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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	CM	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	CM	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
1445.2.a.a	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	$\Q$	None	✓	✓			1445.2.a.a	$1$	$1$	$0$	$-2$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots$
1445.2.a.b	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	$\Q$	None	✓	✓			1445.2.a.a	$1$	$1$	$0$	$2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots$
1445.2.a.c	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	$\Q$	None	✓				85.2.a.a	$1$	$0$	$1$	$-2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots$
1445.2.a.d	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	$\Q$	None	✓	✓			1445.2.a.d	$1$	$0$	$1$	$-1$	$-1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-5q^{7}+\cdots$
1445.2.a.e	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	$\Q$	None	✓	✓			1445.2.a.d	$1$	$0$	$1$	$1$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+5q^{7}+\cdots$
1445.2.a.f	$1445$	$2$	1445.a	1.a	$1$	$2$	$2$	$11.538$	$\Q(\sqrt{2}) $	None	✓				85.2.a.b	$1$	$0$	$-2$	$4$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(2+\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
1445.2.a.g	$1445$	$2$	1445.a	1.a	$1$	$2$	$2$	$11.538$	$\Q(\sqrt{3}) $	None	✓				85.2.a.c	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(3+\cdots)q^{6}+\cdots$
1445.2.a.h	$1445$	$2$	1445.a	1.a	$1$	$2$	$2$	$11.538$	$\Q(\sqrt{17}) $	None	✓	✓			1445.2.a.h	$1$	$0$	$1$	$-1$	$-2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}+(2+\beta )q^{4}-q^{5}+(-4+\cdots)q^{6}+\cdots$
1445.2.a.i	$1445$	$2$	1445.a	1.a	$1$	$2$	$2$	$11.538$	$\Q(\sqrt{17}) $	None	✓	✓			1445.2.a.h	$1$	$0$	$1$	$1$	$2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{3}+(2+\beta )q^{4}+q^{5}+(4+\cdots)q^{6}+\cdots$
1445.2.a.j	$1445$	$2$	1445.a	1.a	$1$	$3$	$3$	$11.538$	3.3.148.1	None	✓				85.2.d.a	$1$	$1$	$1$	$0$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
1445.2.a.k	$1445$	$2$	1445.a	1.a	$1$	$3$	$3$	$11.538$	3.3.148.1	None	✓				85.2.d.a	$1$	$0$	$1$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
1445.2.a.l	$1445$	$2$	1445.a	1.a	$1$	$6$	$6$	$11.538$	6.6.1397493.1	None	✓	✓			1445.2.a.l	$1$	$1$	$-3$	$-3$	$6$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{4})q^{3}+\cdots$
1445.2.a.m	$1445$	$2$	1445.a	1.a	$1$	$6$	$6$	$11.538$	6.6.1397493.1	None	✓	✓			1445.2.a.l	$1$	$1$	$-3$	$3$	$-6$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{5})q^{2}+(\beta _{1}-\beta _{4})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
1445.2.a.n	$1445$	$2$	1445.a	1.a	$1$	$6$	$6$	$11.538$	6.6.7718912.1	None	✓				85.2.e.a	$1$	$1$	$2$	$-4$	$-6$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
1445.2.a.o	$1445$	$2$	1445.a	1.a	$1$	$6$	$6$	$11.538$	6.6.7718912.1	None	✓				85.2.e.a	$1$	$0$	$2$	$4$	$6$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
1445.2.a.p	$1445$	$2$	1445.a	1.a	$1$	$12$	$12$	$11.538$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓		✓		85.2.l.a	$1$	$1$	$-4$	$-8$	$12$	$-16$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(1+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
