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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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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 (23 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1800.4.a.b	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-34$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-34q^{7}+18q^{11}-12q^{13}+106q^{17}+\cdots$
1800.4.a.d	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-24$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-24q^{7}+44q^{11}-22q^{13}+50q^{17}+\cdots$
1800.4.a.i	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-10$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-10q^{7}+14q^{11}+82q^{13}+18q^{17}+\cdots$
1800.4.a.k	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-8$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{7}-20q^{11}-22q^{13}-14q^{17}+\cdots$
1800.4.a.l	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-6q^{7}+19q^{11}+12q^{13}+75q^{17}+\cdots$
1800.4.a.m	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{7}-14q^{11}-q^{13}+46q^{17}+\cdots$
1800.4.a.n	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-72q^{11}+6q^{13}+38q^{17}+\cdots$
1800.4.a.q	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-34q^{11}+68q^{13}+38q^{17}+\cdots$
1800.4.a.u	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}+28q^{11}-2^{4}q^{13}-108q^{17}+\cdots$
1800.4.a.v	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+5q^{7}-14q^{11}+q^{13}-46q^{17}+\cdots$
1800.4.a.w	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+6q^{7}+19q^{11}-12q^{13}-75q^{17}+\cdots$
1800.4.a.y	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$10$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+10q^{7}+46q^{11}-34q^{13}-66q^{17}+\cdots$
1800.4.a.ba	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$12$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+12q^{7}+2^{6}q^{11}-58q^{13}-2^{5}q^{17}+\cdots$
1800.4.a.bb	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$16$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{7}+28q^{11}+26q^{13}-62q^{17}+\cdots$
1800.4.a.bc	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$18$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+18q^{7}-34q^{11}-12q^{13}-102q^{17}+\cdots$
1800.4.a.bd	$1800$	$4$	1800.a	1.a	$1$	$1$	$1$	$106.203$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$18$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+18q^{7}+2^{4}q^{11}+6q^{13}-6q^{17}+\cdots$
1800.4.a.bj	$1800$	$4$	1800.a	1.a	$1$	$2$	$2$	$106.203$	$\Q(\sqrt{181}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$-6$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-3-\beta )q^{7}+(-4-\beta )q^{11}+(-7+\cdots)q^{13}+\cdots$
1800.4.a.bk	$1800$	$4$	1800.a	1.a	$1$	$2$	$2$	$106.203$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-2+3\beta )q^{7}+(-20-8\beta )q^{11}+\cdots$
1800.4.a.bl	$1800$	$4$	1800.a	1.a	$1$	$2$	$2$	$106.203$	$\Q(\sqrt{129}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-3\beta )q^{7}+(-37+\beta )q^{11}+(7^{2}+\cdots)q^{13}+\cdots$
1800.4.a.bq	$1800$	$4$	1800.a	1.a	$1$	$2$	$2$	$106.203$	$\Q(\sqrt{181}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$6$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(3+\beta )q^{7}+(-4-\beta )q^{11}+(7-2\beta )q^{13}+\cdots$
1800.4.a.br	$1800$	$4$	1800.a	1.a	$1$	$3$	$3$	$106.203$	3.3.121909.1	None	✓	$1$	$1$	$0$	$0$	$0$	$-9$	$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-3+\beta _{1})q^{7}+(-3+\beta _{1}+\beta _{2})q^{11}+\cdots$
1800.4.a.bt	$1800$	$4$	1800.a	1.a	$1$	$3$	$3$	$106.203$	3.3.121909.1	None	✓	$1$	$1$	$0$	$0$	$0$	$9$	$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(3-\beta _{1})q^{7}+(-3+\beta _{1}+\beta _{2})q^{11}+\cdots$
1800.4.a.bv	$1800$	$4$	1800.a	1.a	$1$	$4$	$4$	$106.203$	$\Q(\sqrt{6}, \sqrt{46})$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{7}+(\beta _{1}-2\beta _{2})q^{11}+\cdots$

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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.