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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 64 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
1665.1.t.a	$1665$	$1$	1665.t	185.h	$4$	$16$	$8$	$0.831$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-111}) $	None		✓	✓	✓	1665.1.t.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{32}^{9}-\zeta_{32}^{15})q^{2}+(-\zeta_{32}^{2}+\cdots)q^{4}+\cdots$
1665.1.bg.a	$1665$	$1$	1665.bg	555.w	$6$	$8$	$4$	$0.831$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1665.1.bg.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{4}q^{4}-\zeta_{24}^{7}q^{5}-\zeta_{24}^{10}q^{7}+\cdots$
1665.2.a.a	$1665$	$2$	1665.a	1.a	$1$	$1$	$1$	$13.295$	$\Q$	$_{}$	None	None	✓	✓			1665.2.a.a	$1$	$1$	$-2$	$0$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+4q^{7}+2q^{10}+\cdots$
1665.2.a.b	$1665$	$2$	1665.a	1.a	$1$	$1$	$1$	$13.295$	$\Q$	$_{}$	None	None	✓				185.2.a.c	$1$	$1$	$-1$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-2q^{7}+3q^{8}-q^{10}+\cdots$
1665.2.a.c	$1665$	$2$	1665.a	1.a	$1$	$1$	$1$	$13.295$	$\Q$	$_{}$	None	None	✓				185.2.a.b	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-3q^{7}+5q^{11}+4q^{13}+\cdots$
1665.2.a.d	$1665$	$2$	1665.a	1.a	$1$	$1$	$1$	$13.295$	$\Q$	$_{}$	None	None	✓				555.2.a.b	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}+2q^{7}-q^{13}+4q^{16}+\cdots$
1665.2.a.e	$1665$	$2$	1665.a	1.a	$1$	$1$	$1$	$13.295$	$\Q$	$_{}$	None	None	✓				555.2.a.a	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-2q^{7}-4q^{11}+5q^{13}+\cdots$
1665.2.a.f	$1665$	$2$	1665.a	1.a	$1$	$1$	$1$	$13.295$	$\Q$	$_{}$	None	None	✓				185.2.a.a	$1$	$1$	$2$	$0$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}-5q^{7}+2q^{10}+\cdots$
1665.2.a.g	$1665$	$2$	1665.a	1.a	$1$	$1$	$1$	$13.295$	$\Q$	$_{}$	None	None	✓	✓			1665.2.a.a	$1$	$0$	$2$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}+4q^{7}+2q^{10}+\cdots$
1665.2.a.h	$1665$	$2$	1665.a	1.a	$1$	$2$	$2$	$13.295$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				555.2.a.f	$1$	$1$	$-1$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(1-2\beta )q^{7}+\cdots$
1665.2.a.i	$1665$	$2$	1665.a	1.a	$1$	$2$	$2$	$13.295$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				555.2.a.g	$1$	$1$	$-1$	$0$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+q^{7}-3q^{8}+\cdots$
1665.2.a.j	$1665$	$2$	1665.a	1.a	$1$	$2$	$2$	$13.295$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				555.2.a.e	$1$	$0$	$1$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots$
1665.2.a.k	$1665$	$2$	1665.a	1.a	$1$	$2$	$2$	$13.295$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				555.2.a.d	$1$	$1$	$1$	$0$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-q^{5}-3q^{7}+3q^{8}+\cdots$
1665.2.a.l	$1665$	$2$	1665.a	1.a	$1$	$2$	$2$	$13.295$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				555.2.a.c	$1$	$0$	$3$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+(-3+2\beta )q^{7}+\cdots$
1665.2.a.m	$1665$	$2$	1665.a	1.a	$1$	$3$	$3$	$13.295$	3.3.229.1	$_{}$	None	None	✓		✓		555.2.a.i	$1$	$1$	$-2$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}-q^{5}+\cdots$
1665.2.a.n	$1665$	$2$	1665.a	1.a	$1$	$3$	$3$	$13.295$	3.3.469.1	$_{}$	None	None	✓				555.2.a.h	$1$	$0$	$-1$	$0$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
