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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 (38 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
3808.1.e.a	$3808$	$1$	3808.e	952.e	$2$	$1$	$1$	$1.900$	$\Q$	$D_{2}$	$\Q(\sqrt{-119})$ , $\Q(\sqrt{-238})$	$\Q(\sqrt{2})$	✓				952.1.e.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-q^{7}+q^{9}-q^{17}+q^{25}+2q^{31}+\cdots$
3808.1.e.b	$3808$	$1$	3808.e	952.e	$2$	$1$	$1$	$1.900$	$\Q$	$D_{2}$	$\Q(\sqrt{-119})$ , $\Q(\sqrt{-238})$	$\Q(\sqrt{2})$	✓				952.1.e.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{7}+q^{9}+q^{17}+q^{25}-2q^{31}+\cdots$
3808.1.e.c	$3808$	$1$	3808.e	952.e	$2$	$4$	$4$	$1.900$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119})$	None					952.1.e.c	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$		$q+(-\zeta_{10}-\zeta_{10}^{4})q^{3}+(-\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
3808.1.e.d	$3808$	$1$	3808.e	952.e	$2$	$4$	$4$	$1.900$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119})$	None					952.1.e.c	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{3}+(\zeta_{10}^{2}+\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
3808.1.n.a	$3808$	$1$	3808.n	119.d	$2$	$8$	$8$	$1.900$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-17})$	None		✓	✓	✓	3808.1.n.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{3}-\zeta_{16}q^{7}+(1-\zeta_{16}^{2}+\cdots)q^{9}+\cdots$
3808.1.bq.a	$3808$	$1$	3808.bq	119.h	$6$	$16$	$8$	$1.900$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-17})$	None		✓	✓	✓	3808.1.bq.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{48}^{15}-\zeta_{48}^{17})q^{3}-\zeta_{48}^{3}q^{7}+\cdots$
3808.1.by.a	$3808$	$1$	3808.by	952.ai	$6$	$2$	$1$	$1.900$	$\Q(\sqrt{-3})$	$D_{3}$	$\Q(\sqrt{-34})$	None					952.1.bi.a	$4$	$0$	$0$	$0$	$-1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{17}+\cdots$
3808.1.by.b	$3808$	$1$	3808.by	952.ai	$6$	$2$	$1$	$1.900$	$\Q(\sqrt{-3})$	$D_{3}$	$\Q(\sqrt{-34})$	None					952.1.bi.a	$4$	$0$	$0$	$0$	$1$	$1$		$1$		$q-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{17}+\cdots$
3808.1.by.c	$3808$	$1$	3808.by	952.ai	$6$	$4$	$2$	$1.900$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-34})$	None			✓		952.1.bi.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{2}q^{9}+\cdots$
3808.1.cu.a	$3808$	$1$	3808.cu	3808.bu	$8$	$4$	$1$	$1.900$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-119})$	None		✓			3808.1.cu.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
3808.1.cu.b	$3808$	$1$	3808.cu	3808.bu	$8$	$4$	$1$	$1.900$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-119})$	None		✓			3808.1.cu.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
3808.1.cu.c	$3808$	$1$	3808.cu	3808.bu	$8$	$16$	$4$	$1.900$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-119})$	None		✓			3808.1.cu.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}q^{2}+(-\zeta_{40}^{6}-\zeta_{40}^{19})q^{3}+\cdots$
3808.1.cu.d	$3808$	$1$	3808.cu	3808.bu	$8$	$16$	$4$	$1.900$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-119})$	None		✓			3808.1.cu.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{40}q^{2}+(\zeta_{40}^{6}-\zeta_{40}^{19})q^{3}+\zeta_{40}^{2}q^{4}+\cdots$
3808.2.a.a	$3808$	$2$	3808.a	1.a	$1$	$1$	$1$	$30.407$	$\Q$	$_{}$	None	None	✓	✓			3808.2.a.a	$1$	$1$	$0$	$-2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{7}+q^{9}-6q^{11}+6q^{13}+\cdots$
3808.2.a.b	$3808$	$2$	3808.a	1.a	$1$	$1$	$1$	$30.407$	$\Q$	$_{}$	None	None	✓	✓			3808.2.a.a	$1$	$0$	$0$	$2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{7}+q^{9}+6q^{11}+6q^{13}+\cdots$
3808.2.a.c	$3808$	$2$	3808.a	1.a	$1$	$4$	$4$	$30.407$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	✓			3808.2.a.c	$1$	$1$	$0$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{1})q^{5}-q^{7}+\beta _{2}q^{9}+\cdots$
3808.2.a.d	$3808$	$2$	3808.a	1.a	$1$	$4$	$4$	$30.407$	$\Q(\zeta_{20})^+$	$_{}$	None	None	✓	✓			3808.2.a.c	$1$	$1$	$0$	$0$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{1})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots$
3808.2.a.e	$3808$	$2$	3808.a	1.a	$1$	$5$	$5$	$30.407$	5.5.804272.1	$_{}$	None	None	✓	✓			3808.2.a.e	$1$	$0$	$0$	$0$	$-2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
3808.2.a.f	$3808$	$2$	3808.a	1.a	$1$	$5$	$5$	$30.407$	5.5.804272.1	$_{}$	None	None	✓	✓			3808.2.a.e	$1$	$1$	$0$	$0$	$-2$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
