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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 277 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
1600.1.b.a	$1600$	$1$	1600.b	4.b	$2$	$1$	$1$	$0.799$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+2q^{29}-2q^{41}+q^{49}+2q^{61}+\cdots$
1600.1.m.a	$1600$	$1$	1600.m	40.i	$4$	$2$	$1$	$0.799$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{9}-iq^{11}-q^{19}+q^{41}-iq^{49}+\cdots$
1600.1.m.b	$1600$	$1$	1600.m	40.i	$4$	$2$	$1$	$0.799$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{9}+iq^{11}+q^{19}+q^{41}-iq^{49}+\cdots$
1600.1.m.c	$1600$	$1$	1600.m	40.i	$4$	$4$	$2$	$0.799$	$\Q(i, \sqrt{6})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}+2\beta _{2}q^{9}-\beta _{2}q^{11}-\beta _{1}q^{17}+\cdots$
1600.1.m.d	$1600$	$1$	1600.m	40.i	$4$	$4$	$2$	$0.799$	$\Q(i, \sqrt{6})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}+2\beta _{2}q^{9}+\beta _{2}q^{11}+\beta _{1}q^{17}+\cdots$
1600.1.p.a	$1600$	$1$	1600.p	5.c	$4$	$2$	$1$	$0.799$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$-2$	$0$	$-2$		$1$		$q+(-1+i)q^{3}+(-1-i)q^{7}-iq^{9}+\cdots$
1600.1.p.b	$1600$	$1$	1600.p	5.c	$4$	$2$	$1$	$0.799$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{9}+(-1+i)q^{13}+(1+i)q^{17}+\cdots$
1600.1.p.c	$1600$	$1$	1600.p	5.c	$4$	$2$	$1$	$0.799$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q+(1-i)q^{3}+(1+i)q^{7}-iq^{9}+q^{21}+\cdots$
1600.1.bd.a	$1600$	$1$	1600.bd	200.n	$10$	$8$	$2$	$0.799$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$-6$	$0$	$0$		$1$		$q+(-1+\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}+\zeta_{20}^{5}q^{7}+\cdots$
1600.1.bd.b	$1600$	$1$	1600.bd	200.n	$10$	$8$	$2$	$0.799$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$6$	$0$	$0$		$1$		$q+(1-\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}-\zeta_{20}^{5}q^{7}+\cdots$
1600.1.bf.a	$1600$	$1$	1600.bf	100.h	$10$	$4$	$1$	$0.799$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\zeta_{10}q^{5}+\zeta_{10}^{3}q^{9}+(\zeta_{10}^{2}-\zeta_{10}^{4}+\cdots)q^{13}+\cdots$
1600.1.bh.a	$1600$	$1$	1600.bh	100.j	$10$	$4$	$1$	$0.799$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{13}+\cdots$
1600.1.bh.b	$1600$	$1$	1600.bh	100.j	$10$	$8$	$2$	$0.799$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{20}^{9}q^{3}-\zeta_{20}^{8}q^{5}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{7}+\cdots$
1600.1.bw.a	$1600$	$1$	1600.bw	25.f	$20$	$8$	$1$	$0.799$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{3}q^{5}-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{13}+\cdots$
1600.2.a.a	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{7}+6q^{9}-q^{11}+4q^{13}+\cdots$
1600.2.a.b	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots$
1600.2.a.c	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{7}+q^{9}+2q^{13}+6q^{17}+\cdots$
1600.2.a.d	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
1600.2.a.e	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
1600.2.a.f	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots$
1600.2.a.g	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}-5q^{11}+5q^{17}+\cdots$
1600.2.a.h	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}+5q^{11}-5q^{17}+\cdots$
1600.2.a.i	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots$
1600.2.a.j	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}+3q^{11}+4q^{13}+\cdots$
1600.2.a.k	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots$
1600.2.a.l	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}-4q^{13}+8q^{17}-10q^{29}+\cdots$
1600.2.a.m	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}+4q^{13}-8q^{17}-10q^{29}+\cdots$
1600.2.a.n	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}+6q^{13}-2q^{17}+10q^{29}+\cdots$
1600.2.a.o	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots$
1600.2.a.p	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}-3q^{11}+4q^{13}+\cdots$
1600.2.a.q	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}+3q^{11}-4q^{13}+\cdots$
1600.2.a.r	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}-5q^{11}-5q^{17}+\cdots$
1600.2.a.s	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}+5q^{11}+5q^{17}+\cdots$
1600.2.a.t	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
1600.2.a.u	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$
1600.2.a.v	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$
1600.2.a.w	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{7}+q^{9}+2q^{13}+6q^{17}+\cdots$
1600.2.a.x	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{7}+6q^{9}-q^{11}-4q^{13}+\cdots$
1600.2.a.y	$1600$	$2$	1600.a	1.a	$1$	$1$	$1$	$12.776$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots$
1600.2.a.z	$1600$	$2$	1600.a	1.a	$1$	$2$	$2$	$12.776$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$6$	$-$	$2$	$N(\mathrm{U}(1))$	$q+(-1-\beta )q^{3}+(3-\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
1600.2.a.ba	$1600$	$2$	1600.a	1.a	$1$	$2$	$2$	$12.776$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2\beta q^{7}+2q^{9}-\beta q^{11}-4q^{13}+\cdots$
1600.2.a.bb	$1600$	$2$	1600.a	1.a	$1$	$2$	$2$	$12.776$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2\beta q^{7}+2q^{9}+\beta q^{11}+4q^{13}+\cdots$
1600.2.a.bc	$1600$	$2$	1600.a	1.a	$1$	$2$	$2$	$12.776$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{7}+5q^{9}+2\beta q^{11}-2q^{13}+\cdots$
1600.2.a.bd	$1600$	$2$	1600.a	1.a	$1$	$2$	$2$	$12.776$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$-6$	$-$	$2$	$N(\mathrm{U}(1))$	$q+(1+\beta )q^{3}+(-3+\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
1600.2.c.a	$1600$	$2$	1600.c	5.b	$2$	$2$	$2$	$12.776$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}-2iq^{7}-6q^{9}-q^{11}-4iq^{13}+\cdots$
1600.2.c.b	$1600$	$2$	1600.c	5.b	$2$	$2$	$2$	$12.776$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}-2iq^{7}-6q^{9}+q^{11}+4iq^{13}+\cdots$
1600.2.c.c	$1600$	$2$	1600.c	5.b	$2$	$2$	$2$	$12.776$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{7}-q^{9}-4q^{11}-3iq^{13}+\cdots$
1600.2.c.d	$1600$	$2$	1600.c	5.b	$2$	$2$	$2$	$12.776$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{7}-q^{9}-iq^{13}+3iq^{17}+\cdots$
1600.2.c.e	$1600$	$2$	1600.c	5.b	$2$	$2$	$2$	$12.776$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{7}-q^{9}+iq^{13}-3iq^{17}+\cdots$
1600.2.c.f	$1600$	$2$	1600.c	5.b	$2$	$2$	$2$	$12.776$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{7}-q^{9}+4q^{11}+3iq^{13}+\cdots$

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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.