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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 233 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
504.1.e.a	$504$	$1$	504.e	168.e	$2$	$4$	$4$	$0.252$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
504.1.l.a	$504$	$1$	504.l	56.h	$2$	$1$	$1$	$0.252$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$1$	$0$	$0$	$-1$		$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{14}+q^{16}+\cdots$
504.1.l.b	$504$	$1$	504.l	56.h	$2$	$2$	$2$	$0.252$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{42}) $		$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{2}-q^{4}+q^{7}+iq^{8}-iq^{11}+\cdots$
504.1.ba.a	$504$	$1$	504.ba	504.aa	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
504.1.bn.a	$504$	$1$	504.bn	504.an	$6$	$2$	$1$	$0.252$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
504.1.bn.b	$504$	$1$	504.bn	504.an	$6$	$2$	$1$	$0.252$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$-1$	$2$	$1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
504.1.bn.c	$504$	$1$	504.bn	504.an	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$2$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
504.1.bw.a	$504$	$1$	504.bw	56.j	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
504.1.ce.a	$504$	$1$	504.ce	504.be	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}+\zeta_{12}^{3}q^{6}+\cdots$
504.1.cu.a	$504$	$1$	504.cu	21.h	$6$	$4$	$2$	$0.252$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}-\beta _{1}q^{11}-q^{13}+\cdots$
504.2.a.a	$504$	$2$	504.a	1.a	$1$	$1$	$1$	$4.024$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-2q^{11}+2q^{13}-6q^{17}+\cdots$
504.2.a.b	$504$	$2$	504.a	1.a	$1$	$1$	$1$	$4.024$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots$
504.2.a.c	$504$	$2$	504.a	1.a	$1$	$1$	$1$	$4.024$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots$
504.2.a.d	$504$	$2$	504.a	1.a	$1$	$1$	$1$	$4.024$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-6q^{11}-6q^{13}+2q^{17}+\cdots$
504.2.a.e	$504$	$2$	504.a	1.a	$1$	$1$	$1$	$4.024$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots$
504.2.a.f	$504$	$2$	504.a	1.a	$1$	$1$	$1$	$4.024$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+2q^{11}+2q^{13}+6q^{17}+\cdots$
504.2.a.g	$504$	$2$	504.a	1.a	$1$	$1$	$1$	$4.024$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+6q^{11}-6q^{13}-2q^{17}+\cdots$
504.2.a.h	$504$	$2$	504.a	1.a	$1$	$1$	$1$	$4.024$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+q^{7}+2q^{17}-2q^{19}-8q^{23}+\cdots$
504.2.c.a	$504$	$2$	504.c	8.b	$2$	$2$	$2$	$4.024$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}-\beta q^{5}+q^{7}-2\beta q^{8}+\cdots$
504.2.c.b	$504$	$2$	504.c	8.b	$2$	$4$	$4$	$4.024$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots$
504.2.c.c	$504$	$2$	504.c	8.b	$2$	$4$	$4$	$4.024$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+\beta _{2}q^{5}+q^{7}+\cdots$
504.2.c.d	$504$	$2$	504.c	8.b	$2$	$4$	$4$	$4.024$	4.0.2312.1	$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}-q^{7}+\cdots$
504.2.c.e	$504$	$2$	504.c	8.b	$2$	$8$	$8$	$4.024$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}-q^{7}+\beta _{3}q^{8}+\cdots$
504.2.c.f	$504$	$2$	504.c	8.b	$2$	$8$	$8$	$4.024$	8.0.386672896.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$8$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{2}q^{4}+(-\beta _{2}+\beta _{6})q^{5}+\cdots$
504.2.i.a	$504$	$2$	504.i	168.i	$2$	$8$	$8$	$4.024$	8.0.157351936.1	$_{}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{7}+\beta _{3}q^{8}+\cdots$
