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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 154 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
495.1.h.a	$495$	$1$	495.h	55.d	$2$	$1$	$1$	$0.247$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓				55.1.d.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-q^{4}+q^{5}+q^{11}+q^{16}-q^{20}+q^{25}+\cdots$
495.1.h.b	$495$	$1$	495.h	55.d	$2$	$2$	$2$	$0.247$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None	✓	✓			495.1.h.b	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{2}+q^{4}-q^{5}-\beta q^{7}+\beta q^{10}+\cdots$
495.1.h.c	$495$	$1$	495.h	55.d	$2$	$2$	$2$	$0.247$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None	✓	✓			495.1.h.b	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta q^{2}+q^{4}+q^{5}+\beta q^{7}-\beta q^{10}+\cdots$
495.1.o.a	$495$	$1$	495.o	495.o	$6$	$2$	$1$	$0.247$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			495.1.o.a	$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
495.1.o.b	$495$	$1$	495.o	495.o	$6$	$2$	$1$	$0.247$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			495.1.o.a	$4$	$0$	$0$	$1$	$-2$	$0$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{4}-q^{5}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
495.1.bd.a	$495$	$1$	495.bd	495.ad	$12$	$4$	$1$	$0.247$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		✓			495.1.bd.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{2}q^{9}+\cdots$
495.1.bd.b	$495$	$1$	495.bd	495.ad	$12$	$4$	$1$	$0.247$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		✓			495.1.bd.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{5}q^{5}-\zeta_{12}^{2}q^{9}+\cdots$
495.2.a.a	$495$	$2$	495.a	1.a	$1$	$1$	$1$	$3.953$	$\Q$	$_{}$	None	None	✓		✓	✓	55.2.a.a	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+q^{11}+\cdots$
495.2.a.b	$495$	$2$	495.a	1.a	$1$	$2$	$2$	$3.953$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓	✓	55.2.a.b	$1$	$1$	$-2$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}-2q^{7}+\cdots$
495.2.a.c	$495$	$2$	495.a	1.a	$1$	$2$	$2$	$3.953$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				165.2.a.b	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+q^{5}+2q^{7}-\beta q^{8}+\beta q^{10}+\cdots$
495.2.a.d	$495$	$2$	495.a	1.a	$1$	$2$	$2$	$3.953$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				165.2.a.a	$1$	$0$	$2$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots$
495.2.a.e	$495$	$2$	495.a	1.a	$1$	$3$	$3$	$3.953$	3.3.148.1	$_{}$	None	None	✓		✓	✓	165.2.a.c	$1$	$0$	$1$	$0$	$-3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
495.2.a.f	$495$	$2$	495.a	1.a	$1$	$4$	$4$	$3.953$	4.4.48704.2	$_{}$	None	None	✓	✓	✓	✓	495.2.a.f	$1$	$0$	$-2$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+\cdots$
495.2.a.g	$495$	$2$	495.a	1.a	$1$	$4$	$4$	$3.953$	4.4.48704.2	$_{}$	None	None	✓	✓	✓	✓	495.2.a.f	$1$	$0$	$2$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots$
495.2.c.a	$495$	$2$	495.c	5.b	$2$	$4$	$4$	$3.953$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					55.2.b.a	$2$	$0$	$0$	$0$	$3$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
495.2.c.b	$495$	$2$	495.c	5.b	$2$	$4$	$4$	$3.953$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			495.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$
495.2.c.c	$495$	$2$	495.c	5.b	$2$	$4$	$4$	$3.953$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			495.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$
495.2.c.d	$495$	$2$	495.c	5.b	$2$	$6$	$6$	$3.953$	6.0.350464.1	$_{}$	None	None					165.2.c.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{3}-\beta _{5})q^{2}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
495.2.c.e	$495$	$2$	495.c	5.b	$2$	$6$	$6$	$3.953$	6.0.350464.1	$_{}$	None	None					165.2.c.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
495.2.d.a	$495$	$2$	495.d	165.d	$2$	$4$	$4$	$3.953$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			495.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{2}+q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots$
495.2.d.b	$495$	$2$	495.d	165.d	$2$	$4$	$4$	$3.953$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			495.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
495.2.d.c	$495$	$2$	495.d	165.d	$2$	$16$	$16$	$3.953$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-55}) $	None		✓	✓		495.2.d.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{13}q^{2}+(-2-\beta _{3})q^{4}+\beta _{7}q^{5}+\cdots$
495.2.f.a	$495$	$2$	495.f	33.d	$2$	$16$	$16$	$3.953$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	495.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(1+\beta _{1}+\beta _{5})q^{4}+\beta _{7}q^{5}+\cdots$
495.2.i.a	$495$	$2$	495.i	9.c	$3$	$2$	$1$	$3.953$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			495.2.i.a	$2$	$0$	$0$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
495.2.i.b	$495$	$2$	495.i	9.c	$3$	$2$	$1$	$3.953$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			495.2.i.b	$2$	$0$	$0$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
