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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 321 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
126.2.a.a	$126$	$2$	126.a	1.a	$1$	$1$	$1$	$1.006$	$\Q$	None	✓		✓	✓	42.2.a.a	$1$	$0$	$-1$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots$
126.2.a.b	$126$	$2$	126.a	1.a	$1$	$1$	$1$	$1.006$	$\Q$	None	✓		✓	✓	14.2.a.a	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{13}+q^{14}+\cdots$
126.2.e.a	$126$	$2$	126.e	63.h	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None		✓			126.2.e.a	$2$	$0$	$-2$	$0$	$-3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}-3\zeta_{6}q^{5}+\cdots$
126.2.e.b	$126$	$2$	126.e	63.h	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None		✓			126.2.e.b	$2$	$0$	$2$	$0$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots$
126.2.e.c	$126$	$2$	126.e	63.h	$3$	$6$	$3$	$1.006$	6.0.309123.1	None		✓			126.2.e.c	$2$	$0$	$-6$	$2$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-\beta _{2}-\beta _{4})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
126.2.e.d	$126$	$2$	126.e	63.h	$3$	$6$	$3$	$1.006$	6.0.309123.1	None		✓			126.2.e.d	$2$	$0$	$6$	$-2$	$-5$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(\beta _{3}-\beta _{4}-\beta _{5})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
126.2.f.a	$126$	$2$	126.f	9.c	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None		✓			126.2.f.a	$2$	$0$	$1$	$0$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
126.2.f.b	$126$	$2$	126.f	9.c	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None		✓			126.2.f.b	$2$	$0$	$1$	$3$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
126.2.f.c	$126$	$2$	126.f	9.c	$3$	$4$	$2$	$1.006$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			126.2.f.c	$2$	$0$	$-2$	$4$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$
126.2.f.d	$126$	$2$	126.f	9.c	$3$	$4$	$2$	$1.006$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			126.2.f.d	$2$	$0$	$2$	$-1$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
126.2.g.a	$126$	$2$	126.g	7.c	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None		✓			126.2.g.a	$2$	$0$	$-1$	$0$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
126.2.g.b	$126$	$2$	126.g	7.c	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None					42.2.e.b	$2$	$0$	$-1$	$0$	$3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots$
126.2.g.c	$126$	$2$	126.g	7.c	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None					42.2.e.a	$2$	$0$	$1$	$0$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$
126.2.g.d	$126$	$2$	126.g	7.c	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None		✓			126.2.g.a	$2$	$0$	$1$	$0$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots$
126.2.h.a	$126$	$2$	126.h	63.g	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None		✓			126.2.e.b	$2$	$1$	$-1$	$-3$	$-6$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
126.2.h.b	$126$	$2$	126.h	63.g	$3$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	None		✓			126.2.e.a	$2$	$0$	$1$	$-3$	$6$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
126.2.h.c	$126$	$2$	126.h	63.g	$3$	$6$	$3$	$1.006$	6.0.309123.1	None		✓			126.2.e.d	$2$	$0$	$-3$	$4$	$10$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(1-\beta _{5})q^{3}+(-1-\beta _{4})q^{4}+\cdots$
