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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 124 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1323.1.b.a	$1323$	$1$	1323.b	3.b	$2$	$1$	$1$	$0.660$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-q^{13}+q^{16}+2q^{19}+q^{25}+\cdots$
1323.1.b.b	$1323$	$1$	1323.b	3.b	$2$	$1$	$1$	$0.660$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{13}+q^{16}-2q^{19}+q^{25}+\cdots$
1323.1.d.a	$1323$	$1$	1323.d	7.b	$2$	$2$	$2$	$0.660$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q-q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+q^{16}+q^{25}+\cdots$
1323.1.m.a	$1323$	$1$	1323.m	7.d	$6$	$2$	$1$	$0.660$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}-\zeta_{6}q^{16}+\cdots$
1323.1.q.a	$1323$	$1$	1323.q	21.h	$6$	$2$	$1$	$0.660$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{6}q^{4}+q^{13}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{19}+\cdots$
1323.1.br.a	$1323$	$1$	1323.br	147.n	$42$	$12$	$1$	$0.660$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{42}^{13}q^{4}-\zeta_{42}^{3}q^{7}+(-\zeta_{42}-\zeta_{42}^{5}+\cdots)q^{13}+\cdots$
1323.1.bv.a	$1323$	$1$	1323.bv	49.h	$42$	$12$	$1$	$0.660$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\zeta_{42}^{10}q^{4}-\zeta_{42}^{12}q^{7}+(\zeta_{42}^{4}-\zeta_{42}^{20}+\cdots)q^{13}+\cdots$
1323.2.a.a	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-3q^{5}+6q^{10}-2q^{11}+\cdots$
1323.2.a.b	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}-2q^{10}-4q^{11}+\cdots$
1323.2.a.c	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+3q^{5}-6q^{10}-2q^{11}+\cdots$
1323.2.a.d	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-4q^{5}+3q^{8}+4q^{10}+\cdots$
1323.2.a.e	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-3q^{5}+3q^{8}+3q^{10}+\cdots$
1323.2.a.f	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{5}+3q^{8}-3q^{10}+\cdots$
1323.2.a.g	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+4q^{5}+3q^{8}-4q^{10}+\cdots$
1323.2.a.h	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{5}+6q^{11}+4q^{13}+4q^{16}+\cdots$
1323.2.a.i	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-5q^{13}+4q^{16}+7q^{19}-5q^{25}+\cdots$
1323.2.a.j	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-2q^{13}+4q^{16}+7q^{19}-5q^{25}+\cdots$
1323.2.a.k	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+2q^{13}+4q^{16}-7q^{19}-5q^{25}+\cdots$
1323.2.a.l	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{5}-6q^{11}+4q^{13}+4q^{16}+\cdots$
1323.2.a.m	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots$
1323.2.a.n	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{5}-3q^{8}-3q^{10}+\cdots$
1323.2.a.o	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+3q^{5}-3q^{8}+3q^{10}+\cdots$
1323.2.a.p	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots$
1323.2.a.q	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-3q^{5}-6q^{10}+2q^{11}+\cdots$
1323.2.a.r	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}-2q^{10}+4q^{11}+\cdots$
1323.2.a.s	$1323$	$2$	1323.a	1.a	$1$	$1$	$1$	$10.564$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+3q^{5}+6q^{10}+2q^{11}+\cdots$
1323.2.a.t	$1323$	$2$	1323.a	1.a	$1$	$2$	$2$	$10.564$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}-\beta q^{8}-3q^{10}+\cdots$
1323.2.a.u	$1323$	$2$	1323.a	1.a	$1$	$2$	$2$	$10.564$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+4q^{4}-\beta q^{5}+2\beta q^{8}-6q^{10}+\cdots$
1323.2.a.v	$1323$	$2$	1323.a	1.a	$1$	$2$	$2$	$10.564$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+4q^{4}+\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots$
1323.2.a.w	$1323$	$2$	1323.a	1.a	$1$	$2$	$2$	$10.564$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}+\beta q^{5}+3\beta q^{8}+7q^{10}+\cdots$
1323.2.a.x	$1323$	$2$	1323.a	1.a	$1$	$3$	$3$	$10.564$	3.3.321.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1323.2.a.y	$1323$	$2$	1323.a	1.a	$1$	$3$	$3$	$10.564$	3.3.321.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1323.2.a.z	$1323$	$2$	1323.a	1.a	$1$	$3$	$3$	$10.564$	3.3.321.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots$
1323.2.a.ba	$1323$	$2$	1323.a	1.a	$1$	$3$	$3$	$10.564$	3.3.321.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots$
1323.2.a.bb	$1323$	$2$	1323.a	1.a	$1$	$4$	$4$	$10.564$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-8$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2-\beta _{3})q^{5}+\cdots$
1323.2.a.bc	$1323$	$2$	1323.a	1.a	$1$	$4$	$4$	$10.564$	4.4.7168.1	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+\beta _{3}q^{8}+\cdots$
1323.2.a.bd	$1323$	$2$	1323.a	1.a	$1$	$4$	$4$	$10.564$	4.4.7168.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{1}q^{5}+\beta _{3}q^{8}+\cdots$
1323.2.a.be	$1323$	$2$	1323.a	1.a	$1$	$4$	$4$	$10.564$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$8$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(2+\beta _{3})q^{5}+\cdots$
1323.2.c.a	$1323$	$2$	1323.c	21.c	$2$	$2$	$2$	$10.564$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}-4\zeta_{6}q^{13}+4q^{16}-3\zeta_{6}q^{19}+\cdots$
1323.2.c.b	$1323$	$2$	1323.c	21.c	$2$	$4$	$4$	$10.564$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-3q^{4}-\beta _{1}q^{8}-2\beta _{1}q^{11}+\cdots$
1323.2.c.c	$1323$	$2$	1323.c	21.c	$2$	$4$	$4$	$10.564$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{5}+2\beta _{1}q^{8}+2\beta _{2}q^{10}+\cdots$
1323.2.c.d	$1323$	$2$	1323.c	21.c	$2$	$12$	$12$	$10.564$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}+(-1-\beta _{6})q^{4}+\beta _{1}q^{5}+(-\beta _{8}+\cdots)q^{8}+\cdots$
1323.2.c.e	$1323$	$2$	1323.c	21.c	$2$	$16$	$16$	$10.564$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+(-1-\beta _{1}-\beta _{4})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
1323.2.c.f	$1323$	$2$	1323.c	21.c	$2$	$16$	$16$	$10.564$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-1+\beta _{13})q^{4}-\beta _{2}q^{5}+\cdots$
1323.2.f.a	$1323$	$2$	1323.f	9.c	$3$	$2$	$1$	$10.564$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+3q^{8}+\cdots$
1323.2.f.b	$1323$	$2$	1323.f	9.c	$3$	$2$	$1$	$10.564$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+3q^{8}+\cdots$
1323.2.f.c	$1323$	$2$	1323.f	9.c	$3$	$6$	$3$	$10.564$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$-1$	$0$	$5$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots$
1323.2.f.d	$1323$	$2$	1323.f	9.c	$3$	$6$	$3$	$10.564$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$3$	$0$	$-3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$
1323.2.f.e	$1323$	$2$	1323.f	9.c	$3$	$10$	$5$	$10.564$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-4$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(\beta _{6}+\cdots)q^{5}+\cdots$
1323.2.f.f	$1323$	$2$	1323.f	9.c	$3$	$10$	$5$	$10.564$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$-2$	$0$	$4$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots$

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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.