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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (47 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
151.1.b.a	$151$	$1$	151.b	151.b	$2$	$3$	$3$	$0.075$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-151}) $	None	✓	✓	✓	✓	151.1.b.a	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
151.2.a.a	$151$	$2$	151.a	1.a	$1$	$3$	$3$	$1.206$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	✓	✓	✓	151.2.a.a	$1$	$1$	$-2$	$-1$	$-7$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
151.2.a.b	$151$	$2$	151.a	1.a	$1$	$3$	$3$	$1.206$	3.3.257.1	$_{}$	None	None	✓	✓			151.2.a.b	$1$	$0$	$0$	$6$	$5$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+2q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
151.2.a.c	$151$	$2$	151.a	1.a	$1$	$6$	$6$	$1.206$	6.6.4838537.1	$_{}$	None	None	✓	✓	✓		151.2.a.c	$1$	$0$	$1$	$-5$	$6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots$
151.2.c.a	$151$	$2$	151.c	151.c	$3$	$12$	$6$	$1.206$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			151.2.c.a	$2$	$0$	$-4$	$-2$	$-7$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{5}+\beta _{8}+\beta _{11})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots$
151.2.c.b	$151$	$2$	151.c	151.c	$3$	$12$	$6$	$1.206$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			151.2.c.b	$2$	$0$	$2$	$-4$	$6$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}-\beta _{5})q^{2}+\beta _{11}q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
151.2.d.a	$151$	$2$	151.d	151.d	$5$	$12$	$3$	$1.206$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			151.2.d.a	$2$	$0$	$-8$	$-2$	$-3$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{5})q^{2}+(\beta _{6}+\beta _{8})q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots$
151.2.d.b	$151$	$2$	151.d	151.d	$5$	$32$	$8$	$1.206$		$_{}$	None	None		✓	✓		151.2.d.b	$2$	$0$	$2$	$1$	$0$	$2$			$\mathrm{SU}(2)[C_{5}]$
151.2.g.a	$151$	$2$	151.g	151.g	$15$	$96$	$12$	$1.206$		$_{}$	None	None		✓	✓	✓	151.2.g.a	$2$	$0$	$-3$	$-4$	$-9$	$-7$			$\mathrm{SU}(2)[C_{15}]$
151.2.h.a	$151$	$2$	151.h	151.h	$25$	$220$	$11$	$1.206$		$_{}$	None	None		✓	✓	✓	151.2.h.a	$2$	$0$	$-15$	$-20$	$-20$	$-20$			$\mathrm{SU}(2)[C_{25}]$
151.2.k.a	$151$	$2$	151.k	151.k	$75$	$480$	$12$	$1.206$		$_{}$	None	None		✓	✓	✓	151.2.k.a	$2$	$0$	$-45$	$-40$	$-40$	$-40$			$\mathrm{SU}(2)[C_{75}]$
151.3.b.a	$151$	$3$	151.b	151.b	$2$	$7$	$7$	$4.114$	7.7.$\cdots$.1	$_{}$	$\Q(\sqrt{-151}) $	None	✓	✓			151.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(4+\beta _{3}+\beta _{4})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
151.3.b.b	$151$	$3$	151.b	151.b	$2$	$18$	$18$	$4.114$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓	✓		151.3.b.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{11})q^{4}+\beta _{4}q^{5}+\cdots$
