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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 241 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
600.1.n.a	$600$	$1$	600.n	24.h	$2$	$1$	$1$	$0.299$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
600.1.n.b	$600$	$1$	600.n	24.h	$2$	$1$	$1$	$0.299$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
600.1.q.a	$600$	$1$	600.q	120.q	$4$	$4$	$2$	$0.299$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{30}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{6}+\cdots$
600.1.q.b	$600$	$1$	600.q	120.q	$4$	$8$	$4$	$0.299$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{6}q^{4}-\zeta_{24}^{4}q^{6}+\cdots$
600.1.z.a	$600$	$1$	600.z	600.z	$10$	$8$	$2$	$0.299$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+\zeta_{20}q^{5}+\cdots$
600.1.bj.a	$600$	$1$	600.bj	600.aj	$10$	$4$	$1$	$0.299$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$-1$	$-2$		$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}q^{5}+\cdots$
600.1.bj.b	$600$	$1$	600.bj	600.aj	$10$	$4$	$1$	$0.299$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$1$	$-2$		$1$		$q+\zeta_{10}q^{2}-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}q^{5}+\cdots$
600.2.a.a	$600$	$2$	600.a	1.a	$1$	$1$	$1$	$4.791$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots$
600.2.a.b	$600$	$2$	600.a	1.a	$1$	$1$	$1$	$4.791$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}+2q^{11}+3q^{13}+\cdots$
600.2.a.c	$600$	$2$	600.a	1.a	$1$	$1$	$1$	$4.791$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-4q^{11}-6q^{13}+6q^{17}+\cdots$
600.2.a.d	$600$	$2$	600.a	1.a	$1$	$1$	$1$	$4.791$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
600.2.a.e	$600$	$2$	600.a	1.a	$1$	$1$	$1$	$4.791$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+5q^{7}+q^{9}-6q^{11}+3q^{13}+\cdots$
600.2.a.f	$600$	$2$	600.a	1.a	$1$	$1$	$1$	$4.791$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-5q^{7}+q^{9}-6q^{11}-3q^{13}+\cdots$
600.2.a.g	$600$	$2$	600.a	1.a	$1$	$1$	$1$	$4.791$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
600.2.a.h	$600$	$2$	600.a	1.a	$1$	$1$	$1$	$4.791$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots$
600.2.a.i	$600$	$2$	600.a	1.a	$1$	$1$	$1$	$4.791$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots$
600.2.b.a	$600$	$2$	600.b	24.f	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+(1-\beta )q^{3}-2q^{4}+(2+\beta )q^{6}+\cdots$
600.2.b.b	$600$	$2$	600.b	24.f	$2$	$4$	$4$	$4.791$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}-2q^{4}+(-1+\cdots)q^{6}+\cdots$
600.2.b.c	$600$	$2$	600.b	24.f	$2$	$4$	$4$	$4.791$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots$
600.2.b.d	$600$	$2$	600.b	24.f	$2$	$4$	$4$	$4.791$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}-2q^{4}+(-1+\cdots)q^{6}+\cdots$
600.2.b.e	$600$	$2$	600.b	24.f	$2$	$8$	$8$	$4.791$	8.0.1649659456.5	$_{}$	None	None		$2$	$0$	$-1$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots$
600.2.b.f	$600$	$2$	600.b	24.f	$2$	$8$	$8$	$4.791$	8.0.1649659456.5	$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots$
600.2.b.g	$600$	$2$	600.b	24.f	$2$	$12$	$12$	$4.791$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}-\beta _{5}q^{3}+(1+\beta _{4})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots$
600.2.b.h	$600$	$2$	600.b	24.f	$2$	$12$	$12$	$4.791$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
600.2.b.i	$600$	$2$	600.b	24.f	$2$	$16$	$16$	$4.791$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{10}q^{2}+\beta _{5}q^{3}-\beta _{14}q^{4}+(\beta _{7}+\beta _{12}+\cdots)q^{6}+\cdots$