1445.2.a.q	$1445$	$2$	1445.a	1.a	$1$	$12$	$12$	$11.538$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				85.2.l.a	$1$	$0$	$-4$	$8$	$-12$	$16$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(1+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
1445.2.a.r	$1445$	$2$	1445.a	1.a	$1$	$12$	$12$	$11.538$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			1445.2.a.r	$1$	$0$	$3$	$-3$	$-12$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots$
1445.2.a.s	$1445$	$2$	1445.a	1.a	$1$	$12$	$12$	$11.538$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		1445.2.a.r	$1$	$0$	$3$	$3$	$12$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots$
1445.2.b.a	$1445$	$2$	1445.b	5.b	$2$	$4$	$4$	$11.538$	$\Q(\zeta_{8})$	None					85.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}+q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots$
1445.2.b.b	$1445$	$2$	1445.b	5.b	$2$	$8$	$8$	$11.538$	8.0.$\cdots$.11	None					85.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{3}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
1445.2.b.c	$1445$	$2$	1445.b	5.b	$2$	$8$	$8$	$11.538$	8.0.$\cdots$.1	None		✓			1445.2.b.c	$2$	$0$	$0$	$0$	$-1$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{6}q^{3}+(-1+\beta _{1})q^{4}+\beta _{2}q^{5}+\cdots$
1445.2.b.d	$1445$	$2$	1445.b	5.b	$2$	$8$	$8$	$11.538$	8.0.$\cdots$.1	None		✓			1445.2.b.c	$2$	$0$	$0$	$0$	$1$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{6}q^{3}+(-1+\beta _{1})q^{4}-\beta _{2}q^{5}+\cdots$
1445.2.b.e	$1445$	$2$	1445.b	5.b	$2$	$8$	$8$	$11.538$	8.0.619810816.2	None					85.2.b.a	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots$
1445.2.b.f	$1445$	$2$	1445.b	5.b	$2$	$12$	$12$	$11.538$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					85.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{10}q^{3}+(-1+\beta _{8})q^{4}+\cdots$
1445.2.b.g	$1445$	$2$	1445.b	5.b	$2$	$24$	$24$	$11.538$		None		✓			1445.2.b.g	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1445.2.b.h	$1445$	$2$	1445.b	5.b	$2$	$24$	$24$	$11.538$		None		✓			1445.2.b.g	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1445.2.b.i	$1445$	$2$	1445.b	5.b	$2$	$24$	$24$	$11.538$		None					85.2.m.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1445.2.d.a	$1445$	$2$	1445.d	17.b	$2$	$2$	$2$	$11.538$	$\Q(\sqrt{-1}) $	None					85.2.a.a	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-2 i q^{3}-q^{4}+i q^{5}+2 i q^{6}+\cdots$
1445.2.d.b	$1445$	$2$	1445.d	17.b	$2$	$2$	$2$	$11.538$	$\Q(\sqrt{-1}) $	None		✓			1445.2.a.d	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+i q^{3}-q^{4}+i q^{5}-i q^{6}+\cdots$
1445.2.d.c	$1445$	$2$	1445.d	17.b	$2$	$2$	$2$	$11.538$	$\Q(\sqrt{-1}) $	None		✓			1445.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2 i q^{3}-2 q^{4}+i q^{5}-2 i q^{7}+\cdots$
1445.2.d.d	$1445$	$2$	1445.d	17.b	$2$	$4$	$4$	$11.538$	$\Q(i, \sqrt{17})$	None		✓			1445.2.a.h	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{2}-\beta _{1}q^{3}+(3-\beta _{3})q^{4}+\cdots$
1445.2.d.e	$1445$	$2$	1445.d	17.b	$2$	$4$	$4$	$11.538$	$\Q(\zeta_{12})$	None					85.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{3} q^{2}+(\beta_{2}-\beta_1)q^{3}+q^{4}-\beta_1 q^{5}+\cdots$
1445.2.d.f	$1445$	$2$	1445.d	17.b	$2$	$4$	$4$	$11.538$	$\Q(\zeta_{8})$	None					85.2.a.b	$2$	$0$	$4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{3}+1)q^{2}+(\beta_{2}-2\beta_1)q^{3}+(2\beta_{3}+1)q^{4}+\cdots$
