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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 (49 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
267.2.a.a	$267$	$2$	267.a	1.a	$1$	$1$	$1$	$2.132$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+4q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
267.2.a.b	$267$	$2$	267.a	1.a	$1$	$1$	$1$	$2.132$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+2q^{7}+q^{9}+6q^{11}+\cdots$
267.2.a.c	$267$	$2$	267.a	1.a	$1$	$3$	$3$	$2.132$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-4$	$3$	$-7$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+q^{3}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots$
267.2.a.d	$267$	$2$	267.a	1.a	$1$	$3$	$3$	$2.132$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$-3$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1+2\beta _{1}+\cdots)q^{5}+\cdots$
267.2.a.e	$267$	$2$	267.a	1.a	$1$	$3$	$3$	$2.132$	3.3.169.1	None	✓	$1$	$0$	$2$	$3$	$5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
267.2.a.f	$267$	$2$	267.a	1.a	$1$	$4$	$4$	$2.132$	4.4.23377.1	None	✓	$1$	$0$	$1$	$-4$	$3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
267.2.d.a	$267$	$2$	267.d	89.b	$2$	$16$	$16$	$2.132$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-2$	$0$	$8$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{11}q^{3}+(1-\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
267.2.f.a	$267$	$2$	267.f	89.c	$4$	$28$	$14$	$2.132$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
267.2.g.a	$267$	$2$	267.g	267.g	$8$	$4$	$1$	$2.132$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$-4$	$-4$	$8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}+\cdots)q^{3}+\cdots$
267.2.g.b	$267$	$2$	267.g	267.g	$8$	$4$	$1$	$2.132$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$4$	$4$	$8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\cdots$
267.2.g.c	$267$	$2$	267.g	267.g	$8$	$104$	$26$	$2.132$		None		$4$	$0$	$0$	$-8$	$0$	$-24$			$\mathrm{SU}(2)[C_{8}]$
267.2.i.a	$267$	$2$	267.i	89.e	$11$	$80$	$8$	$2.132$		None		$2$	$0$	$-1$	$-8$	$-4$	$-2$			$\mathrm{SU}(2)[C_{11}]$
267.2.i.b	$267$	$2$	267.i	89.e	$11$	$80$	$8$	$2.132$		None		$2$	$0$	$-1$	$8$	$-4$	$2$			$\mathrm{SU}(2)[C_{11}]$
267.2.j.a	$267$	$2$	267.j	89.f	$22$	$160$	$16$	$2.132$		None		$2$	$0$	$2$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{22}]$
267.2.m.a	$267$	$2$	267.m	89.g	$44$	$280$	$14$	$2.132$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{44}]$
267.2.p.a	$267$	$2$	267.p	267.p	$88$	$1120$	$28$	$2.132$		None		$4$	$0$	$0$	$-36$	$0$	$-80$			$\mathrm{SU}(2)[C_{88}]$
267.3.b.a	$267$	$3$	267.b	267.b	$2$	$1$	$1$	$7.275$	$\Q$	$\Q(\sqrt{-267}) $	✓	$2$	$0$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+4q^{4}+9q^{9}-12q^{12}+2^{4}q^{16}+\cdots$
267.3.b.b	$267$	$3$	267.b	267.b	$2$	$1$	$1$	$7.275$	$\Q$	$\Q(\sqrt{-267}) $	✓	$2$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+4q^{4}+9q^{9}+12q^{12}+2^{4}q^{16}+\cdots$
267.3.b.c	$267$	$3$	267.b	267.b	$2$	$56$	$56$	$7.275$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
267.3.c.a	$267$	$3$	267.c	3.b	$2$	$58$	$58$	$7.275$		None		$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
267.3.e.a	$267$	$3$	267.e	267.e	$4$	$116$	$58$	$7.275$		None		$4$	$0$	$0$	$4$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
267.3.h.a	$267$	$3$	267.h	89.d	$8$	$120$	$30$	$7.275$		None		$2$	$0$	$0$	$0$	$-40$	$0$			$\mathrm{SU}(2)[C_{8}]$
267.3.k.a	$267$	$3$	267.k	267.k	$22$	$580$	$58$	$7.275$		None		$4$	$0$	$0$	$-22$	$0$	$-18$			$\mathrm{SU}(2)[C_{22}]$
267.3.l.a	$267$	$3$	267.l	267.l	$22$	$580$	$58$	$7.275$		None		$4$	$0$	$0$	$0$	$0$	$-22$			$\mathrm{SU}(2)[C_{22}]$
267.3.n.a	$267$	$3$	267.n	267.n	$44$	$1160$	$58$	$7.275$		None		$4$	$0$	$0$	$-26$	$0$	$-40$			$\mathrm{SU}(2)[C_{44}]$
267.3.o.a	$267$	$3$	267.o	89.h	$88$	$1200$	$30$	$7.275$		None		$2$	$0$	$0$	$0$	$40$	$0$			$\mathrm{SU}(2)[C_{88}]$