1665.2.a.o	$1665$	$2$	1665.a	1.a	$1$	$5$	$5$	$13.295$	5.5.457904.1	$_{}$	None	None	✓	✓	✓	✓	1665.2.a.o	$1$	$1$	$-2$	$0$	$5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1665.2.a.p	$1665$	$2$	1665.a	1.a	$1$	$5$	$5$	$13.295$	5.5.973904.1	$_{}$	None	None	✓				185.2.a.e	$1$	$0$	$-2$	$0$	$5$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(2+\beta _{3})q^{4}+q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots$
1665.2.a.q	$1665$	$2$	1665.a	1.a	$1$	$5$	$5$	$13.295$	5.5.368464.1	$_{}$	None	None	✓		✓		185.2.a.d	$1$	$0$	$0$	$0$	$-5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(2-\beta _{1}-\beta _{4})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots$
1665.2.a.r	$1665$	$2$	1665.a	1.a	$1$	$5$	$5$	$13.295$	5.5.457904.1	$_{}$	None	None	✓	✓	✓	✓	1665.2.a.o	$1$	$0$	$2$	$0$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1665.2.a.s	$1665$	$2$	1665.a	1.a	$1$	$5$	$5$	$13.295$	5.5.600268.1	$_{}$	None	None	✓				555.2.a.j	$1$	$0$	$3$	$0$	$5$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(2-\beta _{3}+\beta _{4})q^{4}+q^{5}+\cdots$
1665.2.a.t	$1665$	$2$	1665.a	1.a	$1$	$6$	$6$	$13.295$	6.6.95034688.1	$_{}$	None	None	✓	✓	✓		1665.2.a.t	$1$	$1$	$-2$	$0$	$-6$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots$
1665.2.a.u	$1665$	$2$	1665.a	1.a	$1$	$6$	$6$	$13.295$	6.6.95034688.1	$_{}$	None	None	✓	✓	✓		1665.2.a.t	$1$	$0$	$2$	$0$	$6$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots$
1665.2.c.a	$1665$	$2$	1665.c	5.b	$2$	$2$	$2$	$13.295$	$\Q(\sqrt{-1}) $	$_{}$	None	None					555.2.c.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-2 q^{4}+(2 i+1)q^{5}+(2 i-4)q^{10}+\cdots$
1665.2.c.b	$1665$	$2$	1665.c	5.b	$2$	$2$	$2$	$13.295$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1665.2.c.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{4}+(2 i-1)q^{5}+2 i q^{7}-6 q^{11}+\cdots$
1665.2.c.c	$1665$	$2$	1665.c	5.b	$2$	$2$	$2$	$13.295$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1665.2.c.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{4}+(2 i+1)q^{5}-2 i q^{7}+6 q^{11}+\cdots$
1665.2.c.d	$1665$	$2$	1665.c	5.b	$2$	$8$	$8$	$13.295$	8.0.309760000.3	$_{}$	None	None					555.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
1665.2.c.e	$1665$	$2$	1665.c	5.b	$2$	$18$	$18$	$13.295$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None					185.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{13})q^{2}+(-2+\beta _{3}+\beta _{4})q^{4}+\cdots$
1665.2.c.f	$1665$	$2$	1665.c	5.b	$2$	$26$	$26$	$13.295$		$_{}$	None	None					555.2.c.c	$2$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{2}]$
1665.2.c.g	$1665$	$2$	1665.c	5.b	$2$	$32$	$32$	$13.295$		$_{}$	None	None		✓	✓		1665.2.c.g	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1665.2.e.a	$1665$	$2$	1665.e	37.b	$2$	$2$	$2$	$13.295$	$\Q(\sqrt{-1}) $	$_{}$	None	None					555.2.e.a	$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{4}+i q^{5}-4 q^{7}-2 q^{11}-5 i q^{13}+\cdots$
1665.2.e.b	$1665$	$2$	1665.e	37.b	$2$	$2$	$2$	$13.295$	$\Q(\sqrt{-1}) $	$_{}$	None	None					185.2.c.a	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{4}+i q^{5}+q^{7}+3 q^{11}+4 q^{16}+\cdots$
1665.2.e.c	$1665$	$2$	1665.e	37.b	$2$	$10$	$10$	$13.295$	10.0.$\cdots$.1	$_{}$	None	None					555.2.e.b	$2$	$0$	$0$	$0$	$0$	$16$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-1+\beta _{1})q^{4}+\beta _{6}q^{5}+(2+\cdots)q^{7}+\cdots$
1665.2.e.d	$1665$	$2$	1665.e	37.b	$2$	$12$	$12$	$13.295$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					555.2.e.c	$2$	$0$	$0$	$0$	$0$	$8$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+(-2-\beta _{7})q^{4}+\beta _{2}q^{5}+(1+\cdots)q^{7}+\cdots$
