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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 (39 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
131.1.b.a	$131$	$1$	131.b	131.b	$2$	$2$	$2$	$0.065$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$		$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}-\beta q^{7}+\cdots$
131.2.a.a	$131$	$2$	131.a	1.a	$1$	$1$	$1$	$1.046$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-2q^{5}-q^{7}-2q^{9}+2q^{12}+\cdots$
131.2.a.b	$131$	$2$	131.a	1.a	$1$	$10$	$10$	$1.046$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
131.2.c.a	$131$	$2$	131.c	131.c	$5$	$4$	$1$	$1.046$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-5$	$1$	$7$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
131.2.c.b	$131$	$2$	131.c	131.c	$5$	$4$	$1$	$1.046$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$1$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
131.2.c.c	$131$	$2$	131.c	131.c	$5$	$32$	$8$	$1.046$		$_{}$	None	None		$2$	$0$	$1$	$-3$	$-2$	$-5$			$\mathrm{SU}(2)[C_{5}]$
131.2.e.a	$131$	$2$	131.e	131.e	$13$	$120$	$10$	$1.046$		$_{}$	None	None		$2$	$0$	$-10$	$-9$	$-9$	$-5$			$\mathrm{SU}(2)[C_{13}]$
131.2.g.a	$131$	$2$	131.g	131.g	$65$	$480$	$10$	$1.046$		$_{}$	None	None		$2$	$0$	$-50$	$-51$	$-51$	$-50$			$\mathrm{SU}(2)[C_{65}]$
131.3.b.a	$131$	$3$	131.b	131.b	$2$	$5$	$5$	$3.569$	5.5.53628125.1	$_{}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{2}-\beta _{3})q^{3}+4q^{4}+(-2\beta _{1}+\beta _{4})q^{5}+\cdots$
131.3.b.b	$131$	$3$	131.b	131.b	$2$	$16$	$16$	$3.569$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-4+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots$
131.3.d.a	$131$	$3$	131.d	131.d	$10$	$84$	$21$	$3.569$		$_{}$	None	None		$2$	$0$	$-5$	$-7$	$-5$	$-20$			$\mathrm{SU}(2)[C_{10}]$
131.3.f.a	$131$	$3$	131.f	131.f	$26$	$252$	$21$	$3.569$		$_{}$	None	None		$2$	$0$	$-13$	$-15$	$-13$	$-13$			$\mathrm{SU}(2)[C_{26}]$
131.3.h.a	$131$	$3$	131.h	131.h	$130$	$1008$	$21$	$3.569$		$_{}$	None	None		$2$	$0$	$-47$	$-45$	$-47$	$-32$			$\mathrm{SU}(2)[C_{130}]$
131.4.a.a	$131$	$4$	131.a	1.a	$1$	$11$	$11$	$7.729$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-11$	$-27$	$-32$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
131.4.a.b	$131$	$4$	131.a	1.a	$1$	$21$	$21$	$7.729$		$_{}$	None	None	✓	$1$	$0$	$3$	$7$	$33$	$38$	$+$		$\mathrm{SU}(2)$
131.4.c.a	$131$	$4$	131.c	131.c	$5$	$128$	$32$	$7.729$		$_{}$	None	None		$2$	$0$	$-5$	$-1$	$-11$	$-21$			$\mathrm{SU}(2)[C_{5}]$
131.4.e.a	$131$	$4$	131.e	131.e	$13$	$384$	$32$	$7.729$		$_{}$	None	None		$2$	$0$	$-13$	$-9$	$-19$	$-19$			$\mathrm{SU}(2)[C_{13}]$
131.4.g.a	$131$	$4$	131.g	131.g	$65$	$1536$	$32$	$7.729$		$_{}$	None	None		$2$	$0$	$-47$	$-51$	$-41$	$-31$			$\mathrm{SU}(2)[C_{65}]$
131.5.b.a	$131$	$5$	131.b	131.b	$2$	$5$	$5$	$13.541$	5.5.53628125.1	$_{}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(5\beta _{1}+\beta _{4})q^{3}+2^{4}q^{4}+(-4\beta _{2}-9\beta _{3}+\cdots)q^{5}+\cdots$
