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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 (46 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
2888.1.f.a	$2888$	$1$	2888.f	8.d	$2$	$1$	$1$	$1.441$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots$
2888.1.f.b	$2888$	$1$	2888.f	8.d	$2$	$1$	$1$	$1.441$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots$
2888.1.f.c	$2888$	$1$	2888.f	8.d	$2$	$3$	$3$	$1.441$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-3$	$0$	$0$	$0$		$1$		$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{8}+\cdots$
2888.1.f.d	$2888$	$1$	2888.f	8.d	$2$	$3$	$3$	$1.441$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$3$	$0$	$0$	$0$		$1$		$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{8}+\cdots$
2888.1.k.a	$2888$	$1$	2888.k	152.k	$6$	$2$	$1$	$1.441$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
2888.1.k.b	$2888$	$1$	2888.k	152.k	$6$	$6$	$3$	$1.441$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$		$3$		$q-\zeta_{18}^{3}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
2888.1.k.c	$2888$	$1$	2888.k	152.k	$6$	$6$	$3$	$1.441$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$3$	$0$	$0$	$0$		$3$		$q+\zeta_{18}^{3}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots$
2888.1.l.a	$2888$	$1$	2888.l	152.l	$6$	$2$	$1$	$1.441$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-1$	$1$	$0$	$-2$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
2888.1.l.b	$2888$	$1$	2888.l	152.l	$6$	$2$	$1$	$1.441$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$1$	$-1$	$0$	$-2$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
2888.1.s.a	$2888$	$1$	2888.s	152.s	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-38}) $	None		$12$	$0$	$0$	$0$	$0$	$3$		$1$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$
2888.1.s.b	$2888$	$1$	2888.s	152.s	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-38}) $	None		$12$	$0$	$0$	$0$	$0$	$3$		$1$		$q+\zeta_{18}^{5}q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$
2888.1.u.a	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-6$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{2}+(-1-\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots$
2888.1.u.b	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{2}+(-\zeta_{18}-\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots$
2888.1.u.c	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-2}) $	None		$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$
2888.1.u.d	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-2}) $	None		$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$
2888.1.u.e	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{2}+(-\zeta_{18}^{6}+\zeta_{18}^{7})q^{3}+\cdots$
2888.1.u.f	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{2}+(\zeta_{18}+\zeta_{18}^{3})q^{3}-\zeta_{18}q^{4}+\cdots$
2888.1.u.g	$2888$	$1$	2888.u	152.u	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$6$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{2}+(1+\zeta_{18}^{4})q^{3}-\zeta_{18}q^{4}+\cdots$
2888.1.bb.a	$2888$	$1$	2888.bb	2888.ab	$38$	$18$	$1$	$1.441$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$17$	$0$	$0$		$1$		$q-\zeta_{38}^{3}q^{2}+(1-\zeta_{38}^{17})q^{3}+\zeta_{38}^{6}q^{4}+\cdots$
2888.1.bm.a	$2888$	$1$	2888.bm	2888.am	$114$	$36$	$1$	$1.441$	$\Q(\zeta_{57})$	$D_{57}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-20$	$0$	$0$		$1$		$q-\zeta_{114}^{25}q^{2}+(-\zeta_{114}^{15}+\zeta_{114}^{38}+\cdots)q^{3}+\cdots$
2888.1.bs.a	$2888$	$1$	2888.bs	2888.as	$342$	$108$	$1$	$1.441$	$\Q(\zeta_{171})$	$D_{171}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q+\zeta_{342}^{70}q^{2}+(\zeta_{342}^{152}+\zeta_{342}^{156})q^{3}+\cdots$
2888.2.a.a	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}-2q^{9}+3q^{11}-2q^{13}+\cdots$
2888.2.a.b	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots$
2888.2.a.c	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{9}-4q^{11}+5q^{13}+\cdots$
2888.2.a.d	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-2q^{9}+3q^{11}+2q^{13}+\cdots$
2888.2.a.e	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-2q^{9}-4q^{11}-5q^{13}+\cdots$
2888.2.a.f	$2888$	$2$	2888.a	1.a	$1$	$1$	$1$	$23.061$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots$
2888.2.a.g	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{3}+(2+\beta )q^{5}-2q^{7}+(1+4\beta )q^{9}+\cdots$
2888.2.a.h	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots$
2888.2.a.i	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2\beta q^{5}+(3-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
2888.2.a.j	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots$
2888.2.a.k	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{5}+(3-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
2888.2.a.l	$2888$	$2$	2888.a	1.a	$1$	$2$	$2$	$23.061$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+(2+\beta )q^{5}-2q^{7}+(1+4\beta )q^{9}+\cdots$
2888.2.a.m	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-2\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots$
2888.2.a.n	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
2888.2.a.o	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	3.3.961.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots$
2888.2.a.p	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots$
2888.2.a.q	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots$
2888.2.a.r	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
2888.2.a.s	$2888$	$2$	2888.a	1.a	$1$	$3$	$3$	$23.061$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+2\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots$
2888.2.a.t	$2888$	$2$	2888.a	1.a	$1$	$6$	$6$	$23.061$	6.6.3022625.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$2$	$-2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
2888.2.a.u	$2888$	$2$	2888.a	1.a	$1$	$6$	$6$	$23.061$	6.6.3022625.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$2$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
2888.2.a.v	$2888$	$2$	2888.a	1.a	$1$	$8$	$8$	$23.061$	8.8.$\cdots$.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-6$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
2888.2.a.w	$2888$	$2$	2888.a	1.a	$1$	$8$	$8$	$23.061$	8.8.$\cdots$.1	$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
2888.2.a.x	$2888$	$2$	2888.a	1.a	$1$	$9$	$9$	$23.061$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$3$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(1+\beta _{6})q^{7}+\cdots$
2888.2.a.y	$2888$	$2$	2888.a	1.a	$1$	$9$	$9$	$23.061$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$3$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(1+\beta _{6})q^{7}+\cdots$

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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.