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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 122 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
440.1.o.a	$440$	$1$	440.o	440.o	$2$	$1$	$1$	$0.220$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓	✓			440.1.o.a	$2$	$0$	$-1$	$-1$	$1$	$1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
440.1.o.b	$440$	$1$	440.o	440.o	$2$	$1$	$1$	$0.220$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓	✓			440.1.o.a	$2$	$0$	$-1$	$1$	$-1$	$1$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
440.1.o.c	$440$	$1$	440.o	440.o	$2$	$1$	$1$	$0.220$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓	✓			440.1.o.a	$2$	$0$	$1$	$-1$	$1$	$-1$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
440.1.o.d	$440$	$1$	440.o	440.o	$2$	$1$	$1$	$0.220$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓	✓			440.1.o.a	$2$	$0$	$1$	$1$	$-1$	$-1$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
440.1.o.e	$440$	$1$	440.o	440.o	$2$	$4$	$4$	$0.220$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		✓	✓		440.1.o.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
440.1.bh.a	$440$	$1$	440.bh	440.ah	$10$	$4$	$1$	$0.220$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-10}) $	None		✓			440.1.bh.a	$4$	$0$	$-1$	$0$	$-1$	$3$		$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(1+\cdots)q^{7}+\cdots$
440.1.bh.b	$440$	$1$	440.bh	440.ah	$10$	$4$	$1$	$0.220$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-10}) $	None		✓			440.1.bh.a	$4$	$0$	$1$	$0$	$1$	$-3$		$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+(-1+\cdots)q^{7}+\cdots$
440.2.a.a	$440$	$2$	440.a	1.a	$1$	$1$	$1$	$3.513$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	440.2.a.a	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-3q^{9}-q^{11}-8q^{19}+\cdots$
440.2.a.b	$440$	$2$	440.a	1.a	$1$	$1$	$1$	$3.513$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	440.2.a.b	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-3q^{9}+q^{11}-4q^{13}+\cdots$
440.2.a.c	$440$	$2$	440.a	1.a	$1$	$1$	$1$	$3.513$	$\Q$	$_{}$	None	None	✓	✓			440.2.a.c	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}-3q^{9}-q^{11}+6q^{13}+\cdots$
440.2.a.d	$440$	$2$	440.a	1.a	$1$	$1$	$1$	$3.513$	$\Q$	$_{}$	None	None	✓	✓			440.2.a.d	$1$	$0$	$0$	$3$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+q^{7}+6q^{9}-q^{11}-6q^{13}+\cdots$
440.2.a.e	$440$	$2$	440.a	1.a	$1$	$2$	$2$	$3.513$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	440.2.a.e	$1$	$0$	$0$	$-1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}-\beta q^{7}+(1+\beta )q^{9}+q^{11}+\cdots$
440.2.a.f	$440$	$2$	440.a	1.a	$1$	$2$	$2$	$3.513$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	440.2.a.f	$1$	$0$	$0$	$1$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots$
440.2.a.g	$440$	$2$	440.a	1.a	$1$	$2$	$2$	$3.513$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	440.2.a.g	$1$	$0$	$0$	$1$	$-2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots$
440.2.b.a	$440$	$2$	440.b	5.b	$2$	$2$	$2$	$3.513$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			440.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(\beta-1)q^{5}+\beta q^{7}-q^{9}+\cdots$
440.2.b.b	$440$	$2$	440.b	5.b	$2$	$2$	$2$	$3.513$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			440.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(-\beta+1)q^{5}-2\beta q^{7}-q^{9}+\cdots$
440.2.b.c	$440$	$2$	440.b	5.b	$2$	$2$	$2$	$3.513$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			440.2.b.c	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(i+2)q^{5}+i q^{7}+2 q^{9}+\cdots$
440.2.b.d	$440$	$2$	440.b	5.b	$2$	$8$	$8$	$3.513$	8.0.$\cdots$.2	$_{}$	None	None		✓	✓		440.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots$
440.2.c.a	$440$	$2$	440.c	440.c	$2$	$4$	$4$	$3.513$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-10}) $	None		✓			440.2.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}+\beta _{3}q^{5}-2\beta _{1}q^{7}+\cdots$
440.2.c.b	$440$	$2$	440.c	440.c	$2$	$8$	$8$	$3.513$	8.0.$\cdots$.19	$_{}$	$\Q(\sqrt{-55}) $	None		✓			440.2.c.b	$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{2}-\beta _{5})q^{5}+\cdots$
440.2.c.c	$440$	$2$	440.c	440.c	$2$	$56$	$56$	$3.513$		$_{}$	None	None		✓	✓		440.2.c.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
440.2.g.a	$440$	$2$	440.g	8.b	$2$	$4$	$4$	$3.513$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			440.2.g.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{3} q^{2}+(\beta_{2}-\beta_1)q^{3}+2 q^{4}+\cdots$
440.2.g.b	$440$	$2$	440.g	8.b	$2$	$12$	$12$	$3.513$	12.0.$\cdots$.1	$_{}$	None	None		✓			440.2.g.b	$2$	$0$	$0$	$0$	$0$	$4$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+(\beta _{1}+\beta _{3})q^{3}-\beta _{5}q^{4}-\beta _{8}q^{5}+\cdots$
440.2.g.c	$440$	$2$	440.g	8.b	$2$	$24$	$24$	$3.513$		$_{}$	None	None		✓	✓		440.2.g.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
