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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 70 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
621.1.f.a	$621$	$1$	621.f	207.f	$6$	$6$	$3$	$0.310$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None			✓	✓	207.1.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
621.1.k.a	$621$	$1$	621.k	621.k	$18$	$18$	$3$	$0.310$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-23}) $	None		✓	✓	✓	621.1.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{54}+\zeta_{54}^{20})q^{2}-\zeta_{54}^{5}q^{3}+\cdots$
621.2.a.a	$621$	$2$	621.a	1.a	$1$	$1$	$1$	$4.959$	$\Q$	$_{}$	None	None	✓	✓			621.2.a.a	$1$	$1$	$-1$	$0$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-3q^{5}+4q^{7}+3q^{8}+3q^{10}+\cdots$
621.2.a.b	$621$	$2$	621.a	1.a	$1$	$1$	$1$	$4.959$	$\Q$	$_{}$	None	None	✓	✓			621.2.a.a	$1$	$0$	$1$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+3q^{5}+4q^{7}-3q^{8}+3q^{10}+\cdots$
621.2.a.c	$621$	$2$	621.a	1.a	$1$	$2$	$2$	$4.959$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			621.2.a.c	$1$	$1$	$-2$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(1+2\beta )q^{5}+\cdots$
621.2.a.d	$621$	$2$	621.a	1.a	$1$	$2$	$2$	$4.959$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			621.2.a.d	$1$	$1$	$-1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+\beta q^{5}+(-1+\cdots)q^{7}+\cdots$
621.2.a.e	$621$	$2$	621.a	1.a	$1$	$2$	$2$	$4.959$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			621.2.a.e	$1$	$1$	$-1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+\beta q^{5}+(-1+\beta )q^{7}+\cdots$
621.2.a.f	$621$	$2$	621.a	1.a	$1$	$2$	$2$	$4.959$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			621.2.a.f	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-2-\beta )q^{5}+(1+\beta )q^{7}-2\beta q^{8}+\cdots$
621.2.a.g	$621$	$2$	621.a	1.a	$1$	$2$	$2$	$4.959$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			621.2.a.f	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2-\beta )q^{5}+(1-\beta )q^{7}-2\beta q^{8}+\cdots$
621.2.a.h	$621$	$2$	621.a	1.a	$1$	$2$	$2$	$4.959$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			621.2.a.d	$1$	$1$	$1$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-\beta q^{5}+(-1+\cdots)q^{7}+\cdots$
621.2.a.i	$621$	$2$	621.a	1.a	$1$	$2$	$2$	$4.959$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			621.2.a.e	$1$	$0$	$1$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}-\beta q^{5}+(-1+\beta )q^{7}+\cdots$
621.2.a.j	$621$	$2$	621.a	1.a	$1$	$2$	$2$	$4.959$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			621.2.a.c	$1$	$0$	$2$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-1+2\beta )q^{5}+\cdots$
621.2.a.k	$621$	$2$	621.a	1.a	$1$	$6$	$6$	$4.959$	6.6.536092432.1	$_{}$	None	None	✓	✓	✓		621.2.a.k	$1$	$0$	$-1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
621.2.a.l	$621$	$2$	621.a	1.a	$1$	$6$	$6$	$4.959$	6.6.536092432.1	$_{}$	None	None	✓	✓	✓		621.2.a.k	$1$	$0$	$1$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
621.2.c.a	$621$	$2$	621.c	69.c	$2$	$16$	$16$	$4.959$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			621.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+(-1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots$