267.4.a.a	$267$	$4$	267.a	1.a	$1$	$10$	$10$	$15.754$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-8$	$30$	$-41$	$-42$	$-$	$3^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+3q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
267.4.a.b	$267$	$4$	267.a	1.a	$1$	$10$	$10$	$15.754$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$-30$	$-21$	$-28$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(3+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
267.4.a.c	$267$	$4$	267.a	1.a	$1$	$12$	$12$	$15.754$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$2$	$-36$	$29$	$42$	$+$	$3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(2+\beta _{9}+\cdots)q^{5}+\cdots$
267.4.a.d	$267$	$4$	267.a	1.a	$1$	$12$	$12$	$15.754$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$10$	$36$	$49$	$28$	$+$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
267.4.d.a	$267$	$4$	267.d	89.b	$2$	$44$	$44$	$15.754$		None		$2$	$0$	$-4$	$0$	$16$	$0$			$\mathrm{SU}(2)[C_{2}]$
267.4.f.a	$267$	$4$	267.f	89.c	$4$	$92$	$46$	$15.754$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
267.6.a.a	$267$	$6$	267.a	1.a	$1$	$17$	$17$	$42.822$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	$1$	$1$	$-14$	$153$	$-239$	$-156$	$+$	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+9q^{3}+(15-2\beta _{1}+\cdots)q^{4}+\cdots$
267.6.a.b	$267$	$6$	267.a	1.a	$1$	$18$	$18$	$42.822$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$-4$	$-162$	$-133$	$-294$	$+$	$2^{3}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-9q^{3}+(2^{4}+\beta _{2})q^{4}+(-7+\cdots)q^{5}+\cdots$
267.6.a.c	$267$	$6$	267.a	1.a	$1$	$19$	$19$	$42.822$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$0$	$22$	$171$	$211$	$334$	$-$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+9q^{3}+(17+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
267.6.a.d	$267$	$6$	267.a	1.a	$1$	$20$	$20$	$42.822$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$0$	$-180$	$117$	$196$	$-$	$2^{7}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-9q^{3}+(19+\beta _{2})q^{4}+(6-\beta _{1}+\cdots)q^{5}+\cdots$
267.6.d.a	$267$	$6$	267.d	89.b	$2$	$76$	$76$	$42.822$		None		$2$	$0$	$8$	$0$	$-32$	$0$			$\mathrm{SU}(2)[C_{2}]$
267.8.a.a	$267$	$8$	267.a	1.a	$1$	$24$	$24$	$83.407$		None	✓	$1$	$1$	$-14$	$-648$	$-821$	$-1308$	$-$		$\mathrm{SU}(2)$
267.8.a.b	$267$	$8$	267.a	1.a	$1$	$25$	$25$	$83.407$		None	✓	$1$	$1$	$-40$	$675$	$-931$	$-2058$	$-$		$\mathrm{SU}(2)$
267.8.a.c	$267$	$8$	267.a	1.a	$1$	$26$	$26$	$83.407$		None	✓	$1$	$0$	$-6$	$-702$	$429$	$2122$	$+$		$\mathrm{SU}(2)$
267.8.a.d	$267$	$8$	267.a	1.a	$1$	$27$	$27$	$83.407$		None	✓	$1$	$0$	$32$	$729$	$1319$	$1372$	$+$		$\mathrm{SU}(2)$
267.10.a.a	$267$	$10$	267.a	1.a	$1$	$32$	$32$	$137.515$		None	✓	$1$	$1$	$-82$	$2592$	$-5233$	$-18732$	$+$		$\mathrm{SU}(2)$
267.10.a.b	$267$	$10$	267.a	1.a	$1$	$32$	$32$	$137.515$		None	✓	$1$	$1$	$36$	$-2592$	$-2949$	$-9926$	$+$		$\mathrm{SU}(2)$
267.10.a.c	$267$	$10$	267.a	1.a	$1$	$34$	$34$	$137.515$		None	✓	$1$	$0$	$52$	$-2754$	$3301$	$14084$	$-$		$\mathrm{SU}(2)$
267.10.a.d	$267$	$10$	267.a	1.a	$1$	$34$	$34$	$137.515$		None	✓	$1$	$0$	$62$	$2754$	$6017$	$5278$	$-$		$\mathrm{SU}(2)$
267.12.a.a	$267$	$12$	267.a	1.a	$1$	$39$	$39$	$205.148$		None	✓	$1$	$1$	$-78$	$-9477$	$-15471$	$-39468$	$-$		$\mathrm{SU}(2)$
267.12.a.b	$267$	$12$	267.a	1.a	$1$	$40$	$40$	$205.148$		None	✓	$1$	$1$	$-128$	$9720$	$-33341$	$-100842$	$-$		$\mathrm{SU}(2)$
267.12.a.c	$267$	$12$	267.a	1.a	$1$	$41$	$41$	$205.148$		None	✓	$1$	$0$	$-46$	$-9963$	$15779$	$128602$	$+$		$\mathrm{SU}(2)$
267.12.a.d	$267$	$12$	267.a	1.a	$1$	$42$	$42$	$205.148$		None	✓	$1$	$0$	$160$	$10206$	$22909$	$67228$	$+$		$\mathrm{SU}(2)$

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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.