495.2.i.c	$495$	$2$	495.i	9.c	$3$	$16$	$8$	$3.953$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			495.2.i.c	$2$	$0$	$-3$	$0$	$-8$	$-1$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
495.2.i.d	$495$	$2$	495.i	9.c	$3$	$18$	$9$	$3.953$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			495.2.i.d	$2$	$0$	$3$	$0$	$-9$	$5$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
495.2.i.e	$495$	$2$	495.i	9.c	$3$	$20$	$10$	$3.953$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			495.2.i.e	$2$	$0$	$-3$	$0$	$10$	$7$		$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{10}+\beta _{14})q^{2}-\beta _{3}q^{3}+(-2-2\beta _{4}+\cdots)q^{4}+\cdots$
495.2.i.f	$495$	$2$	495.i	9.c	$3$	$22$	$11$	$3.953$		$_{}$	None	None		✓	✓		495.2.i.f	$2$	$0$	$3$	$0$	$11$	$-3$			$\mathrm{SU}(2)[C_{3}]$
495.2.k.a	$495$	$2$	495.k	55.e	$4$	$4$	$2$	$3.953$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None					55.2.e.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q-2\beta _{2}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{11}+\cdots$
495.2.k.b	$495$	$2$	495.k	55.e	$4$	$4$	$2$	$3.953$	$\Q(i, \sqrt{10})$	$_{}$	None	None					55.2.e.a	$4$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(2+\beta _{2})q^{5}+\beta _{3}q^{8}+\cdots$
495.2.k.c	$495$	$2$	495.k	55.e	$4$	$24$	$12$	$3.953$		$_{}$	None	None					165.2.j.a	$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
495.2.k.d	$495$	$2$	495.k	55.e	$4$	$24$	$12$	$3.953$		$_{}$	None	None		✓			495.2.k.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
495.2.l.a	$495$	$2$	495.l	15.e	$4$	$20$	$10$	$3.953$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			495.2.l.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{2}+(\beta _{12}+\beta _{14})q^{4}-\beta _{9}q^{5}+\cdots$
495.2.l.b	$495$	$2$	495.l	15.e	$4$	$20$	$10$	$3.953$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			495.2.l.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{2}+(\beta _{12}+\beta _{14})q^{4}+\beta _{9}q^{5}+\cdots$
495.2.n.a	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.13140625.1	$_{}$	None	None					165.2.m.d	$2$	$0$	$-4$	$0$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
495.2.n.b	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.819390625.1	$_{}$	None	None					165.2.m.b	$2$	$0$	$-2$	$0$	$-2$	$9$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{2}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
495.2.n.c	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	$\Q(\zeta_{15})$	$_{}$	None	None					165.2.m.c	$2$	$0$	$-2$	$0$	$2$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-2\zeta_{15}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots$
495.2.n.d	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.13140625.1	$_{}$	None	None					165.2.m.a	$2$	$0$	$0$	$0$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(-2\beta _{2}+\cdots)q^{4}+\cdots$
495.2.n.e	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.13140625.1	$_{}$	None	None					55.2.g.b	$2$	$0$	$2$	$0$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{6}-\beta _{7})q^{4}+\cdots$
495.2.n.f	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.159390625.1	$_{}$	None	None					55.2.g.a	$2$	$0$	$4$	$0$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
495.2.n.g	$495$	$2$	495.n	11.c	$5$	$16$	$4$	$3.953$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			495.2.n.g	$2$	$0$	$-2$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{1}+\beta _{3}+\beta _{5}-\beta _{10}-\beta _{14}+\cdots)q^{2}+\cdots$
495.2.n.h	$495$	$2$	495.n	11.c	$5$	$16$	$4$	$3.953$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			495.2.n.g	$2$	$0$	$2$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{1}-\beta _{3}-\beta _{5}+\beta _{10}+\beta _{14}+\cdots)q^{2}+\cdots$
495.2.p.a	$495$	$2$	495.p	99.g	$6$	$96$	$48$	$3.953$		$_{}$	None	None		✓	✓	✓	495.2.p.a	$4$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
495.2.r.a	$495$	$2$	495.r	495.r	$6$	$4$	$2$	$3.953$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			495.2.r.a	$4$	$0$	$0$	$-1$	$3$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-\beta _{1}q^{3}+(-2+2\beta _{2})q^{4}+(2\beta _{2}+\beta _{3})q^{5}+\cdots$
495.2.r.b	$495$	$2$	495.r	495.r	$6$	$4$	$2$	$3.953$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			495.2.r.a	$4$	$0$	$0$	$1$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{3}+(-2+2\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
495.2.r.c	$495$	$2$	495.r	495.r	$6$	$128$	$64$	$3.953$		$_{}$	None	None		✓	✓		495.2.r.c	$8$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
495.2.u.a	$495$	$2$	495.u	45.j	$6$	$52$	$26$	$3.953$		$_{}$	None	None		✓			495.2.u.a	$4$	$0$	$0$	$0$	$1$	$0$			$\mathrm{SU}(2)[C_{6}]$
495.2.u.b	$495$	$2$	495.u	45.j	$6$	$68$	$34$	$3.953$		$_{}$	None	None		✓	✓		495.2.u.b	$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
495.2.x.a	$495$	$2$	495.x	33.f	$10$	$64$	$16$	$3.953$		$_{}$	None	None		✓	✓	✓	495.2.x.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$

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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.