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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 (43 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
3075.1.c.a	$3075$	$1$	3075.c	123.b	$2$	$1$	$1$	$1.535$	$\Q$	$D_{3}$	$\Q(\sqrt{-123}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}+q^{9}-q^{11}-q^{12}+q^{16}+\cdots$
3075.1.c.b	$3075$	$1$	3075.c	123.b	$2$	$1$	$1$	$1.535$	$\Q$	$D_{3}$	$\Q(\sqrt{-123}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}+q^{9}+q^{11}-q^{12}+q^{16}+\cdots$
3075.1.c.c	$3075$	$1$	3075.c	123.b	$2$	$1$	$1$	$1.535$	$\Q$	$D_{3}$	$\Q(\sqrt{-123}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{4}+q^{9}-q^{11}+q^{12}+q^{16}+\cdots$
3075.1.c.d	$3075$	$1$	3075.c	123.b	$2$	$1$	$1$	$1.535$	$\Q$	$D_{3}$	$\Q(\sqrt{-123}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{4}+q^{9}+q^{11}+q^{12}+q^{16}+\cdots$
3075.1.c.e	$3075$	$1$	3075.c	123.b	$2$	$4$	$4$	$1.535$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-615}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+\beta _{2}q^{6}+\cdots$
3075.1.c.f	$3075$	$1$	3075.c	123.b	$2$	$4$	$4$	$1.535$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-615}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
3075.1.h.a	$3075$	$1$	3075.h	615.h	$2$	$2$	$2$	$1.535$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-123}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-q^{4}-q^{9}-q^{11}+iq^{12}+\cdots$
3075.1.h.b	$3075$	$1$	3075.h	615.h	$2$	$2$	$2$	$1.535$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-123}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-q^{4}-q^{9}+q^{11}+iq^{12}+\cdots$
3075.1.bi.a	$3075$	$1$	3075.bi	3075.ai	$10$	$8$	$2$	$1.535$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{7})q^{2}-\zeta_{20}^{3}q^{3}+\cdots$
3075.1.ck.a	$3075$	$1$	3075.ck	3075.bk	$10$	$8$	$2$	$1.535$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+\zeta_{20}q^{3}+(-1+\cdots)q^{4}+\cdots$
3075.2.a.a	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}-4q^{7}+\cdots$
3075.2.a.b	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots$
3075.2.a.c	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+2q^{7}+3q^{8}+\cdots$
3075.2.a.d	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-2q^{7}+q^{9}-3q^{11}+\cdots$
3075.2.a.e	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{9}-q^{11}+2q^{12}+\cdots$
3075.2.a.f	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{7}+q^{9}+2q^{12}+q^{13}+\cdots$
3075.2.a.g	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{7}+q^{9}-2q^{12}-q^{13}+\cdots$
3075.2.a.h	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+2q^{7}+q^{9}-3q^{11}+\cdots$
3075.2.a.i	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+4q^{7}+q^{9}+5q^{11}+\cdots$
3075.2.a.j	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots$
3075.2.a.k	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
3075.2.a.l	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}+2q^{7}+\cdots$
3075.2.a.m	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}+2q^{7}+\cdots$
3075.2.a.n	$3075$	$2$	3075.a	1.a	$1$	$1$	$1$	$24.554$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+4q^{7}+\cdots$
3075.2.a.o	$3075$	$2$	3075.a	1.a	$1$	$2$	$2$	$24.554$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
3075.2.a.p	$3075$	$2$	3075.a	1.a	$1$	$2$	$2$	$24.554$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}-\beta q^{6}+(2+\beta )q^{7}-2\beta q^{8}+\cdots$
3075.2.a.q	$3075$	$2$	3075.a	1.a	$1$	$2$	$2$	$24.554$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
3075.2.a.r	$3075$	$2$	3075.a	1.a	$1$	$2$	$2$	$24.554$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+\beta q^{6}+(4+\cdots)q^{8}+\cdots$
3075.2.a.s	$3075$	$2$	3075.a	1.a	$1$	$3$	$3$	$24.554$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$3$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots$
3075.2.a.t	$3075$	$2$	3075.a	1.a	$1$	$3$	$3$	$24.554$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
3075.2.a.u	$3075$	$2$	3075.a	1.a	$1$	$3$	$3$	$24.554$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$2$	$-3$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}+(-1+\cdots)q^{6}+\cdots$
3075.2.a.v	$3075$	$2$	3075.a	1.a	$1$	$4$	$4$	$24.554$	4.4.3981.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
3075.2.a.w	$3075$	$2$	3075.a	1.a	$1$	$5$	$5$	$24.554$	5.5.1122797.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$5$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
3075.2.a.x	$3075$	$2$	3075.a	1.a	$1$	$6$	$6$	$24.554$	6.6.69796620.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-6$	$0$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3075.2.a.y	$3075$	$2$	3075.a	1.a	$1$	$7$	$7$	$24.554$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-7$	$0$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3075.2.a.z	$3075$	$2$	3075.a	1.a	$1$	$7$	$7$	$24.554$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$7$	$0$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3075.2.a.ba	$3075$	$2$	3075.a	1.a	$1$	$8$	$8$	$24.554$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-8$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3075.2.a.bb	$3075$	$2$	3075.a	1.a	$1$	$9$	$9$	$24.554$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-9$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3075.2.a.bc	$3075$	$2$	3075.a	1.a	$1$	$9$	$9$	$24.554$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$9$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3075.2.a.bd	$3075$	$2$	3075.a	1.a	$1$	$10$	$10$	$24.554$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-10$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3075.2.a.be	$3075$	$2$	3075.a	1.a	$1$	$10$	$10$	$24.554$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$10$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
3075.2.a.bf	$3075$	$2$	3075.a	1.a	$1$	$10$	$10$	$24.554$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-10$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
3075.2.a.bg	$3075$	$2$	3075.a	1.a	$1$	$10$	$10$	$24.554$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$10$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$

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Universe	Knowledge

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.