131.5.b.b	$131$	$5$	131.b	131.b	$2$	$38$	$38$	$13.541$		$_{}$	None	None		$2$	$0$	$0$	$-10$	$-20$	$-52$			$\mathrm{SU}(2)[C_{2}]$
131.5.d.a	$131$	$5$	131.d	131.d	$10$	$172$	$43$	$13.541$		$_{}$	None	None		$2$	$0$	$-5$	$5$	$15$	$122$			$\mathrm{SU}(2)[C_{10}]$
131.5.f.a	$131$	$5$	131.f	131.f	$26$	$516$	$43$	$13.541$		$_{}$	None	None		$2$	$0$	$-13$	$-3$	$7$	$39$			$\mathrm{SU}(2)[C_{26}]$
131.5.h.a	$131$	$5$	131.h	131.h	$130$	$2064$	$43$	$13.541$		$_{}$	None	None		$2$	$0$	$-47$	$-57$	$-67$	$-174$			$\mathrm{SU}(2)[C_{130}]$
131.6.a.a	$131$	$6$	131.a	1.a	$1$	$22$	$22$	$21.010$		$_{}$	None	None	✓	$1$	$1$	$-9$	$-17$	$-162$	$-149$	$+$		$\mathrm{SU}(2)$
131.6.a.b	$131$	$6$	131.a	1.a	$1$	$32$	$32$	$21.010$		$_{}$	None	None	✓	$1$	$0$	$3$	$37$	$138$	$341$	$-$		$\mathrm{SU}(2)$
131.7.b.a	$131$	$7$	131.b	131.b	$2$	$5$	$5$	$30.137$	5.5.53628125.1	$_{}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+(-5\beta _{2}+\beta _{4})q^{3}+2^{6}q^{4}+(5\beta _{1}+26\beta _{3}+\cdots)q^{5}+\cdots$
131.7.b.b	$131$	$7$	131.b	131.b	$2$	$60$	$60$	$30.137$		$_{}$	None	None		$2$	$0$	$0$	$-22$	$110$	$550$			$\mathrm{SU}(2)[C_{2}]$
131.8.a.a	$131$	$8$	131.a	1.a	$1$	$33$	$33$	$40.922$		$_{}$	None	None	✓	$1$	$1$	$-9$	$-95$	$-752$	$-2587$	$-$		$\mathrm{SU}(2)$
131.8.a.b	$131$	$8$	131.a	1.a	$1$	$43$	$43$	$40.922$		$_{}$	None	None	✓	$1$	$0$	$15$	$67$	$748$	$843$	$+$		$\mathrm{SU}(2)$
131.9.b.a	$131$	$9$	131.b	131.b	$2$	$5$	$5$	$53.367$	5.5.53628125.1	$_{}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(31\beta _{2}-2\beta _{3})q^{3}+2^{8}q^{4}+(-362\beta _{1}+\cdots)q^{5}+\cdots$
131.9.b.b	$131$	$9$	131.b	131.b	$2$	$82$	$82$	$53.367$		$_{}$	None	None		$2$	$0$	$0$	$110$	$-560$	$-2352$			$\mathrm{SU}(2)[C_{2}]$
131.10.a.a	$131$	$10$	131.a	1.a	$1$	$44$	$44$	$67.470$		$_{}$	None	None	✓	$1$	$1$	$-33$	$-317$	$-3467$	$-9034$	$+$		$\mathrm{SU}(2)$
131.10.a.b	$131$	$10$	131.a	1.a	$1$	$54$	$54$	$67.470$		$_{}$	None	None	✓	$1$	$0$	$15$	$169$	$4033$	$14976$	$-$		$\mathrm{SU}(2)$
131.12.a.a	$131$	$12$	131.a	1.a	$1$	$54$	$54$	$100.653$		$_{}$	None	None	✓	$1$	$1$	$-9$	$-719$	$-26112$	$-63863$	$-$		$\mathrm{SU}(2)$
131.12.a.b	$131$	$12$	131.a	1.a	$1$	$64$	$64$	$100.653$		$_{}$	None	None	✓	$1$	$0$	$87$	$739$	$11388$	$104207$	$+$		$\mathrm{SU}(2)$
131.14.a.a	$131$	$14$	131.a	1.a	$1$	$66$	$66$	$140.473$		$_{}$	None	None	✓	$1$	$1$	$-129$	$-2057$	$-78072$	$-672249$	$+$		$\mathrm{SU}(2)$
131.14.a.b	$131$	$14$	131.a	1.a	$1$	$76$	$76$	$140.473$		$_{}$	None	None	✓	$1$	$0$	$63$	$2317$	$109428$	$504241$	$-$		$\mathrm{SU}(2)$
131.16.a.a	$131$	$16$	131.a	1.a	$1$	$76$	$76$	$186.928$		$_{}$	None	None	✓	$1$	$1$	$-345$	$-5843$	$-598697$	$-6280768$	$-$		$\mathrm{SU}(2)$
131.16.a.b	$131$	$16$	131.a	1.a	$1$	$86$	$86$	$186.928$		$_{}$	None	None	✓	$1$	$0$	$39$	$7279$	$338803$	$1954662$	$+$		$\mathrm{SU}(2)$

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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.