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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 (1-50 of 245 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
360.1.p.a	$360$	$1$	360.p	40.e	$2$	$1$	$1$	$0.180$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots$
360.1.p.b	$360$	$1$	360.p	40.e	$2$	$1$	$1$	$0.180$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots$
360.1.u.a	$360$	$1$	360.u	40.i	$4$	$4$	$2$	$0.180$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots$
360.2.a.a	$360$	$2$	360.a	1.a	$1$	$1$	$1$	$2.875$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots$
360.2.a.b	$360$	$2$	360.a	1.a	$1$	$1$	$1$	$2.875$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{11}+6q^{13}+6q^{17}-4q^{19}+\cdots$
360.2.a.c	$360$	$2$	360.a	1.a	$1$	$1$	$1$	$2.875$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots$
360.2.a.d	$360$	$2$	360.a	1.a	$1$	$1$	$1$	$2.875$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-2q^{11}+4q^{13}+2q^{17}+\cdots$
360.2.a.e	$360$	$2$	360.a	1.a	$1$	$1$	$1$	$2.875$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots$
360.2.b.a	$360$	$2$	360.b	24.f	$2$	$2$	$2$	$2.875$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}-q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots$
360.2.b.b	$360$	$2$	360.b	24.f	$2$	$2$	$2$	$2.875$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}+q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots$
360.2.b.c	$360$	$2$	360.b	24.f	$2$	$6$	$6$	$2.875$	6.0.2580992.1	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots$
360.2.b.d	$360$	$2$	360.b	24.f	$2$	$6$	$6$	$2.875$	6.0.2580992.1	$_{}$	None	None		$2$	$0$	$2$	$0$	$6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots$
360.2.d.a	$360$	$2$	360.d	40.f	$2$	$4$	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-30}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots$
360.2.d.b	$360$	$2$	360.d	40.f	$2$	$4$	$4$	$2.875$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots$
360.2.d.c	$360$	$2$	360.d	40.f	$2$	$4$	$4$	$2.875$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+\beta _{3}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
360.2.d.d	$360$	$2$	360.d	40.f	$2$	$4$	$4$	$2.875$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+2q^{4}+(\beta _{1}+\beta _{2})q^{5}+2\beta _{3}q^{7}+\cdots$
360.2.d.e	$360$	$2$	360.d	40.f	$2$	$6$	$6$	$2.875$	6.0.839056.1	$_{}$	None	None		$2$	$0$	$-1$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
360.2.d.f	$360$	$2$	360.d	40.f	$2$	$6$	$6$	$2.875$	6.0.839056.1	$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots$
360.2.f.a	$360$	$2$	360.f	5.b	$2$	$2$	$2$	$2.875$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots$
360.2.f.b	$360$	$2$	360.f	5.b	$2$	$2$	$2$	$2.875$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+i)q^{5}-4iq^{7}+4q^{11}-4iq^{13}+\cdots$
360.2.f.c	$360$	$2$	360.f	5.b	$2$	$2$	$2$	$2.875$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{5}-iq^{7}+4q^{11}+2iq^{13}+\cdots$
360.2.f.d	$360$	$2$	360.f	5.b	$2$	$2$	$2$	$2.875$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+i)q^{5}+4iq^{7}-4q^{11}+4iq^{13}+\cdots$
360.2.k.a	$360$	$2$	360.k	8.b	$2$	$2$	$2$	$2.875$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$-2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}-2iq^{4}+iq^{5}-4q^{7}+\cdots$
360.2.k.b	$360$	$2$	360.k	8.b	$2$	$2$	$2$	$2.875$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}-2iq^{4}+iq^{5}+2q^{7}+\cdots$
360.2.k.c	$360$	$2$	360.k	8.b	$2$	$2$	$2$	$2.875$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}+2iq^{4}+iq^{5}-4q^{7}+\cdots$
360.2.k.d	$360$	$2$	360.k	8.b	$2$	$4$	$4$	$2.875$	$\Q(i, \sqrt{7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots$
360.2.k.e	$360$	$2$	360.k	8.b	$2$	$4$	$4$	$2.875$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots$
360.2.k.f	$360$	$2$	360.k	8.b	$2$	$6$	$6$	$2.875$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{2}-\beta _{3})q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{7}+\cdots$
360.2.m.a	$360$	$2$	360.m	120.m	$2$	$4$	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots$
360.2.m.b	$360$	$2$	360.m	120.m	$2$	$4$	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots$
360.2.m.c	$360$	$2$	360.m	120.m	$2$	$16$	$16$	$2.875$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots$
360.2.q.a	$360$	$2$	360.q	9.c	$3$	$2$	$1$	$2.875$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+\cdots$
360.2.q.b	$360$	$2$	360.q	9.c	$3$	$4$	$2$	$2.875$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(-2+2\zeta_{12}+\cdots)q^{7}+\cdots$
360.2.q.c	$360$	$2$	360.q	9.c	$3$	$4$	$2$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
360.2.q.d	$360$	$2$	360.q	9.c	$3$	$6$	$3$	$2.875$	6.0.954288.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
360.2.q.e	$360$	$2$	360.q	9.c	$3$	$8$	$4$	$2.875$	8.0.856615824.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$1$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\cdots$
360.2.s.a	$360$	$2$	360.s	15.e	$4$	$4$	$2$	$2.875$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(4\zeta_{8}+4\zeta_{8}^{3})q^{11}+\cdots$
360.2.s.b	$360$	$2$	360.s	15.e	$4$	$8$	$4$	$2.875$	8.0.40960000.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{7}q^{5}+(-1-\beta _{2}-\beta _{5})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots$
360.2.w.a	$360$	$2$	360.w	40.k	$4$	$4$	$2$	$2.875$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
360.2.w.b	$360$	$2$	360.w	40.k	$4$	$4$	$2$	$2.875$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots$
360.2.w.c	$360$	$2$	360.w	40.k	$4$	$8$	$4$	$2.875$	$\Q(\zeta_{20})$	$_{}$	None	None		$4$	$0$	$2$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{20}^{7}q^{2}+\zeta_{20}q^{4}+(1+\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{5}+\cdots$
360.2.w.d	$360$	$2$	360.w	40.k	$4$	$16$	$8$	$2.875$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{15}q^{2}-\beta _{2}q^{4}+(\beta _{10}-\beta _{15})q^{5}+\cdots$
360.2.w.e	$360$	$2$	360.w	40.k	$4$	$24$	$12$	$2.875$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
360.2.x.a	$360$	$2$	360.x	120.w	$4$	$48$	$24$	$2.875$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
360.2.bd.a	$360$	$2$	360.bd	360.ad	$6$	$8$	$4$	$2.875$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{24}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots$
360.2.bd.b	$360$	$2$	360.bd	360.ad	$6$	$128$	$64$	$2.875$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
360.2.bf.a	$360$	$2$	360.bf	72.n	$6$	$4$	$2$	$2.875$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
360.2.bf.b	$360$	$2$	360.bf	72.n	$6$	$92$	$46$	$2.875$		$_{}$	None	None		$4$	$0$	$2$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{6}]$
360.2.bi.a	$360$	$2$	360.bi	45.j	$6$	$4$	$2$	$2.875$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
360.2.bi.b	$360$	$2$	360.bi	45.j	$6$	$32$	$16$	$2.875$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.