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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 (19 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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4096.2.a.a	$4096$	$2$	4096.a	1.a	$1$	$4$	$4$	$32.707$	$\Q(\zeta_{16})^+$	None	✓	$2$	$1$	$0$	$-8$	$0$	$0$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-\beta _{1}q^{5}-2\beta _{1}q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots$
4096.2.a.b	$4096$	$2$	4096.a	1.a	$1$	$4$	$4$	$32.707$	$\Q(\zeta_{16})^+$	None	✓	$2$	$0$	$0$	$0$	$0$	$-8$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{3})q^{3}+\beta _{1}q^{5}+(-2+2\beta _{2}+\cdots)q^{7}+\cdots$
4096.2.a.c	$4096$	$2$	4096.a	1.a	$1$	$4$	$4$	$32.707$	$\Q(\zeta_{16})^+$	$\Q(\sqrt{-1}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-2\beta _{1}-\beta _{3})q^{5}-3q^{9}+(3\beta _{1}+2\beta _{3})q^{13}+\cdots$
4096.2.a.d	$4096$	$2$	4096.a	1.a	$1$	$4$	$4$	$32.707$	$\Q(\zeta_{16})^+$	$\Q(\sqrt{-1}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(\beta _{1}+2\beta _{3})q^{5}-3q^{9}+(2\beta _{1}+3\beta _{3})q^{13}+\cdots$
4096.2.a.e	$4096$	$2$	4096.a	1.a	$1$	$4$	$4$	$32.707$	$\Q(\zeta_{16})^+$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{3})q^{5}-\beta _{2}q^{7}+\cdots$
4096.2.a.f	$4096$	$2$	4096.a	1.a	$1$	$4$	$4$	$32.707$	$\Q(\zeta_{16})^+$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{1}+2\beta _{3})q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots$
4096.2.a.g	$4096$	$2$	4096.a	1.a	$1$	$4$	$4$	$32.707$	$\Q(\zeta_{16})^+$	None	✓	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{3})q^{3}-\beta _{1}q^{5}+(2-2\beta _{2})q^{7}+\cdots$
4096.2.a.h	$4096$	$2$	4096.a	1.a	$1$	$4$	$4$	$32.707$	$\Q(\zeta_{16})^+$	None	✓	$2$	$1$	$0$	$8$	$0$	$0$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+\beta _{1}q^{5}-2\beta _{1}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
4096.2.a.i	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	$\Q(\zeta_{48})^+$	None	✓	$2$	$1$	$0$	$-8$	$0$	$0$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{6})q^{3}+(\beta _{2}+\beta _{5})q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots$
4096.2.a.j	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	$\Q(\zeta_{32})^+$	None	✓	$2$	$1$	$0$	$0$	$-16$	$0$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+(-2+\beta _{2}+\cdots)q^{5}+\cdots$
4096.2.a.k	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	8.8.4848615424.1	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(\beta _{3}-\beta _{7})q^{3}-\beta _{4}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
4096.2.a.l	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	$\Q(\zeta_{32})^+$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+(\beta _{3}-\beta _{6})q^{5}+\cdots$
4096.2.a.m	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	$\Q(\zeta_{32})^+$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+(-\beta _{3}+\beta _{6}+\cdots)q^{5}+\cdots$
4096.2.a.n	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	8.8.$\cdots$.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{2}+\beta _{7})q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
4096.2.a.o	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	8.8.$\cdots$.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
4096.2.a.p	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	8.8.3288334336.1	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q-\beta _{6}q^{3}+(-\beta _{2}+2\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots$
4096.2.a.q	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	8.8.4848615424.1	None	✓	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(\beta _{3}-\beta _{7})q^{3}+\beta _{4}q^{5}+(1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
4096.2.a.r	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	$\Q(\zeta_{32})^+$	None	✓	$2$	$0$	$0$	$0$	$16$	$0$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+(2-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
4096.2.a.s	$4096$	$2$	4096.a	1.a	$1$	$8$	$8$	$32.707$	$\Q(\zeta_{48})^+$	None	✓	$2$	$0$	$0$	$8$	$0$	$0$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-\beta _{2}-\beta _{4})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$

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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.