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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 (35 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
107.1.b.a	$107$	$1$	107.b	107.b	$2$	$1$	$1$	$0.053$	$\Q$	$D_{3}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots$
107.2.a.a	$107$	$2$	107.a	1.a	$1$	$2$	$2$	$0.854$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
107.2.a.b	$107$	$2$	107.a	1.a	$1$	$7$	$7$	$0.854$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$5$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1-\beta _{2}+\beta _{5})q^{4}+\cdots$
107.2.c.a	$107$	$2$	107.c	107.c	$53$	$416$	$8$	$0.854$		$_{}$	None	None		$2$	$0$	$-48$	$-49$	$-49$	$-45$			$\mathrm{SU}(2)[C_{53}]$
107.3.b.a	$107$	$3$	107.b	107.b	$2$	$3$	$3$	$2.916$	3.3.321.1	$_{}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{3}+4q^{4}+(9+\beta _{1}-3\beta _{2})q^{9}+\cdots$
107.3.b.b	$107$	$3$	107.b	107.b	$2$	$14$	$14$	$2.916$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-3+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
107.3.d.a	$107$	$3$	107.d	107.d	$106$	$884$	$17$	$2.916$		$_{}$	None	None		$2$	$0$	$-53$	$-55$	$-53$	$-53$			$\mathrm{SU}(2)[C_{106}]$
107.4.a.a	$107$	$4$	107.a	1.a	$1$	$10$	$10$	$6.313$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-17$	$-31$	$-44$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-2+\beta _{5})q^{3}+(2+\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots$
107.4.a.b	$107$	$4$	107.a	1.a	$1$	$16$	$16$	$6.313$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$13$	$39$	$68$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{8})q^{3}+(5+\beta _{2})q^{4}+\cdots$
107.4.c.a	$107$	$4$	107.c	107.c	$53$	$1352$	$26$	$6.313$		$_{}$	None	None		$2$	$0$	$-55$	$-49$	$-61$	$-77$			$\mathrm{SU}(2)[C_{53}]$
107.5.b.a	$107$	$5$	107.b	107.b	$2$	$3$	$3$	$11.061$	3.3.321.1	$_{}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-3\beta _{2})q^{3}+2^{4}q^{4}+(3^{4}-9\beta _{1}+\cdots)q^{9}+\cdots$
107.5.b.b	$107$	$5$	107.b	107.b	$2$	$32$	$32$	$11.061$		$_{}$	None	None		$2$	$0$	$0$	$-10$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
107.5.d.a	$107$	$5$	107.d	107.d	$106$	$1820$	$35$	$11.061$		$_{}$	None	None		$2$	$0$	$-53$	$-43$	$-53$	$-53$			$\mathrm{SU}(2)[C_{106}]$
107.6.a.a	$107$	$6$	107.a	1.a	$1$	$19$	$19$	$17.161$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-8$	$-35$	$-201$	$-404$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-2-\beta _{3})q^{3}+(11+\beta _{1}+\cdots)q^{4}+\cdots$
107.6.a.b	$107$	$6$	107.a	1.a	$1$	$25$	$25$	$17.161$		$_{}$	None	None	✓	$1$	$0$	$4$	$55$	$149$	$380$	$-$		$\mathrm{SU}(2)$
107.6.c.a	$107$	$6$	107.c	107.c	$53$	$2288$	$44$	$17.161$		$_{}$	None	None		$2$	$0$	$-49$	$-73$	$-1$	$-29$			$\mathrm{SU}(2)[C_{53}]$
107.7.b.a	$107$	$7$	107.b	107.b	$2$	$1$	$1$	$24.616$	$\Q$	$_{}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$-53$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-53q^{3}+2^{6}q^{4}+2080q^{9}-2581q^{11}+\cdots$
