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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 201 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
272.1.g.a	$272$	$1$	272.g	68.d	$2$	$2$	$2$	$0.136$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-17}) $	None	✓	✓	✓	✓	272.1.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}+\beta q^{7}+q^{9}+\beta q^{11}-q^{17}+\cdots$
272.1.u.a	$272$	$1$	272.u	68.g	$8$	$4$	$1$	$0.136$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	272.1.u.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{13}+\cdots$
272.2.a.a	$272$	$2$	272.a	1.a	$1$	$1$	$1$	$2.172$	$\Q$	$_{}$	None	None	✓		✓	✓	136.2.a.b	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-2q^{11}-6q^{13}-q^{17}+\cdots$
272.2.a.b	$272$	$2$	272.a	1.a	$1$	$1$	$1$	$2.172$	$\Q$	$_{}$	None	None	✓		✓	✓	17.2.a.a	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-3q^{9}-2q^{13}+q^{17}+\cdots$
272.2.a.c	$272$	$2$	272.a	1.a	$1$	$1$	$1$	$2.172$	$\Q$	$_{}$	None	None	✓				136.2.a.a	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots$
272.2.a.d	$272$	$2$	272.a	1.a	$1$	$1$	$1$	$2.172$	$\Q$	$_{}$	None	None	✓				34.2.a.a	$1$	$0$	$0$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots$
272.2.a.e	$272$	$2$	272.a	1.a	$1$	$2$	$2$	$2.172$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		68.2.a.a	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+2\beta q^{5}+(1-\beta )q^{7}+\cdots$
272.2.a.f	$272$	$2$	272.a	1.a	$1$	$2$	$2$	$2.172$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		136.2.a.c	$1$	$0$	$0$	$2$	$4$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+2q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
272.2.b.a	$272$	$2$	272.b	17.b	$2$	$2$	$2$	$2.172$	$\Q(\sqrt{-2}) $	$_{}$	None	None					34.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+\beta q^{5}-5q^{9}-\beta q^{11}+2q^{13}+\cdots$
272.2.b.b	$272$	$2$	272.b	17.b	$2$	$2$	$2$	$2.172$	$\Q(\sqrt{-1}) $	$_{}$	None	None					136.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+\beta q^{7}-q^{9}+\beta q^{11}-2 q^{13}+\cdots$
272.2.b.c	$272$	$2$	272.b	17.b	$2$	$2$	$2$	$2.172$	$\Q(\sqrt{-2}) $	$_{}$	None	None					68.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-2\beta q^{5}-3\beta q^{7}+q^{9}-\beta q^{11}+\cdots$
272.2.b.d	$272$	$2$	272.b	17.b	$2$	$2$	$2$	$2.172$	$\Q(\sqrt{-2}) $	$_{}$	None	None					136.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-\beta q^{7}+3q^{9}+2\beta q^{11}+2q^{13}+\cdots$
272.2.j.a	$272$	$2$	272.j	272.j	$4$	$68$	$34$	$2.172$		$_{}$	None	None		✓	✓	✓	272.2.j.a	$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
272.2.l.a	$272$	$2$	272.l	16.e	$4$	$2$	$1$	$2.172$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			272.2.l.a	$2$	$0$	$-2$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+(-i+1)q^{3}+2 i q^{4}+\cdots$
272.2.l.b	$272$	$2$	272.l	16.e	$4$	$30$	$15$	$2.172$		$_{}$	None	None		✓			272.2.l.b	$2$	$0$	$2$	$-2$	$-2$	$0$			$\mathrm{SU}(2)[C_{4}]$
272.2.l.c	$272$	$2$	272.l	16.e	$4$	$32$	$16$	$2.172$		$_{}$	None	None		✓	✓		272.2.l.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
272.2.o.a	$272$	$2$	272.o	17.c	$4$	$2$	$1$	$2.172$	$\Q(\sqrt{-1}) $	$_{}$	None	None					136.2.k.d	$2$	$1$	$0$	$-4$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i-2)q^{3}+(-i-1)q^{5}+(2 i-2)q^{7}+\cdots$
272.2.o.b	$272$	$2$	272.o	17.c	$4$	$2$	$1$	$2.172$	$\Q(\sqrt{-1}) $	$_{}$	None	None					136.2.k.c	$2$	$0$	$0$	$-2$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{3}+(i+1)q^{5}+(-i+1)q^{7}+\cdots$