440.2.l.a	$440$	$2$	440.l	40.f	$2$	$2$	$2$	$3.513$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			440.2.l.a	$2$	$1$	$-2$	$-4$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i-1)q^{2}-2 q^{3}-2 i q^{4}+(-2 i-1)q^{5}+\cdots$
440.2.l.b	$440$	$2$	440.l	40.f	$2$	$2$	$2$	$3.513$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			440.2.l.a	$2$	$0$	$2$	$4$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+1)q^{2}+2 q^{3}+2 i q^{4}+(2 i+1)q^{5}+\cdots$
440.2.l.c	$440$	$2$	440.l	40.f	$2$	$56$	$56$	$3.513$		$_{}$	None	None		✓	✓		440.2.l.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
440.2.p.a	$440$	$2$	440.p	88.g	$2$	$48$	$48$	$3.513$		$_{}$	None	None		✓	✓	✓	440.2.p.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
440.2.r.a	$440$	$2$	440.r	40.k	$4$	$2$	$1$	$3.513$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			440.2.r.a	$2$	$1$	$-2$	$-2$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}+(i-1)q^{3}-2 i q^{4}+\cdots$
440.2.r.b	$440$	$2$	440.r	40.k	$4$	$2$	$1$	$3.513$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			440.2.r.b	$2$	$1$	$-2$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+(i-1)q^{3}+2 i q^{4}+\cdots$
440.2.r.c	$440$	$2$	440.r	40.k	$4$	$2$	$1$	$3.513$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			440.2.r.b	$2$	$0$	$-2$	$-2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+(i-1)q^{3}+2 i q^{4}+\cdots$
440.2.r.d	$440$	$2$	440.r	40.k	$4$	$2$	$1$	$3.513$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			440.2.r.a	$2$	$0$	$2$	$-2$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{2}+(i-1)q^{3}-2 i q^{4}+\cdots$
440.2.r.e	$440$	$2$	440.r	40.k	$4$	$4$	$2$	$3.513$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			440.2.r.e	$2$	$0$	$0$	$-4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$
440.2.r.f	$440$	$2$	440.r	40.k	$4$	$4$	$2$	$3.513$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			440.2.r.e	$2$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots$
440.2.r.g	$440$	$2$	440.r	40.k	$4$	$48$	$24$	$3.513$		$_{}$	None	None		✓			440.2.r.g	$4$	$0$	$0$	$12$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
440.2.r.h	$440$	$2$	440.r	40.k	$4$	$56$	$28$	$3.513$		$_{}$	None	None		✓	✓		440.2.r.h	$4$	$0$	$4$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
440.2.t.a	$440$	$2$	440.t	440.t	$4$	$4$	$2$	$3.513$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			440.2.t.a	$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots$
440.2.t.b	$440$	$2$	440.t	440.t	$4$	$4$	$2$	$3.513$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			440.2.t.a	$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
440.2.t.c	$440$	$2$	440.t	440.t	$4$	$128$	$64$	$3.513$		$_{}$	None	None		✓	✓		440.2.t.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
440.2.v.a	$440$	$2$	440.v	55.e	$4$	$4$	$2$	$3.513$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			440.2.v.a	$4$	$0$	$0$	$4$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_1+1)q^{3}+(-\beta_1-2)q^{5}+(2\beta_{3}+2\beta_{2})q^{7}+\cdots$
440.2.v.b	$440$	$2$	440.v	55.e	$4$	$32$	$16$	$3.513$		$_{}$	None	None		✓	✓		440.2.v.b	$4$	$0$	$0$	$-4$	$8$	$0$			$\mathrm{SU}(2)[C_{4}]$
440.2.y.a	$440$	$2$	440.y	11.c	$5$	$8$	$2$	$3.513$	8.0.13140625.1	$_{}$	None	None		✓			440.2.y.a	$2$	$0$	$0$	$1$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}-\beta _{5})q^{3}+\beta _{7}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
440.2.y.b	$440$	$2$	440.y	11.c	$5$	$12$	$3$	$3.513$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			440.2.y.b	$2$	$0$	$0$	$-1$	$3$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{4})q^{3}+(1-\beta _{6}+\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots$
440.2.y.c	$440$	$2$	440.y	11.c	$5$	$12$	$3$	$3.513$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			440.2.y.c	$2$	$0$	$0$	$-1$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{3}+\beta _{8})q^{3}-\beta _{6}q^{5}+(1+\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots$
440.2.y.d	$440$	$2$	440.y	11.c	$5$	$16$	$4$	$3.513$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		440.2.y.d	$2$	$0$	$0$	$-3$	$-4$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots$
440.2.z.a	$440$	$2$	440.z	88.k	$10$	$192$	$48$	$3.513$		$_{}$	None	None		✓	✓	✓	440.2.z.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
440.2.bd.a	$440$	$2$	440.bd	440.ad	$10$	$272$	$68$	$3.513$		$_{}$	None	None		✓	✓	✓	440.2.bd.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
440.2.bi.a	$440$	$2$	440.bi	88.o	$10$	$8$	$2$	$3.513$	$\Q(\zeta_{20})$	$_{}$	None	None		✓			440.2.bi.a	$4$	$0$	$-2$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots$
440.2.bi.b	$440$	$2$	440.bi	88.o	$10$	$8$	$2$	$3.513$	$\Q(\zeta_{20})$	$_{}$	None	None		✓			440.2.bi.b	$4$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots$
440.2.bi.c	$440$	$2$	440.bi	88.o	$10$	$176$	$44$	$3.513$		$_{}$	None	None		✓	✓		440.2.bi.c	$4$	$0$	$8$	$0$	$0$	$18$			$\mathrm{SU}(2)[C_{10}]$

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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.