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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 (30 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7524.2.a.a	$7524$	$2$	7524.a	1.a	$1$	$1$	$1$	$60.079$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-q^{11}+q^{13}+3q^{17}+\cdots$
7524.2.a.b	$7524$	$2$	7524.a	1.a	$1$	$1$	$1$	$60.079$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{11}+4q^{13}+2q^{17}+q^{19}+\cdots$
7524.2.a.c	$7524$	$2$	7524.a	1.a	$1$	$1$	$1$	$60.079$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{11}-2q^{13}+4q^{17}+q^{19}+\cdots$
7524.2.a.d	$7524$	$2$	7524.a	1.a	$1$	$1$	$1$	$60.079$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{11}+2q^{13}+4q^{17}-q^{19}-4q^{23}+\cdots$
7524.2.a.e	$7524$	$2$	7524.a	1.a	$1$	$1$	$1$	$60.079$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{11}+2q^{13}-4q^{17}-q^{19}+4q^{23}+\cdots$
7524.2.a.f	$7524$	$2$	7524.a	1.a	$1$	$1$	$1$	$60.079$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+q^{11}+5q^{13}-3q^{17}+q^{19}+\cdots$
7524.2.a.g	$7524$	$2$	7524.a	1.a	$1$	$1$	$1$	$60.079$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+q^{11}+q^{13}-3q^{17}+\cdots$
7524.2.a.h	$7524$	$2$	7524.a	1.a	$1$	$2$	$2$	$60.079$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{7}-q^{11}-\beta q^{13}-\beta q^{17}+\cdots$
7524.2.a.i	$7524$	$2$	7524.a	1.a	$1$	$3$	$3$	$60.079$	3.3.321.1	None	✓	$1$	$1$	$0$	$0$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+(-2+\beta _{1})q^{7}+q^{11}+(1+\cdots)q^{13}+\cdots$
7524.2.a.j	$7524$	$2$	7524.a	1.a	$1$	$3$	$3$	$60.079$	3.3.993.1	None	✓	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}-q^{11}+(-1-\beta _{1}+\cdots)q^{13}+\cdots$
7524.2.a.k	$7524$	$2$	7524.a	1.a	$1$	$3$	$3$	$60.079$	3.3.785.1	None	✓	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+q^{11}+\cdots$
7524.2.a.l	$7524$	$2$	7524.a	1.a	$1$	$3$	$3$	$60.079$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$0$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots$
7524.2.a.m	$7524$	$2$	7524.a	1.a	$1$	$3$	$3$	$60.079$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$0$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}+\cdots$
7524.2.a.n	$7524$	$2$	7524.a	1.a	$1$	$4$	$4$	$60.079$	4.4.171777.1	None	✓	$1$	$1$	$0$	$0$	$-1$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{5}+(1+\beta _{1})q^{7}-q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
7524.2.a.o	$7524$	$2$	7524.a	1.a	$1$	$4$	$4$	$60.079$	4.4.23665.1	None	✓	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots$
7524.2.a.p	$7524$	$2$	7524.a	1.a	$1$	$4$	$4$	$60.079$	4.4.161473.1	None	✓	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(1+\beta _{3})q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots$
7524.2.a.q	$7524$	$2$	7524.a	1.a	$1$	$6$	$6$	$60.079$	6.6.744786576.1	None	✓	$1$	$0$	$0$	$0$	$-5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{5})q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
7524.2.a.r	$7524$	$2$	7524.a	1.a	$1$	$6$	$6$	$60.079$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{5}+\beta _{4}q^{7}-q^{11}+\beta _{3}q^{13}+\cdots$
7524.2.a.s	$7524$	$2$	7524.a	1.a	$1$	$7$	$7$	$60.079$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{5}-\beta _{6}q^{7}+q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
7524.2.a.t	$7524$	$2$	7524.a	1.a	$1$	$7$	$7$	$60.079$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$-2$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{5}+(1-\beta _{1})q^{7}-q^{11}+\beta _{6}q^{13}+\cdots$
7524.2.a.u	$7524$	$2$	7524.a	1.a	$1$	$7$	$7$	$60.079$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{5}+(1-\beta _{1})q^{7}+q^{11}+\beta _{6}q^{13}+\cdots$
7524.2.a.v	$7524$	$2$	7524.a	1.a	$1$	$7$	$7$	$60.079$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{5}-\beta _{6}q^{7}-q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
7524.2.c.a	$7524$	$2$	7524.c	33.d	$2$	$72$	$72$	$60.079$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
7524.2.f.a	$7524$	$2$	7524.f	57.d	$2$	$64$	$64$	$60.079$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
7524.2.l.a	$7524$	$2$	7524.l	209.d	$2$	$4$	$4$	$60.079$	$\Q(\sqrt{-3}, \sqrt{-19})$	$\Q(\sqrt{-19}) $		$4$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots$
7524.2.l.b	$7524$	$2$	7524.l	209.d	$2$	$8$	$8$	$60.079$	8.0.$\cdots$.6	$\Q(\sqrt{-627}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{6}q^{11}-\beta _{1}q^{13}+\beta _{3}q^{17}-\beta _{4}q^{19}+\cdots$
7524.2.l.c	$7524$	$2$	7524.l	209.d	$2$	$8$	$8$	$60.079$	8.0.2702336256.1	$\Q(\sqrt{-19}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{5}+\beta _{7})q^{5}+(\beta _{3}-\beta _{4})q^{7}+(\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots$
7524.2.l.d	$7524$	$2$	7524.l	209.d	$2$	$16$	$16$	$60.079$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$-4$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+(\beta _{9}-\beta _{12})q^{7}+(-\beta _{3}-\beta _{9}+\cdots)q^{11}+\cdots$
7524.2.l.e	$7524$	$2$	7524.l	209.d	$2$	$24$	$24$	$60.079$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
7524.2.l.f	$7524$	$2$	7524.l	209.d	$2$	$40$	$40$	$60.079$		None		$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.