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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 79 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
645.2.a.a	$645$	$2$	645.a	1.a	$1$	$1$	$1$	$5.150$	$\Q$	None	✓	✓			645.2.a.a	$1$	$0$	$-2$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+4q^{7}+\cdots$
645.2.a.b	$645$	$2$	645.a	1.a	$1$	$1$	$1$	$5.150$	$\Q$	None	✓	✓			645.2.a.b	$1$	$1$	$-2$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-4q^{7}+\cdots$
645.2.a.c	$645$	$2$	645.a	1.a	$1$	$1$	$1$	$5.150$	$\Q$	None	✓	✓			645.2.a.c	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}-2q^{7}+q^{9}-5q^{11}+\cdots$
645.2.a.d	$645$	$2$	645.a	1.a	$1$	$1$	$1$	$5.150$	$\Q$	None	✓	✓			645.2.a.d	$1$	$0$	$1$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots$
645.2.a.e	$645$	$2$	645.a	1.a	$1$	$1$	$1$	$5.150$	$\Q$	None	✓	✓			645.2.a.e	$1$	$0$	$1$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
645.2.a.f	$645$	$2$	645.a	1.a	$1$	$1$	$1$	$5.150$	$\Q$	None	✓	✓			645.2.a.f	$1$	$0$	$2$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots$
645.2.a.g	$645$	$2$	645.a	1.a	$1$	$2$	$2$	$5.150$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	645.2.a.g	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}+\beta q^{7}-2\beta q^{8}+\cdots$
645.2.a.h	$645$	$2$	645.a	1.a	$1$	$3$	$3$	$5.150$	3.3.148.1	None	✓	✓	✓	✓	645.2.a.h	$1$	$1$	$-2$	$3$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
645.2.a.i	$645$	$2$	645.a	1.a	$1$	$3$	$3$	$5.150$	3.3.148.1	None	✓	✓	✓	✓	645.2.a.i	$1$	$1$	$0$	$-3$	$3$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+\cdots$
645.2.a.j	$645$	$2$	645.a	1.a	$1$	$3$	$3$	$5.150$	3.3.316.1	None	✓	✓	✓	✓	645.2.a.j	$1$	$0$	$1$	$3$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
645.2.a.k	$645$	$2$	645.a	1.a	$1$	$5$	$5$	$5.150$	5.5.135076.1	None	✓	✓	✓		645.2.a.k	$1$	$0$	$-4$	$-5$	$-5$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}-q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
645.2.a.l	$645$	$2$	645.a	1.a	$1$	$5$	$5$	$5.150$	5.5.220036.1	None	✓	✓	✓	✓	645.2.a.l	$1$	$0$	$2$	$5$	$5$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+q^{3}+(\beta _{1}-\beta _{3})q^{4}+q^{5}+\cdots$
645.2.b.a	$645$	$2$	645.b	5.b	$2$	$4$	$4$	$5.150$	$\Q(\zeta_{8})$	None		✓			645.2.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}+\beta_1)q^{2}-\beta_1 q^{3}+(-2\beta_{3}-1)q^{4}+\cdots$
645.2.b.b	$645$	$2$	645.b	5.b	$2$	$4$	$4$	$5.150$	$\Q(\zeta_{12})$	None		✓			645.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+2\zeta_{12}^{2})q^{2}+\zeta_{12}^{3}q^{3}-q^{4}+\cdots$
645.2.b.c	$645$	$2$	645.b	5.b	$2$	$16$	$16$	$5.150$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			645.2.b.c	$2$	$0$	$0$	$0$	$2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}+(\beta _{3}-\beta _{10}+\cdots)q^{5}+\cdots$
645.2.b.d	$645$	$2$	645.b	5.b	$2$	$20$	$20$	$5.150$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓		645.2.b.d	$2$	$0$	$0$	$0$	$4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
