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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	503	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9054.2.a.a	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots$
9054.2.a.b	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{7}-q^{8}-q^{11}+5q^{13}+\cdots$
9054.2.a.c	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+2q^{11}+4q^{13}+\cdots$
9054.2.a.d	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-5q^{13}+\cdots$
9054.2.a.e	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
9054.2.a.f	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+3q^{7}-q^{8}-q^{10}+\cdots$
9054.2.a.g	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$3$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-3q^{7}-q^{8}-3q^{10}+\cdots$
9054.2.a.h	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$3$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots$
9054.2.a.i	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$3$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots$
9054.2.a.j	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$4$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-2q^{7}-q^{8}-4q^{10}+\cdots$
9054.2.a.k	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$4$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}+q^{7}-q^{8}-4q^{10}+\cdots$
9054.2.a.l	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-4$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}-2q^{7}+q^{8}-4q^{10}+\cdots$
9054.2.a.m	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$2$	$1$	$0$	$-3$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}-5q^{7}+q^{8}-3q^{10}+\cdots$
9054.2.a.n	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$2$	$1$	$0$	$-3$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}-3q^{7}+q^{8}-3q^{10}+\cdots$
9054.2.a.o	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-3$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots$
9054.2.a.p	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
9054.2.a.q	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-2q^{11}+4q^{13}+\cdots$
9054.2.a.r	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-4q^{11}+2q^{13}+\cdots$
9054.2.a.s	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+2q^{13}+q^{16}-7q^{17}+\cdots$
9054.2.a.t	$9054$	$2$	9054.a	1.a	$1$	$1$	$1$	$72.297$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots$
9054.2.a.u	$9054$	$2$	9054.a	1.a	$1$	$2$	$2$	$72.297$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-2$	$0$	$1$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-2\beta q^{7}-q^{8}-\beta q^{10}+\cdots$
9054.2.a.v	$9054$	$2$	9054.a	1.a	$1$	$2$	$2$	$72.297$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$1$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+2\beta q^{7}-q^{8}-\beta q^{10}+\cdots$
9054.2.a.w	$9054$	$2$	9054.a	1.a	$1$	$2$	$2$	$72.297$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$2$	$0$	$-1$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta q^{5}-2\beta q^{7}+q^{8}-\beta q^{10}+\cdots$
9054.2.a.x	$9054$	$2$	9054.a	1.a	$1$	$2$	$2$	$72.297$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$0$	$-1$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta q^{5}+2\beta q^{7}+q^{8}-\beta q^{10}+\cdots$
9054.2.a.y	$9054$	$2$	9054.a	1.a	$1$	$2$	$2$	$72.297$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$-4$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}+(-2+\beta )q^{7}+\cdots$
9054.2.a.z	$9054$	$2$	9054.a	1.a	$1$	$4$	$4$	$72.297$	4.4.1957.1	None	✓	$1$	$1$	$-4$	$0$	$4$	$-8$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots$
9054.2.a.ba	$9054$	$2$	9054.a	1.a	$1$	$5$	$5$	$72.297$	5.5.205225.1	None	✓	$1$	$0$	$-5$	$0$	$3$	$-9$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1}+\beta _{3}+\beta _{4})q^{5}+\cdots$
9054.2.a.bb	$9054$	$2$	9054.a	1.a	$1$	$5$	$5$	$72.297$	5.5.36497.1	None	✓	$1$	$0$	$5$	$0$	$1$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{2}-\beta _{3})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
9054.2.a.bc	$9054$	$2$	9054.a	1.a	$1$	$6$	$6$	$72.297$	6.6.28406549.1	None	✓	$1$	$1$	$6$	$0$	$-1$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots$
9054.2.a.bd	$9054$	$2$	9054.a	1.a	$1$	$8$	$8$	$72.297$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$0$	$-8$	$-8$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
9054.2.a.be	$9054$	$2$	9054.a	1.a	$1$	$8$	$8$	$72.297$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$8$	$0$	$8$	$-8$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{1})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
9054.2.a.bf	$9054$	$2$	9054.a	1.a	$1$	$9$	$9$	$72.297$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$-9$	$0$	$7$	$-5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{4})q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots$
9054.2.a.bg	$9054$	$2$	9054.a	1.a	$1$	$9$	$9$	$72.297$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$9$	$0$	$-1$	$-11$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots$
9054.2.a.bh	$9054$	$2$	9054.a	1.a	$1$	$10$	$10$	$72.297$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$0$	$-6$	$-2$	$+$	$-$	$-$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{3})q^{5}+\beta _{1}q^{7}+\cdots$
9054.2.a.bi	$9054$	$2$	9054.a	1.a	$1$	$12$	$12$	$72.297$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-12$	$0$	$-5$	$8$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{9}q^{5}+(1+\beta _{10})q^{7}+\cdots$
9054.2.a.bj	$9054$	$2$	9054.a	1.a	$1$	$12$	$12$	$72.297$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$12$	$0$	$-7$	$-2$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{7}+\beta _{10})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
9054.2.a.bk	$9054$	$2$	9054.a	1.a	$1$	$12$	$12$	$72.297$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$12$	$0$	$3$	$11$	$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(1-\beta _{9})q^{7}+q^{8}+\cdots$
9054.2.a.bl	$9054$	$2$	9054.a	1.a	$1$	$13$	$13$	$72.297$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$13$	$0$	$4$	$6$	$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{7}q^{7}+q^{8}+\cdots$
9054.2.a.bm	$9054$	$2$	9054.a	1.a	$1$	$17$	$17$	$72.297$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	$1$	$0$	$-17$	$0$	$-7$	$13$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+(1-\beta _{3})q^{7}-q^{8}+\cdots$
9054.2.a.bn	$9054$	$2$	9054.a	1.a	$1$	$25$	$25$	$72.297$		None	✓	$1$	$0$	$-25$	$0$	$-7$	$17$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
9054.2.a.bo	$9054$	$2$	9054.a	1.a	$1$	$25$	$25$	$72.297$		None	✓	$1$	$0$	$25$	$0$	$7$	$17$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

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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.