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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 95 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
3420.1.h.a	$3420$	$1$	3420.h	95.d	$2$	$2$	$2$	$1.707$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{11}+(\zeta_{6}+\cdots)q^{17}+\cdots$
3420.1.h.b	$3420$	$1$	3420.h	95.d	$2$	$4$	$4$	$1.707$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-19}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{5}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{7}+(-\zeta_{12}+\cdots)q^{11}+\cdots$
3420.1.u.a	$3420$	$1$	3420.u	285.j	$4$	$8$	$4$	$1.707$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{24}q^{5}+(\zeta_{24}^{8}-\zeta_{24}^{10})q^{7}+(-\zeta_{24}+\cdots)q^{11}+\cdots$
3420.1.u.b	$3420$	$1$	3420.u	285.j	$4$	$8$	$4$	$1.707$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{24}^{7}q^{5}+(-\zeta_{24}^{8}+\zeta_{24}^{10})q^{7}+\cdots$
3420.1.bh.a	$3420$	$1$	3420.bh	95.h	$6$	$2$	$1$	$1.707$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{5}-q^{11}-\zeta_{6}q^{19}-\zeta_{6}q^{25}+\cdots$
3420.1.bn.a	$3420$	$1$	3420.bn	3420.an	$6$	$16$	$8$	$1.707$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{48}^{5}q^{2}+\zeta_{48}q^{3}+\zeta_{48}^{10}q^{4}+\cdots$
3420.1.bn.b	$3420$	$1$	3420.bn	3420.an	$6$	$16$	$8$	$1.707$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{48}^{9}q^{2}+\zeta_{48}^{19}q^{3}+\zeta_{48}^{18}q^{4}+\cdots$
3420.1.df.a	$3420$	$1$	3420.df	380.p	$6$	$4$	$2$	$1.707$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
3420.1.df.b	$3420$	$1$	3420.df	380.p	$6$	$4$	$2$	$1.707$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
3420.1.es.a	$3420$	$1$	3420.es	95.m	$12$	$4$	$1$	$1.707$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$-4$		$1$		$q-\zeta_{12}^{2}q^{5}+(-1+\zeta_{12}^{3})q^{7}+q^{11}+\cdots$
3420.1.es.b	$3420$	$1$	3420.es	95.m	$12$	$4$	$1$	$1.707$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{2}q^{5}-q^{11}+(-\zeta_{12}+\zeta_{12}^{4}+\cdots)q^{13}+\cdots$
3420.1.es.c	$3420$	$1$	3420.es	95.m	$12$	$4$	$1$	$1.707$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$-4$		$1$		$q+\zeta_{12}^{2}q^{5}+(-1+\zeta_{12}^{3})q^{7}-q^{11}+\cdots$
3420.1.fk.a	$3420$	$1$	3420.fk	380.aa	$18$	$12$	$2$	$1.707$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{5}q^{2}+\zeta_{36}^{10}q^{4}+\zeta_{36}q^{5}+\cdots$
3420.1.fk.b	$3420$	$1$	3420.fk	380.aa	$18$	$12$	$2$	$1.707$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{3}q^{2}+\zeta_{36}^{6}q^{4}-\zeta_{36}q^{5}+\zeta_{36}^{9}q^{8}+\cdots$
3420.2.a.a	$3420$	$2$	3420.a	1.a	$1$	$1$	$1$	$27.309$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-2q^{11}+6q^{13}+2q^{17}+\cdots$
3420.2.a.b	$3420$	$2$	3420.a	1.a	$1$	$1$	$1$	$27.309$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-4q^{11}+2q^{17}+q^{19}+\cdots$
3420.2.a.c	$3420$	$2$	3420.a	1.a	$1$	$1$	$1$	$27.309$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-4q^{13}+2q^{17}-q^{19}+\cdots$
3420.2.a.d	$3420$	$2$	3420.a	1.a	$1$	$1$	$1$	$27.309$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+4q^{11}-4q^{13}-6q^{17}+\cdots$
3420.2.a.e	$3420$	$2$	3420.a	1.a	$1$	$1$	$1$	$27.309$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-4q^{13}-6q^{17}+q^{19}+\cdots$
3420.2.a.f	$3420$	$2$	3420.a	1.a	$1$	$1$	$1$	$27.309$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+6q^{13}-2q^{17}-q^{19}+\cdots$
3420.2.a.g	$3420$	$2$	3420.a	1.a	$1$	$2$	$2$	$27.309$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-2+2\beta )q^{7}+2q^{11}+(-2+\cdots)q^{13}+\cdots$
3420.2.a.h	$3420$	$2$	3420.a	1.a	$1$	$2$	$2$	$27.309$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-2\beta q^{11}+(-1+\beta )q^{13}+\cdots$
3420.2.a.i	$3420$	$2$	3420.a	1.a	$1$	$2$	$2$	$27.309$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(1-\beta )q^{13}+\cdots$