126.2.h.d	$126$	$2$	126.h	63.g	$3$	$6$	$3$	$1.006$	6.0.309123.1	None		✓			126.2.e.c	$2$	$0$	$3$	$2$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
126.2.k.a	$126$	$2$	126.k	21.g	$6$	$8$	$4$	$1.006$	$\Q(\zeta_{24})$	None		✓	✓	✓	126.2.k.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta_{3}+\beta_1)q^{2}+(-\beta_{2}+1)q^{4}+\cdots$
126.2.l.a	$126$	$2$	126.l	63.i	$6$	$16$	$8$	$1.006$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	126.2.l.a	$2$	$0$	$0$	$0$	$0$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{6}q^{2}-\beta _{11}q^{3}-q^{4}+(1+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$
126.2.m.a	$126$	$2$	126.m	63.o	$6$	$16$	$8$	$1.006$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	126.2.m.a	$4$	$0$	$0$	$0$	$0$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{10}q^{2}-\beta _{1}q^{3}+\beta _{5}q^{4}+(\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots$
126.2.t.a	$126$	$2$	126.t	63.s	$6$	$16$	$8$	$1.006$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	126.2.l.a	$2$	$0$	$0$	$0$	$0$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{6})q^{2}+(-\beta _{11}-\beta _{14})q^{3}+\cdots$
126.3.b.a	$126$	$3$	126.b	3.b	$2$	$4$	$4$	$3.433$	$\Q(\sqrt{-2}, \sqrt{7})$	None		✓	✓	✓	126.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-2q^{4}+(-\beta _{1}+2\beta _{2})q^{5}+\cdots$
126.3.c.a	$126$	$3$	126.c	7.b	$2$	$4$	$4$	$3.433$	$\Q(\sqrt{2}, \sqrt{-33})$	None		✓			126.3.c.a	$4$	$0$	$0$	$0$	$0$	$-16$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+2q^{4}-\beta _{2}q^{5}+(-4+\beta _{3})q^{7}+\cdots$
126.3.c.b	$126$	$3$	126.c	7.b	$2$	$4$	$4$	$3.433$	$\Q(\sqrt{2}, \sqrt{-3})$	None					42.3.c.a	$2$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+2q^{4}+(2\beta _{2}-\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots$
126.3.i.a	$126$	$3$	126.i	63.n	$6$	$32$	$16$	$3.433$		None		✓	✓	✓	126.3.i.a	$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{6}]$
126.3.j.a	$126$	$3$	126.j	63.k	$6$	$32$	$16$	$3.433$		None		✓	✓	✓	126.3.j.a	$2$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
126.3.n.a	$126$	$3$	126.n	7.d	$6$	$4$	$2$	$3.433$	$\Q(\sqrt{2}, \sqrt{-3})$	None					42.3.g.a	$2$	$0$	$0$	$0$	$-12$	$-10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-2+2\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots$
126.3.n.b	$126$	$3$	126.n	7.d	$6$	$4$	$2$	$3.433$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			126.3.n.b	$4$	$0$	$0$	$0$	$0$	$14$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(2\beta _{1}+4\beta _{3})q^{5}+\cdots$
126.3.n.c	$126$	$3$	126.n	7.d	$6$	$4$	$2$	$3.433$	$\Q(\sqrt{2}, \sqrt{-3})$	None					14.3.d.a	$2$	$0$	$0$	$0$	$6$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(1-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
126.3.o.a	$126$	$3$	126.o	63.l	$6$	$32$	$16$	$3.433$		None		✓	✓	✓	126.3.o.a	$4$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
126.3.p.a	$126$	$3$	126.p	63.t	$6$	$32$	$16$	$3.433$		None		✓	✓	✓	126.3.j.a	$2$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
126.3.q.a	$126$	$3$	126.q	9.d	$6$	$24$	$12$	$3.433$		None		✓	✓	✓	126.3.q.a	$2$	$0$	$0$	$0$	$36$	$0$			$\mathrm{SU}(2)[C_{6}]$
126.3.r.a	$126$	$3$	126.r	63.j	$6$	$32$	$16$	$3.433$		None		✓	✓	✓	126.3.i.a	$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{6}]$
126.3.s.a	$126$	$3$	126.s	21.h	$6$	$4$	$2$	$3.433$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			126.3.s.a	$4$	$0$	$0$	$0$	$0$	$-14$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+3\beta _{1}q^{5}+(-7+\cdots)q^{7}+\cdots$