621.2.c.b	$621$	$2$	621.c	69.c	$2$	$16$	$16$	$4.959$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			621.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-1+\beta _{4})q^{4}-\beta _{13}q^{5}+\cdots$
621.2.e.a	$621$	$2$	621.e	9.c	$3$	$16$	$8$	$4.959$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					207.2.e.a	$2$	$0$	$1$	$0$	$0$	$7$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{3}-\beta _{9}-\beta _{14})q^{4}+\cdots$
621.2.e.b	$621$	$2$	621.e	9.c	$3$	$28$	$14$	$4.959$		$_{}$	None	None			✓		207.2.e.b	$2$	$0$	$1$	$0$	$0$	$-9$			$\mathrm{SU}(2)[C_{3}]$
621.2.g.a	$621$	$2$	621.g	207.g	$6$	$12$	$6$	$4.959$	12.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-23}) $	None					207.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{6}]$	$q-\beta _{7}q^{2}+(2+2\beta _{3}-\beta _{4}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots$
621.2.g.b	$621$	$2$	621.g	207.g	$6$	$32$	$16$	$4.959$		$_{}$	None	None			✓		207.2.g.b	$4$	$0$	$6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
621.2.i.a	$621$	$2$	621.i	27.e	$9$	$180$	$30$	$4.959$		$_{}$	None	None		✓			621.2.i.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
621.2.i.b	$621$	$2$	621.i	27.e	$9$	$216$	$36$	$4.959$		$_{}$	None	None		✓	✓		621.2.i.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
621.2.j.a	$621$	$2$	621.j	23.c	$11$	$80$	$8$	$4.959$		$_{}$	None	None		✓			621.2.j.a	$2$	$0$	$-2$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{11}]$
621.2.j.b	$621$	$2$	621.j	23.c	$11$	$80$	$8$	$4.959$		$_{}$	None	None		✓			621.2.j.b	$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{11}]$
621.2.j.c	$621$	$2$	621.j	23.c	$11$	$80$	$8$	$4.959$		$_{}$	None	None		✓			621.2.j.c	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{11}]$
621.2.j.d	$621$	$2$	621.j	23.c	$11$	$80$	$8$	$4.959$		$_{}$	None	None		✓			621.2.j.a	$2$	$0$	$2$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{11}]$
621.2.m.a	$621$	$2$	621.m	621.m	$18$	$36$	$6$	$4.959$		$_{}$	$\Q(\sqrt{-23}) $	None		✓			621.2.m.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{18}]$
621.2.m.b	$621$	$2$	621.m	621.m	$18$	$384$	$64$	$4.959$		$_{}$	None	None		✓	✓		621.2.m.b	$4$	$0$	$-12$	$-12$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
621.2.o.a	$621$	$2$	621.o	69.g	$22$	$160$	$16$	$4.959$		$_{}$	None	None		✓			621.2.o.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
621.2.o.b	$621$	$2$	621.o	69.g	$22$	$160$	$16$	$4.959$		$_{}$	None	None		✓			621.2.o.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
621.2.q.a	$621$	$2$	621.q	207.m	$33$	$440$	$22$	$4.959$		$_{}$	None	None			✓	✓	207.2.m.a	$4$	$0$	$9$	$0$	$11$	$-9$			$\mathrm{SU}(2)[C_{33}]$
621.2.s.a	$621$	$2$	621.s	207.o	$66$	$440$	$22$	$4.959$		$_{}$	None	None			✓	✓	207.2.o.a	$4$	$0$	$27$	$0$	$33$	$-11$			$\mathrm{SU}(2)[C_{66}]$
621.2.u.a	$621$	$2$	621.u	621.u	$99$	$4200$	$70$	$4.959$		$_{}$	None	None		✓	✓	✓	621.2.u.a	$4$	$0$	$-54$	$-54$	$-60$	$-54$			$\mathrm{SU}(2)[C_{99}]$
621.2.v.a	$621$	$2$	621.v	621.v	$198$	$4200$	$70$	$4.959$		$_{}$	None	None		✓	✓	✓	621.2.v.a	$4$	$0$	$-54$	$-54$	$-66$	$-66$			$\mathrm{SU}(2)[C_{198}]$