3808.2.a.g	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.147697840.1	$_{}$	None	None	✓	✓	✓		3808.2.a.g	$1$	$1$	$0$	$-4$	$-4$	$6$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1-\beta _{5})q^{5}+q^{7}+\cdots$
3808.2.a.h	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.109859312.1	$_{}$	None	None	✓	✓			3808.2.a.h	$1$	$1$	$0$	$-4$	$4$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{5})q^{3}+(1-\beta _{1})q^{5}-q^{7}+\cdots$
3808.2.a.i	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.80686992.1	$_{}$	None	None	✓	✓	✓		3808.2.a.i	$1$	$1$	$0$	$-2$	$-6$	$6$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{4})q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
3808.2.a.j	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.4022000.1	$_{}$	None	None	✓	✓	✓		3808.2.a.j	$1$	$1$	$0$	$-2$	$2$	$-6$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}-\beta _{1}q^{5}-q^{7}+(1-\beta _{5})q^{9}+\cdots$
3808.2.a.k	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.93059344.1	$_{}$	None	None	✓	✓	✓		3808.2.a.k	$1$	$0$	$0$	$0$	$4$	$-6$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{5})q^{5}-q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots$
3808.2.a.l	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.93059344.1	$_{}$	None	None	✓	✓			3808.2.a.k	$1$	$0$	$0$	$0$	$4$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{5})q^{5}+q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots$
3808.2.a.m	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.80686992.1	$_{}$	None	None	✓	✓			3808.2.a.i	$1$	$1$	$0$	$2$	$-6$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{4})q^{5}-q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
3808.2.a.n	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.4022000.1	$_{}$	None	None	✓	✓			3808.2.a.j	$1$	$0$	$0$	$2$	$2$	$6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}-\beta _{1}q^{5}+q^{7}+(1-\beta _{5})q^{9}+\cdots$
3808.2.a.o	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.147697840.1	$_{}$	None	None	✓	✓			3808.2.a.g	$1$	$0$	$0$	$4$	$-4$	$-6$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1-\beta _{5})q^{5}-q^{7}+\cdots$
3808.2.a.p	$3808$	$2$	3808.a	1.a	$1$	$6$	$6$	$30.407$	6.6.109859312.1	$_{}$	None	None	✓	✓			3808.2.a.h	$1$	$0$	$0$	$4$	$4$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{5})q^{3}+(1-\beta _{1})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots$
3808.2.a.q	$3808$	$2$	3808.a	1.a	$1$	$8$	$8$	$30.407$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		3808.2.a.q	$1$	$0$	$0$	$-2$	$6$	$-8$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}+(1+\beta _{5})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
3808.2.a.r	$3808$	$2$	3808.a	1.a	$1$	$8$	$8$	$30.407$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		3808.2.a.q	$1$	$0$	$0$	$2$	$6$	$8$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{3}+(1+\beta _{5})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
3808.2.b.a	$3808$	$2$	3808.b	8.b	$2$	$2$	$2$	$30.407$	$\Q(\sqrt{-2})$	$_{}$	None	None					952.2.b.c	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{3}+2\beta q^{5}-q^{7}-5q^{9}+\beta q^{11}+\cdots$
3808.2.b.b	$3808$	$2$	3808.b	8.b	$2$	$2$	$2$	$30.407$	$\Q(\sqrt{-2})$	$_{}$	None	None					952.2.b.a	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+\beta q^{5}-q^{7}+q^{9}-4\beta q^{11}+\cdots$
3808.2.b.c	$3808$	$2$	3808.b	8.b	$2$	$2$	$2$	$30.407$	$\Q(\sqrt{-2})$	$_{}$	None	None					952.2.b.b	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{7}+3q^{9}+\beta q^{11}+3\beta q^{13}+q^{17}+\cdots$
3808.2.b.d	$3808$	$2$	3808.b	8.b	$2$	$16$	$16$	$30.407$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					952.2.b.d	$2$	$0$	$0$	$0$	$0$	$-16$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}-\beta _{9}q^{5}-q^{7}+\beta _{13}q^{9}+\beta _{1}q^{11}+\cdots$
3808.2.b.e	$3808$	$2$	3808.b	8.b	$2$	$16$	$16$	$30.407$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					952.2.b.e	$2$	$0$	$0$	$0$	$0$	$16$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{8}q^{5}+q^{7}+(-1+\beta _{7}+\cdots)q^{9}+\cdots$
3808.2.b.f	$3808$	$2$	3808.b	8.b	$2$	$28$	$28$	$30.407$		$_{}$	None	None					952.2.b.f	$2$	$0$	$0$	$0$	$0$	$28$			$\mathrm{SU}(2)[C_{2}]$
3808.2.b.g	$3808$	$2$	3808.b	8.b	$2$	$30$	$30$	$30.407$		$_{}$	None	None			✓		952.2.b.g	$2$	$0$	$0$	$0$	$0$	$-30$			$\mathrm{SU}(2)[C_{2}]$

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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.