^{5}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
6027.2.a.q	$6027$	$2$	6027.a	1.a	$1$	$3$	$3$	$48.126$	3.3.1620.1	None	✓	$1$	$0$	$0$	$3$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+\beta _{1}q^{5}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
6027.2.a.r	$6027$	$2$	6027.a	1.a	$1$	$3$	$3$	$48.126$	3.3.785.1	None	✓	$1$	$1$	$1$	$-3$	$-3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
6027.2.a.s	$6027$	$2$	6027.a	1.a	$1$	$3$	$3$	$48.126$	3.3.316.1	None	✓	$1$	$1$	$1$	$3$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
6027.2.a.t	$6027$	$2$	6027.a	1.a	$1$	$3$	$3$	$48.126$	3.3.785.1	None	✓	$1$	$0$	$1$	$3$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
6027.2.a.u	$6027$	$2$	6027.a	1.a	$1$	$4$	$4$	$48.126$	4.4.8468.1	None	✓	$1$	$0$	$1$	$4$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
6027.2.a.v	$6027$	$2$	6027.a	1.a	$1$	$5$	$5$	$48.126$	5.5.981328.1	None	✓	$1$	$1$	$-3$	$5$	$-1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
6027.2.a.w	$6027$	$2$	6027.a	1.a	$1$	$5$	$5$	$48.126$	5.5.626512.1	None	✓	$1$	$1$	$3$	$-5$	$-3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
6027.2.a.x	$6027$	$2$	6027.a	1.a	$1$	$5$	$5$	$48.126$	5.5.1197392.1	None	✓	$1$	$0$	$3$	$5$	$9$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
6027.2.a.y	$6027$	$2$	6027.a	1.a	$1$	$7$	$7$	$48.126$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$4$	$-7$	$-1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
6027.2.a.z	$6027$	$2$	6027.a	1.a	$1$	$8$	$8$	$48.126$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-2$	$-8$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
6027.2.a.ba	$6027$	$2$	6027.a	1.a	$1$	$8$	$8$	$48.126$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-2$	$8$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
6027.2.a.bb	$6027$	$2$	6027.a	1.a	$1$	$8$	$8$	$48.126$	8.8.7457527933.1	None	✓	$1$	$1$	$1$	$-8$	$-7$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(2+\beta _{6})q^{4}+\cdots$
6027.2.a.bc	$6027$	$2$	6027.a	1.a	$1$	$8$	$8$	$48.126$	8.8.7457527933.1	None	✓	$1$	$0$	$1$	$8$	$7$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+q^{3}+(2+\beta _{6})q^{4}+\cdots$
6027.2.a.bd	$6027$	$2$	6027.a	1.a	$1$	$10$	$10$	$48.126$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$4$	$-10$	$-6$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
6027.2.a.be	$6027$	$2$	6027.a	1.a	$1$	$10$	$10$	$48.126$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$4$	$10$	$6$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots$
6027.2.a.bf	$6027$	$2$	6027.a	1.a	$1$	$12$	$12$	$48.126$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-2$	$-12$	$-12$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
6027.2.a.bg	$6027$	$2$	6027.a	1.a	$1$	$12$	$12$	$48.126$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$-2$	$12$	$12$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots$
6027.2.a.bh	$6027$	$2$	6027.a	1.a	$1$	$13$	$13$	$48.126$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$-4$	$-13$	$8$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{8}+\cdots)q^{5}+\cdots$
6027.2.a.bi	$6027$	$2$	6027.a	1.a	$1$	$13$	$13$	$48.126$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$1$	$-4$	$13$	$-8$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{8}+\cdots)q^{5}+\cdots$
6027.2.a.bj	$6027$	$2$	6027.a	1.a	$1$	$14$	$14$	$48.126$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$-2$	$-14$	$10$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$
6027.2.a.bk	$6027$	$2$	6027.a	1.a	$1$	$14$	$14$	$48.126$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-2$	$14$	$-10$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{3}+\cdots)q^{5}+\cdots$
6027.2.a.bl	$6027$	$2$	6027.a	1.a	$1$	$16$	$16$	$48.126$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-4$	$-16$	$12$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{5}+\cdots)q^{5}+\cdots$
6027.2.a.bm	$6027$	$2$	6027.a	1.a	$1$	$16$	$16$	$48.126$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-4$	$16$	$-12$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$
6027.2.a.bn	$6027$	$2$	6027.a	1.a	$1$	$24$	$24$	$48.126$		None	✓	$1$	$0$	$8$	$-24$	$-4$	$0$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
6027.2.a.bo	$6027$	$2$	6027.a	1.a	$1$	$24$	$24$	$48.126$		None	✓	$1$	$0$	$8$	$24$	$4$	$0$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.