621.3.b.a	$621$	$3$	621.b	3.b	$2$	$4$	$4$	$16.921$	$\Q(\sqrt{-7}, \sqrt{-23})$	$_{}$	None	None		✓			621.3.b.a	$2$	$0$	$0$	$0$	$0$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{2}+(-3-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
621.3.b.b	$621$	$3$	621.b	3.b	$2$	$4$	$4$	$16.921$	$\Q(\sqrt{-7}, \sqrt{-23})$	$_{}$	None	None		✓			621.3.b.b	$2$	$0$	$0$	$0$	$0$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-3q^{4}-\beta _{1}q^{5}+(-1+\beta _{3})q^{7}+\cdots$
621.3.b.c	$621$	$3$	621.b	3.b	$2$	$6$	$6$	$16.921$	6.0.94221248.1	$_{}$	None	None		✓			621.3.b.c	$2$	$0$	$0$	$0$	$0$	$30$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-1-2\beta _{1})q^{4}+(2\beta _{3}+2\beta _{4}+\cdots)q^{5}+\cdots$
621.3.b.d	$621$	$3$	621.b	3.b	$2$	$16$	$16$	$16.921$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			621.3.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
621.3.b.e	$621$	$3$	621.b	3.b	$2$	$28$	$28$	$16.921$		$_{}$	None	None		✓	✓		621.3.b.e	$2$	$0$	$0$	$0$	$0$	$-20$			$\mathrm{SU}(2)[C_{2}]$
621.3.d.a	$621$	$3$	621.d	23.b	$2$	$32$	$32$	$16.921$		$_{}$	None	None		✓			621.3.d.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
621.3.d.b	$621$	$3$	621.d	23.b	$2$	$32$	$32$	$16.921$		$_{}$	None	None		✓			621.3.d.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
621.3.f.a	$621$	$3$	621.f	207.f	$6$	$12$	$6$	$16.921$	12.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-23}) $	None					207.3.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$3^{11}$	$\mathrm{U}(1)[D_{6}]$	$q-\beta _{3}q^{2}+(4\beta _{2}-\beta _{4}-\beta _{8})q^{4}+(-3+\cdots)q^{8}+\cdots$
621.3.f.b	$621$	$3$	621.f	207.f	$6$	$80$	$40$	$16.921$		$_{}$	None	None			✓		207.3.f.b	$4$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
621.3.h.a	$621$	$3$	621.h	9.d	$6$	$88$	$44$	$16.921$		$_{}$	None	None			✓	✓	207.3.h.a	$2$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{6}]$
621.4.a.a	$621$	$4$	621.a	1.a	$1$	$9$	$9$	$36.640$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓			621.4.a.a	$1$	$1$	$-2$	$0$	$-7$	$-3$	$-$	$3^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$
621.4.a.b	$621$	$4$	621.a	1.a	$1$	$9$	$9$	$36.640$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓			621.4.a.a	$1$	$1$	$2$	$0$	$7$	$-3$	$-$	$3^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots$
621.4.a.c	$621$	$4$	621.a	1.a	$1$	$10$	$10$	$36.640$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓	✓		621.4.a.c	$1$	$1$	$-4$	$0$	$-10$	$-8$	$-$	$2^{5}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
621.4.a.d	$621$	$4$	621.a	1.a	$1$	$10$	$10$	$36.640$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓			621.4.a.c	$1$	$0$	$4$	$0$	$10$	$-8$	$+$	$2^{5}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
621.4.a.e	$621$	$4$	621.a	1.a	$1$	$12$	$12$	$36.640$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓		621.4.a.e	$1$	$1$	$-4$	$0$	$-10$	$-14$	$-$	$2^{9}\cdot 3^{6}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(-1-\beta _{7})q^{5}+\cdots$
621.4.a.f	$621$	$4$	621.a	1.a	$1$	$12$	$12$	$36.640$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓			621.4.a.e	$1$	$0$	$4$	$0$	$10$	$-14$	$+$	$2^{9}\cdot 3^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(1+\beta _{7})q^{5}+\cdots$

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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.