272.2.o.c	$272$	$2$	272.o	17.c	$4$	$2$	$1$	$2.172$	$\Q(\sqrt{-1}) $	$_{}$	None	None					34.2.c.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{5}-3 i q^{9}+(-4 i+4)q^{11}+\cdots$
272.2.o.d	$272$	$2$	272.o	17.c	$4$	$2$	$1$	$2.172$	$\Q(\sqrt{-1}) $	$_{}$	None	None					136.2.k.a	$2$	$0$	$0$	$2$	$-6$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(-3 i-3)q^{5}+(-3 i+3)q^{7}+\cdots$
272.2.o.e	$272$	$2$	272.o	17.c	$4$	$2$	$1$	$2.172$	$\Q(\sqrt{-1}) $	$_{}$	None	None					136.2.k.b	$2$	$0$	$0$	$2$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(2 i+2)q^{5}+(2 i-2)q^{7}+\cdots$
272.2.o.f	$272$	$2$	272.o	17.c	$4$	$2$	$1$	$2.172$	$\Q(\sqrt{-1}) $	$_{}$	None	None					34.2.c.a	$2$	$0$	$0$	$2$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(2 i+2)q^{5}+(-2 i+2)q^{7}+\cdots$
272.2.o.g	$272$	$2$	272.o	17.c	$4$	$4$	$2$	$2.172$	$\Q(i, \sqrt{13})$	$_{}$	None	None			✓		68.2.e.a	$2$	$0$	$0$	$2$	$-4$	$-2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1})q^{5}+\cdots$
272.2.r.a	$272$	$2$	272.r	272.r	$4$	$68$	$34$	$2.172$		$_{}$	None	None		✓	✓	✓	272.2.r.a	$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
272.2.s.a	$272$	$2$	272.s	272.s	$4$	$68$	$34$	$2.172$		$_{}$	None	None		✓	✓	✓	272.2.j.a	$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
272.2.v.a	$272$	$2$	272.v	17.d	$8$	$4$	$1$	$2.172$	$\Q(\zeta_{8})$	$_{}$	None	None					136.2.n.b	$2$	$1$	$0$	$-4$	$-8$	$-4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1-\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots$
272.2.v.b	$272$	$2$	272.v	17.d	$8$	$4$	$1$	$2.172$	$\Q(\zeta_{8})$	$_{}$	None	None					34.2.d.a	$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8})q^{5}+\cdots$
272.2.v.c	$272$	$2$	272.v	17.d	$8$	$4$	$1$	$2.172$	$\Q(\zeta_{8})$	$_{}$	None	None					68.2.h.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(1-\zeta_{8})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
272.2.v.d	$272$	$2$	272.v	17.d	$8$	$4$	$1$	$2.172$	$\Q(\zeta_{8})$	$_{}$	None	None					17.2.d.a	$2$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(1+\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
272.2.v.e	$272$	$2$	272.v	17.d	$8$	$4$	$1$	$2.172$	$\Q(\zeta_{8})$	$_{}$	None	None					136.2.n.a	$2$	$0$	$0$	$4$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(1+\zeta_{8})q^{3}+(1-\zeta_{8})q^{5}+(1+2\zeta_{8}+\cdots)q^{7}+\cdots$
272.2.v.f	$272$	$2$	272.v	17.d	$8$	$12$	$3$	$2.172$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None			✓		136.2.n.c	$2$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{2}q^{3}+\beta _{8}q^{5}+(-1+\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots$
272.2.w.a	$272$	$2$	272.w	272.w	$8$	$4$	$1$	$2.172$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			272.2.w.a	$2$	$0$	$4$	$0$	$4$	$8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(1+\zeta_{8}^{2})q^{2}+(-\zeta_{8}+\zeta_{8}^{2})q^{3}+2\zeta_{8}^{2}q^{4}+\cdots$
272.2.w.b	$272$	$2$	272.w	272.w	$8$	$132$	$33$	$2.172$		$_{}$	None	None		✓	✓		272.2.w.b	$2$	$0$	$-8$	$-4$	$-8$	$-8$			$\mathrm{SU}(2)[C_{8}]$
272.2.y.a	$272$	$2$	272.y	272.y	$8$	$4$	$1$	$2.172$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			272.2.w.a	$2$	$1$	$-4$	$-4$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1-\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}^{3})q^{3}+\cdots$