151.3.e.a	$151$	$3$	151.e	151.e	$6$	$48$	$24$	$4.114$		$_{}$	None	None		✓	✓	✓	151.3.e.a	$2$	$0$	$0$	$0$	$-1$	$21$			$\mathrm{SU}(2)[C_{6}]$
151.3.f.a	$151$	$3$	151.f	151.f	$10$	$100$	$25$	$4.114$		$_{}$	None	None		✓	✓	✓	151.3.f.a	$2$	$0$	$-10$	$-5$	$-3$	$-5$			$\mathrm{SU}(2)[C_{10}]$
151.3.i.a	$151$	$3$	151.i	151.i	$30$	$192$	$24$	$4.114$		$_{}$	None	None		✓	✓	✓	151.3.i.a	$2$	$0$	$-5$	$-10$	$-9$	$-31$			$\mathrm{SU}(2)[C_{30}]$
151.3.j.a	$151$	$3$	151.j	151.j	$50$	$500$	$25$	$4.114$		$_{}$	None	None		✓	✓	✓	151.3.j.a	$2$	$0$	$-15$	$-20$	$-20$	$-20$			$\mathrm{SU}(2)[C_{50}]$
151.3.l.a	$151$	$3$	151.l	151.l	$150$	$960$	$24$	$4.114$		$_{}$	None	None		✓	✓	✓	151.3.l.a	$2$	$0$	$-45$	$-40$	$-40$	$-40$			$\mathrm{SU}(2)[C_{150}]$
151.4.a.a	$151$	$4$	151.a	1.a	$1$	$15$	$15$	$8.909$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	151.4.a.a	$1$	$1$	$-6$	$-10$	$-61$	$-26$	$-$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{6})q^{3}+(3+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
151.4.a.b	$151$	$4$	151.a	1.a	$1$	$22$	$22$	$8.909$		$_{}$	None	None	✓	✓	✓	✓	151.4.a.b	$1$	$0$	$6$	$8$	$59$	$30$	$+$		$\mathrm{SU}(2)$
151.4.c.a	$151$	$4$	151.c	151.c	$3$	$4$	$2$	$8.909$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			151.4.c.a	$2$	$0$	$0$	$20$	$12$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\beta _{1}+\beta _{3})q^{2}+5q^{3}-3\beta _{3}q^{4}+\cdots$
151.4.c.b	$151$	$4$	151.c	151.c	$3$	$70$	$35$	$8.909$		$_{}$	None	None		✓	✓		151.4.c.b	$2$	$0$	$0$	$-12$	$-13$	$4$			$\mathrm{SU}(2)[C_{3}]$
151.4.d.a	$151$	$4$	151.d	151.d	$5$	$148$	$37$	$8.909$		$_{}$	None	None		✓	✓	✓	151.4.d.a	$2$	$0$	$-10$	$-3$	$-3$	$-9$			$\mathrm{SU}(2)[C_{5}]$
151.4.g.a	$151$	$4$	151.g	151.g	$15$	$296$	$37$	$8.909$		$_{}$	None	None		✓	✓	✓	151.4.g.a	$2$	$0$	$-5$	$-18$	$-9$	$-9$			$\mathrm{SU}(2)[C_{15}]$
151.4.h.a	$151$	$4$	151.h	151.h	$25$	$740$	$37$	$8.909$		$_{}$	None	None		✓	✓	✓	151.4.h.a	$2$	$0$	$-15$	$-20$	$-20$	$-20$			$\mathrm{SU}(2)[C_{25}]$
151.4.k.a	$151$	$4$	151.k	151.k	$75$	$1480$	$37$	$8.909$		$_{}$	None	None		✓	✓	✓	151.4.k.a	$2$	$0$	$-45$	$-40$	$-40$	$-40$			$\mathrm{SU}(2)[C_{75}]$
151.5.b.a	$151$	$5$	151.b	151.b	$2$	$7$	$7$	$15.609$	7.7.$\cdots$.1	$_{}$	$\Q(\sqrt{-151}) $	None	✓	✓			151.5.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(2^{4}+3\beta _{1}-2\beta _{6})q^{4}+(-3\beta _{3}+\cdots)q^{5}+\cdots$
151.5.b.b	$151$	$5$	151.b	151.b	$2$	$42$	$42$	$15.609$		$_{}$	None	None		✓	✓		151.5.b.b	$2$	$0$	$-8$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
151.5.e.a	$151$	$5$	151.e	151.e	$6$	$100$	$50$	$15.609$		$_{}$	None	None		✓	✓	✓	151.5.e.a	$2$	$0$	$-4$	$0$	$-1$	$-39$			$\mathrm{SU}(2)[C_{6}]$
151.5.f.a	$151$	$5$	151.f	151.f	$10$	$196$	$49$	$15.609$		$_{}$	None	None		✓	✓	✓	151.5.f.a	$2$	$0$	$-2$	$-5$	$-3$	$-5$			$\mathrm{SU}(2)[C_{10}]$