645.2.d.a	$645$	$2$	645.d	645.d	$2$	$8$	$8$	$5.150$	8.0.40960000.1	None		✓			645.2.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+2q^{4}+(\beta _{4}-\beta _{5})q^{5}-2\beta _{6}q^{7}+\cdots$
645.2.d.b	$645$	$2$	645.d	645.d	$2$	$16$	$16$	$5.150$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			645.2.d.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{6}-\beta _{7}+\beta _{15})q^{2}+(-\beta _{7}+\beta _{15})q^{3}+\cdots$
645.2.d.c	$645$	$2$	645.d	645.d	$2$	$16$	$16$	$5.150$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			645.2.d.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}+\beta _{8}+\beta _{12})q^{2}-\beta _{8}q^{3}+(-2+\cdots)q^{4}+\cdots$
645.2.d.d	$645$	$2$	645.d	645.d	$2$	$16$	$16$	$5.150$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			645.2.d.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}+(\beta _{8}+\beta _{11}-\beta _{13})q^{3}+\beta _{1}q^{4}+\cdots$
645.2.d.e	$645$	$2$	645.d	645.d	$2$	$28$	$28$	$5.150$		$\Q(\sqrt{-215}) $		✓	✓		645.2.d.e	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{2}]$
645.2.g.a	$645$	$2$	645.g	129.d	$2$	$30$	$30$	$5.150$		None		✓			645.2.g.a	$2$	$0$	$0$	$0$	$-30$	$0$			$\mathrm{SU}(2)[C_{2}]$
645.2.g.b	$645$	$2$	645.g	129.d	$2$	$30$	$30$	$5.150$		None		✓			645.2.g.a	$2$	$0$	$0$	$0$	$30$	$0$			$\mathrm{SU}(2)[C_{2}]$
645.2.i.a	$645$	$2$	645.i	43.c	$3$	$2$	$1$	$5.150$	$\Q(\sqrt{-3}) $	None		✓			645.2.i.a	$2$	$0$	$2$	$1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-\zeta_{6})q^{3}-q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
645.2.i.b	$645$	$2$	645.i	43.c	$3$	$2$	$1$	$5.150$	$\Q(\sqrt{-3}) $	None		✓			645.2.i.b	$2$	$0$	$2$	$1$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots$
645.2.i.c	$645$	$2$	645.i	43.c	$3$	$6$	$3$	$5.150$	6.0.64827.1	None		✓			645.2.i.c	$2$	$0$	$2$	$-3$	$3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}-\beta _{5}q^{3}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
645.2.i.d	$645$	$2$	645.i	43.c	$3$	$8$	$4$	$5.150$	8.0.$\cdots$.2	None		✓			645.2.i.d	$2$	$0$	$2$	$-4$	$4$	$-6$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-1-\beta _{2})q^{3}+(2+\beta _{4}-\beta _{7})q^{4}+\cdots$
645.2.i.e	$645$	$2$	645.i	43.c	$3$	$14$	$7$	$5.150$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			645.2.i.e	$2$	$0$	$-2$	$7$	$7$	$9$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}-\beta _{8}q^{3}+(1-\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
645.2.i.f	$645$	$2$	645.i	43.c	$3$	$14$	$7$	$5.150$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓			645.2.i.f	$2$	$0$	$0$	$-7$	$-7$	$1$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{3})q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+\cdots$
645.2.i.g	$645$	$2$	645.i	43.c	$3$	$14$	$7$	$5.150$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			645.2.i.g	$2$	$0$	$2$	$7$	$-7$	$1$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(1-\beta _{9})q^{3}+(2-\beta _{3})q^{4}+\cdots$