107.7.b.b	$107$	$7$	107.b	107.b	$2$	$2$	$2$	$24.616$	$\Q(\sqrt{321}) $	$_{}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$53$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(3^{3}-\beta )q^{3}+2^{6}q^{4}+(80-53\beta )q^{9}+\cdots$
107.7.b.c	$107$	$7$	107.b	107.b	$2$	$50$	$50$	$24.616$		$_{}$	None	None		$2$	$0$	$0$	$-22$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
107.8.a.a	$107$	$8$	107.a	1.a	$1$	$28$	$28$	$33.425$		$_{}$	None	None	✓	$1$	$1$	$-16$	$-149$	$-751$	$-3076$	$-$		$\mathrm{SU}(2)$
107.8.a.b	$107$	$8$	107.a	1.a	$1$	$34$	$34$	$33.425$		$_{}$	None	None	✓	$1$	$0$	$8$	$121$	$999$	$2412$	$+$		$\mathrm{SU}(2)$
107.9.b.a	$107$	$9$	107.b	107.b	$2$	$3$	$3$	$43.590$	3.3.321.1	$_{}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3\cdot 7$	$\mathrm{U}(1)[D_{2}]$	$q+(-2^{4}\beta _{1}-5\beta _{2})q^{3}+2^{8}q^{4}+(3^{8}+\cdots)q^{9}+\cdots$
107.9.b.b	$107$	$9$	107.b	107.b	$2$	$68$	$68$	$43.590$		$_{}$	None	None		$2$	$0$	$0$	$110$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
107.10.a.a	$107$	$10$	107.a	1.a	$1$	$37$	$37$	$55.109$		$_{}$	None	None	✓	$1$	$1$	$-16$	$-479$	$-5001$	$-16732$	$+$		$\mathrm{SU}(2)$
107.10.a.b	$107$	$10$	107.a	1.a	$1$	$43$	$43$	$55.109$		$_{}$	None	None	✓	$1$	$0$	$32$	$331$	$3749$	$21684$	$-$		$\mathrm{SU}(2)$
107.11.b.a	$107$	$11$	107.b	107.b	$2$	$3$	$3$	$67.983$	3.3.321.1	$_{}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(-53\beta _{1}+78\beta _{2})q^{3}+2^{10}q^{4}+(3^{10}+\cdots)q^{9}+\cdots$
107.11.b.b	$107$	$11$	107.b	107.b	$2$	$86$	$86$	$67.983$		$_{}$	None	None		$2$	$0$	$0$	$-46$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
107.12.a.a	$107$	$12$	107.a	1.a	$1$	$45$	$45$	$82.213$		$_{}$	None	None	✓	$1$	$1$	$-32$	$-1205$	$-23581$	$-116660$	$-$		$\mathrm{SU}(2)$
107.12.a.b	$107$	$12$	107.a	1.a	$1$	$51$	$51$	$82.213$		$_{}$	None	None	✓	$1$	$0$	$64$	$1225$	$20169$	$152252$	$+$		$\mathrm{SU}(2)$
107.14.a.a	$107$	$14$	107.a	1.a	$1$	$55$	$55$	$114.737$		$_{}$	None	None	✓	$1$	$1$	$-128$	$-3515$	$-125001$	$-1140324$	$+$		$\mathrm{SU}(2)$
107.14.a.b	$107$	$14$	107.a	1.a	$1$	$61$	$61$	$114.737$		$_{}$	None	None	✓	$1$	$0$	$64$	$3775$	$93749$	$742060$	$-$		$\mathrm{SU}(2)$
107.16.a.a	$107$	$16$	107.a	1.a	$1$	$63$	$63$	$152.682$		$_{}$	None	None	✓	$1$	$1$	$-256$	$-10217$	$-520861$	$-7000492$	$-$		$\mathrm{SU}(2)$
107.16.a.b	$107$	$16$	107.a	1.a	$1$	$69$	$69$	$152.682$		$_{}$	None	None	✓	$1$	$0$	$128$	$11653$	$572889$	$6176196$	$+$		$\mathrm{SU}(2)$
107.18.a.a	$107$	$18$	107.a	1.a	$1$	$72$	$72$	$196.048$		$_{}$	None	None	✓	$1$	$1$	$-256$	$-24443$	$-2099151$	$-66984244$	$+$		$\mathrm{SU}(2)$
107.18.a.b	$107$	$18$	107.a	1.a	$1$	$78$	$78$	$196.048$		$_{}$	None	None	✓	$1$	$0$	$512$	$41167$	$3369599$	$25252572$	$-$		$\mathrm{SU}(2)$

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Classical	Maass
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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.