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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 142 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
2205.1.e.a	$2205$	$1$	2205.e	35.c	$2$	$4$	$4$	$1.100$	4.0.2048.2	$D_{8}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots$
2205.1.e.b	$2205$	$1$	2205.e	35.c	$2$	$4$	$4$	$1.100$	4.0.2048.2	$D_{8}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots$
2205.1.f.a	$2205$	$1$	2205.f	15.d	$2$	$4$	$4$	$1.100$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-q^{4}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{11}+\cdots$
2205.1.q.a	$2205$	$1$	2205.q	315.q	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots$
2205.1.q.b	$2205$	$1$	2205.q	315.q	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots$
2205.1.v.a	$2205$	$1$	2205.v	315.v	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$2$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+q^{5}-\zeta_{6}q^{9}+(-\zeta_{6}+\cdots)q^{11}+\cdots$
2205.1.v.b	$2205$	$1$	2205.v	315.v	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$-2$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}-q^{5}-\zeta_{6}q^{9}+(-\zeta_{6}+\cdots)q^{11}+\cdots$
2205.1.y.a	$2205$	$1$	2205.y	105.o	$6$	$8$	$4$	$1.100$	$\Q(\zeta_{24})$	$D_{4}$	None	$\Q(\sqrt{5}) $		$16$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+\zeta_{24}^{4}q^{4}-\zeta_{24}^{2}q^{5}+(-\zeta_{24}+\zeta_{24}^{7}+\cdots)q^{11}+\cdots$
2205.1.ba.a	$2205$	$1$	2205.ba	45.h	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-2$	$1$	$0$		$1$		$q-q^{3}-\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+q^{9}+(-1+\cdots)q^{11}+\cdots$
2205.1.ba.b	$2205$	$1$	2205.ba	45.h	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$2$	$-1$	$0$		$1$		$q+q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+q^{9}+(-1+\cdots)q^{11}+\cdots$
2205.1.bi.a	$2205$	$1$	2205.bi	35.i	$6$	$8$	$4$	$1.100$	8.0.339738624.1	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\beta _{5}q^{2}+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots$
2205.1.bi.b	$2205$	$1$	2205.bi	35.i	$6$	$8$	$4$	$1.100$	8.0.339738624.1	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q+\beta _{5}q^{2}+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{4}-\beta _{4}q^{5}+\cdots$
2205.1.bn.a	$2205$	$1$	2205.bn	315.an	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$2$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}-\zeta_{6}q^{9}-q^{11}+\cdots$
2205.1.bn.b	$2205$	$1$	2205.bn	315.an	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$-2$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}-\zeta_{6}q^{9}-q^{11}+\cdots$
2205.1.br.a	$2205$	$1$	2205.br	315.ar	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-\zeta_{6}q^{3}-q^{4}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{9}+(1+\cdots)q^{11}+\cdots$
2205.1.br.b	$2205$	$1$	2205.br	315.ar	$6$	$2$	$1$	$1.100$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q+\zeta_{6}q^{3}-q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{9}+(1+\cdots)q^{11}+\cdots$
2205.1.bu.a	$2205$	$1$	2205.bu	315.at	$12$	$8$	$2$	$1.100$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$8$	$0$	$0$	$0$		$1$		$q+(1-\zeta_{24}^{6})q^{2}-\zeta_{24}^{11}q^{3}-\zeta_{24}^{6}q^{4}+\cdots$
2205.1.bz.a	$2205$	$1$	2205.bz	45.k	$12$	$8$	$2$	$1.100$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q+(-\zeta_{24}^{4}+\zeta_{24}^{10})q^{2}+\zeta_{24}^{3}q^{3}+\cdots$
2205.1.ci.a	$2205$	$1$	2205.ci	315.bh	$12$	$8$	$2$	$1.100$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q+(-\zeta_{24}^{4}-\zeta_{24}^{10})q^{2}-\zeta_{24}q^{3}+\cdots$
2205.2.a.a	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+2q^{11}+\cdots$
2205.2.a.b	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+6q^{13}+\cdots$
2205.2.a.c	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+2q^{11}+\cdots$
2205.2.a.d	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}+q^{13}+4q^{16}+6q^{17}+\cdots$
2205.2.a.e	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}+3q^{11}-5q^{13}+4q^{16}+\cdots$
2205.2.a.f	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-q^{13}+4q^{16}-6q^{17}+\cdots$
2205.2.a.g	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-2q^{11}+\cdots$
2205.2.a.h	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}-2q^{11}+\cdots$
2205.2.a.i	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+4q^{11}+\cdots$
2205.2.a.j	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}-2q^{10}-q^{11}+\cdots$
2205.2.a.k	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}-2q^{10}+6q^{11}+\cdots$
2205.2.a.l	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}+2q^{10}-q^{11}+\cdots$
2205.2.a.m	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}+2q^{10}+6q^{11}+\cdots$
2205.2.a.n	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}+(-3+\cdots)q^{8}+\cdots$
2205.2.a.o	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}+(-3+\cdots)q^{8}+\cdots$
2205.2.a.p	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{8}+\cdots$
2205.2.a.q	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{8}+\cdots$
2205.2.a.r	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{8}+\cdots$
2205.2.a.s	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{5}-2\beta q^{8}-\beta q^{10}+(-2+\cdots)q^{11}+\cdots$
2205.2.a.t	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{5}-2\beta q^{8}-\beta q^{10}+(3-2\beta )q^{11}+\cdots$
2205.2.a.u	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{5}-2\beta q^{8}+\beta q^{10}+(-2+\cdots)q^{11}+\cdots$
2205.2.a.v	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{5}-2\beta q^{8}+\beta q^{10}+(3-2\beta )q^{11}+\cdots$
2205.2.a.w	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}-q^{5}-\beta q^{8}+\beta q^{10}+\cdots$
2205.2.a.x	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(4+\beta )q^{8}+\cdots$
2205.2.a.y	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(3+\beta )q^{8}+\cdots$
2205.2.a.z	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+(6+2\beta )q^{8}+\cdots$
2205.2.a.ba	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}+q^{5}+(6+2\beta )q^{8}+\cdots$
2205.2.a.bb	$2205$	$2$	2205.a	1.a	$1$	$3$	$3$	$17.607$	3.3.404.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
2205.2.a.bc	$2205$	$2$	2205.a	1.a	$1$	$3$	$3$	$17.607$	3.3.404.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
2205.2.a.bd	$2205$	$2$	2205.a	1.a	$1$	$3$	$3$	$17.607$	3.3.404.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
2205.2.a.be	$2205$	$2$	2205.a	1.a	$1$	$3$	$3$	$17.607$	3.3.404.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$

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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.