126.3.s.b	$126$	$3$	126.s	21.h	$6$	$4$	$2$	$3.433$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			126.3.s.b	$4$	$0$	$0$	$0$	$0$	$26$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+\beta _{1}q^{5}+(5+3\beta _{2}+\cdots)q^{7}+\cdots$
126.4.a.a	$126$	$4$	126.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	None	✓				42.4.a.a	$1$	$0$	$-2$	$0$	$-18$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-18q^{5}+7q^{7}-8q^{8}+\cdots$
126.4.a.b	$126$	$4$	126.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	None	✓	✓	✓	✓	126.4.a.b	$1$	$1$	$-2$	$0$	$-6$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-6q^{5}+7q^{7}-8q^{8}+\cdots$
126.4.a.c	$126$	$4$	126.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	None	✓		✓	✓	42.4.a.b	$1$	$1$	$-2$	$0$	$-2$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-2q^{5}-7q^{7}-8q^{8}+\cdots$
126.4.a.d	$126$	$4$	126.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	None	✓				14.4.a.b	$1$	$0$	$-2$	$0$	$12$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+12q^{5}+7q^{7}-8q^{8}+\cdots$
126.4.a.e	$126$	$4$	126.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	None	✓	✓	✓	✓	126.4.a.e	$1$	$0$	$-2$	$0$	$22$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+22q^{5}-7q^{7}-8q^{8}+\cdots$
126.4.a.f	$126$	$4$	126.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	None	✓	✓	✓	✓	126.4.a.e	$1$	$1$	$2$	$0$	$-22$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}-22q^{5}-7q^{7}+8q^{8}+\cdots$
126.4.a.g	$126$	$4$	126.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	None	✓	✓	✓	✓	126.4.a.b	$1$	$0$	$2$	$0$	$6$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+6q^{5}+7q^{7}+8q^{8}+\cdots$
126.4.a.h	$126$	$4$	126.a	1.a	$1$	$1$	$1$	$7.434$	$\Q$	None	✓		✓	✓	14.4.a.a	$1$	$0$	$2$	$0$	$14$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+14q^{5}-7q^{7}+8q^{8}+\cdots$
126.4.d.a	$126$	$4$	126.d	21.c	$2$	$8$	$8$	$7.434$	8.0.$\cdots$.6	None		✓	✓	✓	126.4.d.a	$4$	$0$	$0$	$0$	$0$	$40$		$2^{9}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-4q^{4}-\beta _{5}q^{5}+(5+\beta _{7})q^{7}+\cdots$
126.4.e.a	$126$	$4$	126.e	63.h	$3$	$24$	$12$	$7.434$		None		✓			126.4.e.a	$2$	$0$	$-48$	$-2$	$10$	$-5$			$\mathrm{SU}(2)[C_{3}]$
126.4.e.b	$126$	$4$	126.e	63.h	$3$	$24$	$12$	$7.434$		None		✓			126.4.e.b	$2$	$0$	$48$	$2$	$10$	$17$			$\mathrm{SU}(2)[C_{3}]$
126.4.f.a	$126$	$4$	126.f	9.c	$3$	$6$	$3$	$7.434$	6.0.309123.1	None		✓			126.4.f.a	$2$	$0$	$6$	$-12$	$-9$	$-21$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+2\beta _{3}q^{2}+(-2-\beta _{1}+\beta _{5})q^{3}+(-4+\cdots)q^{4}+\cdots$
126.4.f.b	$126$	$4$	126.f	9.c	$3$	$8$	$4$	$7.434$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			126.4.f.b	$2$	$0$	$-8$	$9$	$1$	$28$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2-2\beta _{1})q^{2}+(2+\beta _{1}-\beta _{2})q^{3}+\cdots$
126.4.f.c	$126$	$4$	126.f	9.c	$3$	$10$	$5$	$7.434$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓			126.4.f.c	$2$	$0$	$10$	$4$	$1$	$35$		$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\beta _{3})q^{2}-\beta _{2}q^{3}-4\beta _{3}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$

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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.