1445.2.d.g	$1445$	$2$	1445.d	17.b	$2$	$12$	$12$	$11.538$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					85.2.e.a	$2$	$0$	$-4$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$
1445.2.d.h	$1445$	$2$	1445.d	17.b	$2$	$12$	$12$	$11.538$	12.0.$\cdots$.1	None		✓			1445.2.a.l	$2$	$0$	$6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{8})q^{2}+(\beta _{1}-\beta _{9})q^{3}+(1-\beta _{7}+\cdots)q^{4}+\cdots$
1445.2.d.i	$1445$	$2$	1445.d	17.b	$2$	$24$	$24$	$11.538$		None		✓			1445.2.a.r	$2$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1445.2.d.j	$1445$	$2$	1445.d	17.b	$2$	$24$	$24$	$11.538$		None					85.2.l.a	$2$	$0$	$8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1445.4.a.a	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	$\Q$	None	✓				5.4.a.a	$1$	$1$	$-4$	$-2$	$5$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-2q^{3}+8q^{4}+5q^{5}+8q^{6}+\cdots$
1445.4.a.b	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	$\Q$	None	✓	✓			1445.4.a.b	$1$	$0$	$-3$	$-2$	$-5$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}-2q^{3}+q^{4}-5q^{5}+6q^{6}+\cdots$
1445.4.a.c	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	$\Q$	None	✓	✓			1445.4.a.b	$1$	$0$	$-3$	$2$	$5$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+2q^{3}+q^{4}+5q^{5}-6q^{6}+\cdots$
1445.4.a.d	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	$\Q$	None	✓				85.4.d.a	$1$	$2$	$-1$	$-8$	$-5$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-8q^{3}-7q^{4}-5q^{5}+8q^{6}+\cdots$
1445.4.a.e	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	$\Q$	None	✓				85.4.d.a	$1$	$1$	$-1$	$8$	$5$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+8q^{3}-7q^{4}+5q^{5}-8q^{6}+\cdots$
1445.4.a.f	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	$\Q$	None	✓				85.4.a.c	$1$	$0$	$3$	$-10$	$-5$	$22$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-10q^{3}+q^{4}-5q^{5}-30q^{6}+\cdots$
1445.4.a.g	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	$\Q$	None	✓				85.4.a.b	$1$	$1$	$3$	$5$	$5$	$22$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+5q^{3}+q^{4}+5q^{5}+15q^{6}+\cdots$
1445.4.a.h	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	$\Q$	None	✓				85.4.a.a	$1$	$0$	$3$	$7$	$-5$	$22$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+7q^{3}+q^{4}-5q^{5}+21q^{6}+\cdots$
1445.4.a.i	$1445$	$4$	1445.a	1.a	$1$	$2$	$2$	$85.258$	$\Q(\sqrt{3}) $	None	✓				85.4.a.d	$1$	$0$	$-4$	$2$	$-10$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{2}+(1-\beta )q^{3}+(-1-4\beta )q^{4}+\cdots$
1445.4.a.j	$1445$	$4$	1445.a	1.a	$1$	$3$	$3$	$85.258$	3.3.1304.1	None	✓				85.4.a.e	$1$	$1$	$-6$	$4$	$15$	$-8$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots$
1445.4.a.k	$1445$	$4$	1445.a	1.a	$1$	$3$	$3$	$85.258$	3.3.568.1	None	✓				85.4.a.f	$1$	$1$	$3$	$-9$	$15$	$-34$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(-4+3\beta _{1})q^{3}+\cdots$
1445.4.a.l	$1445$	$4$	1445.a	1.a	$1$	$5$	$5$	$85.258$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓				85.4.a.g	$1$	$0$	$2$	$1$	$-25$	$-10$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+\beta _{2}q^{3}+(6-2\beta _{1}+\beta _{3})q^{4}+\cdots$

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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.