272.2.y.b	$272$	$2$	272.y	272.y	$8$	$132$	$33$	$2.172$		$_{}$	None	None		✓	✓		272.2.w.b	$2$	$0$	$0$	$0$	$-4$	$8$			$\mathrm{SU}(2)[C_{8}]$
272.2.bd.a	$272$	$2$	272.bd	272.ad	$16$	$272$	$34$	$2.172$		$_{}$	None	None		✓	✓	✓	272.2.bd.a	$2$	$0$	$-8$	$-8$	$-8$	$-16$			$\mathrm{SU}(2)[C_{16}]$
272.2.bf.a	$272$	$2$	272.bf	68.i	$16$	$8$	$1$	$2.172$	$\Q(\zeta_{16})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			272.2.bf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{16}]$	$q+(\zeta_{16}^{2}+\zeta_{16}^{3}-2\zeta_{16}^{6}+2\zeta_{16}^{7})q^{5}+\cdots$
272.2.bf.b	$272$	$2$	272.bf	68.i	$16$	$16$	$2$	$2.172$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			272.2.bf.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{16}]$	$q-\beta _{7}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{10}+\cdots)q^{5}+\cdots$
272.2.bf.c	$272$	$2$	272.bf	68.i	$16$	$48$	$6$	$2.172$		$_{}$	None	None		✓	✓		272.2.bf.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
272.2.bj.a	$272$	$2$	272.bj	272.aj	$16$	$272$	$34$	$2.172$		$_{}$	None	None		✓	✓	✓	272.2.bd.a	$2$	$0$	$-8$	$-8$	$-8$	$-16$			$\mathrm{SU}(2)[C_{16}]$
272.3.d.a	$272$	$3$	272.d	4.b	$2$	$4$	$4$	$7.411$	$\Q(\sqrt{-14 +2 \sqrt{17}})$	$_{}$	None	None		✓			272.3.d.a	$2$	$0$	$0$	$0$	$12$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(3+\beta _{2})q^{5}+\beta _{3}q^{7}+(-5+\cdots)q^{9}+\cdots$
272.3.d.b	$272$	$3$	272.d	4.b	$2$	$12$	$12$	$7.411$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		272.3.d.b	$2$	$0$	$0$	$0$	$-12$	$0$		$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+\beta _{4}q^{7}+(-2+\cdots)q^{9}+\cdots$
272.3.g.a	$272$	$3$	272.g	68.d	$2$	$2$	$2$	$7.411$	$\Q(\sqrt{17}) $	$_{}$	$\Q(\sqrt{-17}) $	None	✓	✓			272.3.g.a	$2$	$0$	$0$	$-2$	$0$	$-18$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-\beta )q^{3}+(-9-\beta )q^{7}+(9+2\beta )q^{9}+\cdots$
272.3.g.b	$272$	$3$	272.g	68.d	$2$	$2$	$2$	$7.411$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			272.3.g.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}-9 q^{9}-10 q^{13}+(-\beta-15)q^{17}+\cdots$
272.3.g.c	$272$	$3$	272.g	68.d	$2$	$2$	$2$	$7.411$	$\Q(\sqrt{17}) $	$_{}$	$\Q(\sqrt{-17}) $	None	✓	✓			272.3.g.a	$2$	$0$	$0$	$2$	$0$	$18$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(1+\beta )q^{3}+(9+\beta )q^{7}+(9+2\beta )q^{9}+\cdots$
272.3.g.d	$272$	$3$	272.g	68.d	$2$	$12$	$12$	$7.411$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		272.3.g.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{23}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-\beta _{7}q^{5}+(-\beta _{3}-\beta _{6})q^{7}+\cdots$
272.3.i.a	$272$	$3$	272.i	272.i	$4$	$140$	$70$	$7.411$		$_{}$	None	None		✓	✓	✓	272.3.i.a	$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
272.3.k.a	$272$	$3$	272.k	272.k	$4$	$140$	$70$	$7.411$		$_{}$	None	None		✓	✓	✓	272.3.k.a	$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
272.3.p.a	$272$	$3$	272.p	68.f	$4$	$2$	$1$	$7.411$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			272.3.p.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{5}+9 i q^{9}+24 q^{13}+\cdots$
272.3.p.b	$272$	$3$	272.p	68.f	$4$	$2$	$1$	$7.411$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			272.3.p.b	$4$	$0$	$0$	$0$	$14$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(7 i+7)q^{5}+9 i q^{9}-24 q^{13}+\cdots$

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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.