3420.2.a.j	$3420$	$2$	3420.a	1.a	$1$	$3$	$3$	$27.309$	3.3.404.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta _{2})q^{7}+(1-\beta _{1}+2\beta _{2})q^{11}+\cdots$
3420.2.a.k	$3420$	$2$	3420.a	1.a	$1$	$3$	$3$	$27.309$	3.3.1524.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}-\beta _{1}q^{7}+(1+\beta _{2})q^{11}+(2-\beta _{1}+\cdots)q^{13}+\cdots$
3420.2.a.l	$3420$	$2$	3420.a	1.a	$1$	$3$	$3$	$27.309$	3.3.564.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{1})q^{11}+\cdots$
3420.2.a.m	$3420$	$2$	3420.a	1.a	$1$	$3$	$3$	$27.309$	3.3.564.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+(1-\beta _{2})q^{7}+(-2-\beta _{1}+\beta _{2})q^{11}+\cdots$
3420.2.a.n	$3420$	$2$	3420.a	1.a	$1$	$3$	$3$	$27.309$	3.3.404.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta _{2})q^{7}+(-1+\beta _{1}-2\beta _{2})q^{11}+\cdots$
3420.2.a.o	$3420$	$2$	3420.a	1.a	$1$	$3$	$3$	$27.309$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{1})q^{11}+\cdots$
3420.2.e.a	$3420$	$2$	3420.e	285.b	$2$	$16$	$16$	$27.309$	16.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-19}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{8}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{5}+(-\beta _{11}+\beta _{12})q^{7}+(-\beta _{9}+\cdots)q^{11}+\cdots$
3420.2.e.b	$3420$	$2$	3420.e	285.b	$2$	$24$	$24$	$27.309$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3420.2.f.a	$3420$	$2$	3420.f	5.b	$2$	$4$	$4$	$27.309$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(3-\beta _{2})q^{11}+\cdots$
3420.2.f.b	$3420$	$2$	3420.f	5.b	$2$	$6$	$6$	$27.309$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{4})q^{5}-\beta _{5}q^{7}+(1-\beta _{2})q^{11}+\cdots$
3420.2.f.c	$3420$	$2$	3420.f	5.b	$2$	$6$	$6$	$27.309$	6.0.14077504.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-3-\beta _{1}+\cdots)q^{11}+\cdots$
3420.2.f.d	$3420$	$2$	3420.f	5.b	$2$	$8$	$8$	$27.309$	8.0.796594176.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}-\beta _{5}q^{7}-\beta _{1}q^{11}-\beta _{5}q^{13}+\cdots$
3420.2.f.e	$3420$	$2$	3420.f	5.b	$2$	$10$	$10$	$27.309$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{5}+\beta _{4}q^{7}+(-1+\beta _{5})q^{11}+\cdots$
3420.2.f.f	$3420$	$2$	3420.f	5.b	$2$	$12$	$12$	$27.309$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{5}q^{7}+\beta _{3}q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots$
3420.2.j.a	$3420$	$2$	3420.j	57.d	$2$	$24$	$24$	$27.309$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
3420.2.t.a	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}-5q^{7}-6q^{11}+\zeta_{6}q^{13}+\cdots$
3420.2.t.b	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}-4q^{7}+3q^{11}-6\zeta_{6}q^{13}+\cdots$
3420.2.t.c	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}-3q^{7}+2q^{11}+\zeta_{6}q^{13}+\cdots$
3420.2.t.d	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}-2q^{7}-2q^{11}+4\zeta_{6}q^{13}+\cdots$
3420.2.t.e	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+2q^{7}-3q^{11}+6\zeta_{6}q^{13}+\cdots$
3420.2.t.f	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+2q^{7}+q^{11}-6\zeta_{6}q^{13}+\cdots$
3420.2.t.g	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+2q^{7}+6q^{11}+(5+\cdots)q^{17}+\cdots$
3420.2.t.h	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+2q^{7}+6q^{11}+4\zeta_{6}q^{13}+\cdots$
3420.2.t.i	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+4q^{7}+2q^{11}-6\zeta_{6}q^{13}+\cdots$
3420.2.t.j	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{5}-2q^{7}-3q^{11}+(-4+\cdots)q^{17}+\cdots$
3420.2.t.k	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{5}-2q^{7}+q^{11}-4\zeta_{6}q^{13}+\cdots$
3420.2.t.l	$3420$	$2$	3420.t	19.c	$3$	$2$	$1$	$27.309$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{5}-2q^{7}+2q^{11}+(1-\zeta_{6})q^{17}+\cdots$

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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.