645.2.j.a	$645$	$2$	645.j	15.e	$4$	$168$	$84$	$5.150$		None		✓	✓	✓	645.2.j.a	$4$	$0$	$0$	$-4$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
645.2.m.a	$645$	$2$	645.m	215.g	$4$	$88$	$44$	$5.150$		None		✓	✓	✓	645.2.m.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
645.2.o.a	$645$	$2$	645.o	645.o	$6$	$168$	$84$	$5.150$		None		✓	✓	✓	645.2.o.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
645.2.q.a	$645$	$2$	645.q	215.i	$6$	$88$	$44$	$5.150$		None		✓	✓	✓	645.2.q.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{6}]$
645.2.s.a	$645$	$2$	645.s	129.h	$6$	$4$	$2$	$5.150$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			645.2.s.a	$2$	$1$	$-4$	$-2$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots$
645.2.s.b	$645$	$2$	645.s	129.h	$6$	$4$	$2$	$5.150$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			645.2.s.a	$2$	$0$	$4$	$-1$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
645.2.s.c	$645$	$2$	645.s	129.h	$6$	$54$	$27$	$5.150$		None		✓			645.2.s.c	$2$	$0$	$-4$	$1$	$27$	$6$			$\mathrm{SU}(2)[C_{6}]$
645.2.s.d	$645$	$2$	645.s	129.h	$6$	$54$	$27$	$5.150$		None		✓			645.2.s.c	$2$	$0$	$4$	$2$	$-27$	$6$			$\mathrm{SU}(2)[C_{6}]$
645.2.u.a	$645$	$2$	645.u	43.e	$7$	$6$	$1$	$5.150$	$\Q(\zeta_{14})$	None		✓			645.2.u.a	$2$	$0$	$-5$	$1$	$-1$	$10$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
645.2.u.b	$645$	$2$	645.u	43.e	$7$	$36$	$6$	$5.150$		None		✓			645.2.u.b	$2$	$0$	$1$	$-6$	$6$	$4$			$\mathrm{SU}(2)[C_{7}]$
645.2.u.c	$645$	$2$	645.u	43.e	$7$	$36$	$6$	$5.150$		None		✓			645.2.u.c	$2$	$0$	$3$	$-6$	$-6$	$-16$			$\mathrm{SU}(2)[C_{7}]$
645.2.u.d	$645$	$2$	645.u	43.e	$7$	$42$	$7$	$5.150$		None		✓			645.2.u.d	$2$	$0$	$6$	$7$	$-7$	$-10$			$\mathrm{SU}(2)[C_{7}]$
645.2.u.e	$645$	$2$	645.u	43.e	$7$	$48$	$8$	$5.150$		None		✓	✓		645.2.u.e	$2$	$0$	$3$	$8$	$8$	$-28$			$\mathrm{SU}(2)[C_{7}]$
645.2.w.a	$645$	$2$	645.w	645.w	$12$	$336$	$84$	$5.150$		None		✓	✓	✓	645.2.w.a	$8$	$0$	$0$	$-2$	$0$	$-4$			$\mathrm{SU}(2)[C_{12}]$
645.2.x.a	$645$	$2$	645.x	215.l	$12$	$176$	$44$	$5.150$		None		✓	✓	✓	645.2.x.a	$4$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{12}]$
645.2.z.a	$645$	$2$	645.z	129.j	$14$	$180$	$30$	$5.150$		None		✓			645.2.z.a	$2$	$0$	$0$	$0$	$-30$	$0$			$\mathrm{SU}(2)[C_{14}]$
645.2.z.b	$645$	$2$	645.z	129.j	$14$	$180$	$30$	$5.150$		None		✓			645.2.z.a	$2$	$0$	$0$	$0$	$30$	$0$			$\mathrm{SU}(2)[C_{14}]$
645.2.bd.a	$645$	$2$	645.bd	215.p	$14$	$264$	$44$	$5.150$		None		✓	✓	✓	645.2.bd.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{14}]$
645.2.bf.a	$645$	$2$	645.bf	645.af	$14$	$504$	$84$	$5.150$		None		✓	✓	✓	645.2.bf.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
645.2.bg.a	$645$	$2$	645.bg	43.g	$21$	$84$	$7$	$5.150$		None		✓			645.2.bg.a	$2$	$0$	$-4$	$7$	$-7$	$1$			$\mathrm{SU}(2)[C_{21}]$

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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.