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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 (22 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	83	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5312.2.a.a	$5312$	$2$	5312.a	1.a	$1$	$1$	$1$	$42.417$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$2$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{5}+3q^{7}+6q^{9}-3q^{11}+\cdots$
5312.2.a.e	$5312$	$2$	5312.a	1.a	$1$	$1$	$1$	$42.417$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots$
5312.2.a.g	$5312$	$2$	5312.a	1.a	$1$	$1$	$1$	$42.417$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$-1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-q^{7}-2q^{9}+3q^{11}+\cdots$
5312.2.a.i	$5312$	$2$	5312.a	1.a	$1$	$1$	$1$	$42.417$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+3q^{7}-2q^{9}+q^{11}+\cdots$
5312.2.a.j	$5312$	$2$	5312.a	1.a	$1$	$1$	$1$	$42.417$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}-2q^{9}+q^{11}+4q^{13}+\cdots$
5312.2.a.k	$5312$	$2$	5312.a	1.a	$1$	$1$	$1$	$42.417$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots$
5312.2.a.m	$5312$	$2$	5312.a	1.a	$1$	$1$	$1$	$42.417$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$2$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots$
5312.2.a.q	$5312$	$2$	5312.a	1.a	$1$	$2$	$2$	$42.417$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$-3$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{7}+\cdots$
5312.2.a.r	$5312$	$2$	5312.a	1.a	$1$	$2$	$2$	$42.417$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$-1$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{3}-\beta q^{5}+(1-\beta )q^{7}+(1+4\beta )q^{9}+\cdots$
5312.2.a.s	$5312$	$2$	5312.a	1.a	$1$	$2$	$2$	$42.417$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+\beta q^{5}+(3+\beta )q^{7}-2\beta q^{9}+\cdots$
5312.2.a.v	$5312$	$2$	5312.a	1.a	$1$	$2$	$2$	$42.417$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$2$	$-3$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+(-2+\beta )q^{5}+(-1-\beta )q^{7}+\cdots$
5312.2.a.x	$5312$	$2$	5312.a	1.a	$1$	$2$	$2$	$42.417$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$-6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}+(-3+\beta )q^{7}+2\beta q^{9}+\cdots$
5312.2.a.ba	$5312$	$2$	5312.a	1.a	$1$	$3$	$3$	$42.417$	3.3.148.1	None	✓	$1$	$1$	$0$	$-1$	$4$	$-5$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{1}+2\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
5312.2.a.be	$5312$	$2$	5312.a	1.a	$1$	$4$	$4$	$42.417$	4.4.15529.1	None	✓	$1$	$1$	$0$	$-3$	$0$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{3})q^{7}+\cdots$
5312.2.a.bf	$5312$	$2$	5312.a	1.a	$1$	$4$	$4$	$42.417$	4.4.2225.1	None	✓	$1$	$1$	$0$	$-2$	$-1$	$5$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-\beta _{1}q^{5}+(1+\beta _{1})q^{7}+\cdots$
5312.2.a.bg	$5312$	$2$	5312.a	1.a	$1$	$4$	$4$	$42.417$	4.4.2225.1	None	✓	$1$	$1$	$0$	$2$	$-1$	$-5$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}-\beta _{1}q^{5}+(-1-\beta _{1})q^{7}+\cdots$
5312.2.a.bi	$5312$	$2$	5312.a	1.a	$1$	$5$	$5$	$42.417$	5.5.265504.1	None	✓	$1$	$1$	$0$	$-3$	$-2$	$-3$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{3}-\beta _{3}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
5312.2.a.bk	$5312$	$2$	5312.a	1.a	$1$	$5$	$5$	$42.417$	5.5.356173.1	None	✓	$1$	$1$	$0$	$2$	$1$	$-7$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{2}+\beta _{4})q^{5}+(-1+\beta _{4})q^{7}+\cdots$
5312.2.a.bn	$5312$	$2$	5312.a	1.a	$1$	$6$	$6$	$42.417$	6.6.9059636.1	None	✓	$1$	$1$	$0$	$-1$	$-2$	$3$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(-1-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+\cdots$
5312.2.a.bo	$5312$	$2$	5312.a	1.a	$1$	$6$	$6$	$42.417$	6.6.9059636.1	None	✓	$1$	$1$	$0$	$1$	$-2$	$-3$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-1-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+\cdots$
5312.2.a.bq	$5312$	$2$	5312.a	1.a	$1$	$8$	$8$	$42.417$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$1$	$-10$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-1-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
5312.2.a.bu	$5312$	$2$	5312.a	1.a	$1$	$11$	$11$	$42.417$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$0$	$-1$	$-5$	$-10$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-1-\beta _{10})q^{7}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.