151.5.i.a	$151$	$5$	151.i	151.i	$30$	$400$	$50$	$15.609$		$_{}$	None	None		✓	✓	✓	151.5.i.a	$2$	$0$	$-1$	$-10$	$-9$	$29$			$\mathrm{SU}(2)[C_{30}]$
151.5.j.a	$151$	$5$	151.j	151.j	$50$	$980$	$49$	$15.609$		$_{}$	None	None		✓	✓	✓	151.5.j.a	$2$	$0$	$-15$	$-20$	$-20$	$-20$			$\mathrm{SU}(2)[C_{50}]$
151.5.l.a	$151$	$5$	151.l	151.l	$150$	$2000$	$50$	$15.609$		$_{}$	None	None		✓	✓	✓	151.5.l.a	$2$	$0$	$-45$	$-40$	$-40$	$-40$			$\mathrm{SU}(2)[C_{150}]$
151.6.a.a	$151$	$6$	151.a	1.a	$1$	$28$	$28$	$24.218$		$_{}$	None	None	✓	✓	✓	✓	151.6.a.a	$1$	$1$	$-12$	$-37$	$-301$	$-255$	$+$		$\mathrm{SU}(2)$
151.6.a.b	$151$	$6$	151.a	1.a	$1$	$35$	$35$	$24.218$		$_{}$	None	None	✓	✓	✓	✓	151.6.a.b	$1$	$0$	$12$	$17$	$299$	$137$	$-$		$\mathrm{SU}(2)$
151.7.b.a	$151$	$7$	151.b	151.b	$2$	$7$	$7$	$34.738$	7.7.$\cdots$.1	$_{}$	$\Q(\sqrt{-151}) $	None	✓	✓			151.7.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(5\beta _{1}+\beta _{6})q^{2}+(2^{6}+6\beta _{2}+19\beta _{5}+\cdots)q^{4}+\cdots$
151.7.b.b	$151$	$7$	151.b	151.b	$2$	$68$	$68$	$34.738$		$_{}$	None	None		✓	✓		151.7.b.b	$2$	$0$	$8$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
151.8.a.a	$151$	$8$	151.a	1.a	$1$	$40$	$40$	$47.170$		$_{}$	None	None	✓	✓	✓	✓	151.8.a.a	$1$	$1$	$-32$	$-55$	$-1501$	$-1175$	$-$		$\mathrm{SU}(2)$
151.8.a.b	$151$	$8$	151.a	1.a	$1$	$47$	$47$	$47.170$		$_{}$	None	None	✓	✓	✓	✓	151.8.a.b	$1$	$0$	$16$	$107$	$1499$	$1569$	$+$		$\mathrm{SU}(2)$
151.10.a.a	$151$	$10$	151.a	1.a	$1$	$53$	$53$	$77.770$		$_{}$	None	None	✓	✓	✓	✓	151.10.a.a	$1$	$1$	$-32$	$-244$	$-7501$	$-7698$	$+$		$\mathrm{SU}(2)$
151.10.a.b	$151$	$10$	151.a	1.a	$1$	$60$	$60$	$77.770$		$_{}$	None	None	✓	✓	✓	✓	151.10.a.b	$1$	$0$	$64$	$242$	$7499$	$11510$	$-$		$\mathrm{SU}(2)$
151.12.a.a	$151$	$12$	151.a	1.a	$1$	$65$	$65$	$116.020$		$_{}$	None	None	✓	✓	✓	✓	151.12.a.a	$1$	$1$	$-96$	$-739$	$-42331$	$-86411$	$-$		$\mathrm{SU}(2)$
151.12.a.b	$151$	$12$	151.a	1.a	$1$	$72$	$72$	$116.020$		$_{}$	None	None	✓	✓	✓	✓	151.12.a.b	$1$	$0$	$96$	$719$	$32669$	$48045$	$+$		$\mathrm{SU}(2)$
151.14.a.a	$151$	$14$	151.a	1.a	$1$	$78$	$78$	$161.919$		$_{}$	None	None	✓	✓	✓	✓	151.14.a.a	$1$	$1$	$-192$	$-2917$	$-187501$	$-468075$	$+$		$\mathrm{SU}(2)$
151.14.a.b	$151$	$14$	151.a	1.a	$1$	$85$	$85$	$161.919$		$_{}$	None	None	✓	✓	✓	✓	151.14.a.b	$1$	$0$	$192$	$1457$	$187499$	$473117$	$-$		$\mathrm{SU}(2)$
151.16.a.a	$151$	$16$	151.a	1.a	$1$	$90$	$90$	$215.467$		$_{}$	None	None	✓	✓	✓	✓	151.16.a.a	$1$	$1$	$-512$	$-3214$	$-989611$	$-2366810$	$-$		$\mathrm{SU}(2)$
151.16.a.b	$151$	$16$	151.a	1.a	$1$	$97$	$97$	$215.467$		$_{}$	None	None	✓	✓	✓	✓	151.16.a.b	$1$	$0$	$256$	$9908$	$885389$	$4221534$	$+$		$\mathrm{SU}(2)$

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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.