1665.2.e.e	$1665$	$2$	1665.e	37.b	$2$	$12$	$12$	$13.295$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None					185.2.c.b	$2$	$0$	$0$	$0$	$0$	$-18$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{9}+\beta _{10})q^{4}-\beta _{4}q^{5}+\cdots$
1665.2.e.f	$1665$	$2$	1665.e	37.b	$2$	$24$	$24$	$13.295$		$_{}$	None	None		✓	✓		1665.2.e.f	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1665.2.g.a	$1665$	$2$	1665.g	185.d	$2$	$4$	$4$	$13.295$	$\Q(\sqrt{-5}, \sqrt{37})$	$_{}$	$\Q(\sqrt{-555}) $	None		✓			1665.2.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}-\beta _{1}q^{5}+\beta _{3}q^{13}+4q^{16}+\cdots$
1665.2.g.b	$1665$	$2$	1665.g	185.d	$2$	$16$	$16$	$13.295$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					185.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(1-\beta _{2})q^{4}-\beta _{14}q^{5}+\beta _{3}q^{7}+\cdots$
1665.2.g.c	$1665$	$2$	1665.g	185.d	$2$	$16$	$16$	$13.295$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1665.2.g.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+(1+\beta _{5})q^{4}+(-\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots$
1665.2.g.d	$1665$	$2$	1665.g	185.d	$2$	$16$	$16$	$13.295$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-111}) $	None		✓			1665.2.g.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{12}q^{2}+(2+\beta _{15})q^{4}+\beta _{6}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
1665.2.g.e	$1665$	$2$	1665.g	185.d	$2$	$40$	$40$	$13.295$		$_{}$	None	None			✓		555.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1665.2.v.a	$1665$	$2$	1665.v	111.g	$4$	$48$	$24$	$13.295$		$_{}$	None	None		✓			1665.2.v.a	$4$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{4}]$
1665.2.v.b	$1665$	$2$	1665.v	111.g	$4$	$48$	$24$	$13.295$		$_{}$	None	None		✓			1665.2.v.b	$4$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{4}]$
1665.3.d.a	$1665$	$3$	1665.d	3.b	$2$	$96$	$96$	$45.368$		$_{}$	None	None		✓	✓	✓	1665.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1665.4.a.a	$1665$	$4$	1665.a	1.a	$1$	$1$	$1$	$98.238$	$\Q$	$_{}$	None	None	✓	✓			1665.4.a.a	$1$	$1$	$-1$	$0$	$-5$	$-27$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}-5q^{5}-3^{3}q^{7}+15q^{8}+\cdots$
1665.4.a.b	$1665$	$4$	1665.a	1.a	$1$	$1$	$1$	$98.238$	$\Q$	$_{}$	None	None	✓				555.4.a.b	$1$	$1$	$-1$	$0$	$-5$	$25$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}-5q^{5}+5^{2}q^{7}+15q^{8}+\cdots$
1665.4.a.c	$1665$	$4$	1665.a	1.a	$1$	$1$	$1$	$98.238$	$\Q$	$_{}$	None	None	✓				555.4.a.a	$1$	$1$	$-1$	$0$	$-5$	$25$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}-5q^{5}+5^{2}q^{7}+15q^{8}+\cdots$
1665.4.a.d	$1665$	$4$	1665.a	1.a	$1$	$1$	$1$	$98.238$	$\Q$	$_{}$	None	None	✓	✓			1665.4.a.a	$1$	$2$	$1$	$0$	$5$	$-27$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-7q^{4}+5q^{5}-3^{3}q^{7}-15q^{8}+\cdots$
1665.4.a.e	$1665$	$4$	1665.a	1.a	$1$	$7$	$7$	$98.238$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓				555.4.a.d	$1$	$1$	$-2$	$0$	$35$	$-14$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots$
1665.4.a.f	$1665$	$4$	1665.a	1.a	$1$	$7$	$7$	$98.238$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓				185.4.a.b	$1$	$1$	$-1$	$0$	$35$	$-77$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{5}-\beta _{6})q^{4}+5q^{5}+\cdots$

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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.