504.2.i.b	$504$	$2$	504.i	168.i	$2$	$24$	$24$	$4.024$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
504.2.j.a	$504$	$2$	504.j	24.f	$2$	$24$	$24$	$4.024$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
504.2.k.a	$504$	$2$	504.k	21.c	$2$	$8$	$8$	$4.024$	$\Q(\zeta_{16})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{16}^{7}q^{5}+(1+\zeta_{16}^{4})q^{7}+(\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{11}+\cdots$
504.2.p.a	$504$	$2$	504.p	56.e	$2$	$2$	$2$	$4.024$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+\beta )q^{2}+(-1-\beta )q^{4}+(-1+\cdots)q^{7}+\cdots$
504.2.p.b	$504$	$2$	504.p	56.e	$2$	$4$	$4$	$4.024$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\zeta_{12})q^{2}-2\zeta_{12}q^{4}+2\zeta_{12}^{3}q^{5}+\cdots$
504.2.p.c	$504$	$2$	504.p	56.e	$2$	$4$	$4$	$4.024$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-42}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots$
504.2.p.d	$504$	$2$	504.p	56.e	$2$	$4$	$4$	$4.024$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}+(2-\beta _{2})q^{4}+(-1+2\beta _{2}+\cdots)q^{7}+\cdots$
504.2.p.e	$504$	$2$	504.p	56.e	$2$	$4$	$4$	$4.024$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{12})q^{2}+2\zeta_{12}q^{4}-2\zeta_{12}^{3}q^{5}+\cdots$
504.2.p.f	$504$	$2$	504.p	56.e	$2$	$4$	$4$	$4.024$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}+\beta _{3}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
504.2.p.g	$504$	$2$	504.p	56.e	$2$	$16$	$16$	$4.024$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{3}q^{4}+\beta _{5}q^{5}+\beta _{8}q^{7}+\cdots$
504.2.q.a	$504$	$2$	504.q	63.h	$3$	$2$	$1$	$4.024$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
504.2.q.b	$504$	$2$	504.q	63.h	$3$	$2$	$1$	$4.024$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
504.2.q.c	$504$	$2$	504.q	63.h	$3$	$22$	$11$	$4.024$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$1$	$5$			$\mathrm{SU}(2)[C_{3}]$
504.2.q.d	$504$	$2$	504.q	63.h	$3$	$22$	$11$	$4.024$		$_{}$	None	None		$2$	$0$	$0$	$2$	$3$	$-5$			$\mathrm{SU}(2)[C_{3}]$
504.2.r.a	$504$	$2$	504.r	9.c	$3$	$2$	$1$	$4.024$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots$
504.2.r.b	$504$	$2$	504.r	9.c	$3$	$2$	$1$	$4.024$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-\zeta_{6}q^{7}+\cdots$
504.2.r.c	$504$	$2$	504.r	9.c	$3$	$6$	$3$	$4.024$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
504.2.r.d	$504$	$2$	504.r	9.c	$3$	$8$	$4$	$4.024$	8.0.508277025.1	$_{}$	None	None		$2$	$0$	$0$	$-4$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}-\beta _{6})q^{3}+(1+\beta _{1}+2\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$
504.2.r.e	$504$	$2$	504.r	9.c	$3$	$8$	$4$	$4.024$	8.0.2091141441.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
504.2.r.f	$504$	$2$	504.r	9.c	$3$	$10$	$5$	$4.024$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$5$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
504.2.s.a	$504$	$2$	504.s	7.c	$3$	$2$	$1$	$4.024$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-4+4\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}-3q^{13}+\cdots$
504.2.s.b	$504$	$2$	504.s	7.c	$3$	$2$	$1$	$4.024$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+5\zeta_{6}q^{11}+\cdots$
504.2.s.c	$504$	$2$	504.s	7.c	$3$	$2$	$1$	$4.024$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots$
504.2.s.d	$504$	$2$	504.s	7.c	$3$	$2$	$1$	$4.024$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots$
504.2.s.e	$504$	$2$	504.s	7.c	$3$	$2$	$1$	$4.024$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-\zeta_{6}q^{11}+\cdots$

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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.