600.2.d.a	$600$	$2$	600.d	40.f	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}-q^{3}-2iq^{4}+(1-i)q^{6}+\cdots$
600.2.d.b	$600$	$2$	600.d	40.f	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}+q^{3}-2iq^{4}+(-1+\cdots)q^{6}+\cdots$
600.2.d.c	$600$	$2$	600.d	40.f	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}-q^{3}+2iq^{4}+(-1-i)q^{6}+\cdots$
600.2.d.d	$600$	$2$	600.d	40.f	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots$
600.2.d.e	$600$	$2$	600.d	40.f	$2$	$6$	$6$	$4.791$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
600.2.d.f	$600$	$2$	600.d	40.f	$2$	$6$	$6$	$4.791$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+q^{3}-\beta _{1}q^{4}-\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
600.2.d.g	$600$	$2$	600.d	40.f	$2$	$8$	$8$	$4.791$	8.0.214798336.3	$_{}$	None	None		$2$	$0$	$-2$	$-8$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}-q^{3}+(-1-\beta _{1}+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
600.2.d.h	$600$	$2$	600.d	40.f	$2$	$8$	$8$	$4.791$	8.0.214798336.3	$_{}$	None	None		$2$	$0$	$2$	$8$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+q^{3}+(-1-\beta _{1}+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
600.2.f.a	$600$	$2$	600.f	5.b	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+5iq^{7}-q^{9}-6q^{11}-3iq^{13}+\cdots$
600.2.f.b	$600$	$2$	600.f	5.b	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-q^{9}-4q^{11}+6iq^{13}+6iq^{17}+\cdots$
600.2.f.c	$600$	$2$	600.f	5.b	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-4iq^{7}-q^{9}-6iq^{13}+2iq^{17}+\cdots$
600.2.f.d	$600$	$2$	600.f	5.b	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-3iq^{7}-q^{9}+2q^{11}-3iq^{13}+\cdots$
600.2.f.e	$600$	$2$	600.f	5.b	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-q^{9}+4q^{11}+2iq^{13}+2iq^{17}+\cdots$
600.2.k.a	$600$	$2$	600.k	8.b	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\cdots$
600.2.k.b	$600$	$2$	600.k	8.b	$2$	$2$	$2$	$4.791$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}+iq^{3}+2iq^{4}+(-1+i)q^{6}+\cdots$
600.2.k.c	$600$	$2$	600.k	8.b	$2$	$6$	$6$	$4.791$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{2}-\beta _{3})q^{4}+\beta _{4}q^{6}+\cdots$
600.2.k.d	$600$	$2$	600.k	8.b	$2$	$8$	$8$	$4.791$	8.0.214798336.3	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
600.2.k.e	$600$	$2$	600.k	8.b	$2$	$8$	$8$	$4.791$	8.0.214798336.3	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
600.2.k.f	$600$	$2$	600.k	8.b	$2$	$12$	$12$	$4.791$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{6}+\cdots$
600.2.m.a	$600$	$2$	600.m	120.m	$2$	$4$	$4$	$4.791$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+2q^{4}+\cdots$
600.2.m.b	$600$	$2$	600.m	120.m	$2$	$8$	$8$	$4.791$	$\Q(\zeta_{24})$	$_{}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{3}q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots$
600.2.m.c	$600$	$2$	600.m	120.m	$2$	$16$	$16$	$4.791$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-1+\beta _{11}+\cdots)q^{6}+\cdots$
600.2.m.d	$600$	$2$	600.m	120.m	$2$	$16$	$16$	$4.791$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}-\beta _{14}q^{6}+\cdots$
600.2.m.e	$600$	$2$	600.m	120.m	$2$	$24$	$24$	$4.791$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
600.2.r.a	$600$	$2$	600.r	15.e	$4$	$4$	$2$	$4.791$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$

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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.