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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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
436.1.v.a	$436$	$1$	436.v	436.v	$54$	$18$	$1$	$0.218$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{15}q^{2}-\zeta_{54}^{3}q^{4}+(\zeta_{54}^{8}+\zeta_{54}^{14}+\cdots)q^{5}+\cdots$
489.1.p.a	$489$	$1$	489.p	489.p	$54$	$18$	$1$	$0.244$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{54}^{14}q^{3}-\zeta_{54}^{23}q^{4}+(\zeta_{54}^{12}+\cdots)q^{7}+\cdots$
589.1.bg.a	$589$	$1$	589.bg	589.ag	$18$	$18$	$3$	$0.294$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{17}-\zeta_{54}^{25})q^{2}+(-\zeta_{54}^{7}+\cdots)q^{4}+\cdots$
621.1.k.a	$621$	$1$	621.k	621.k	$18$	$18$	$3$	$0.310$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}+\zeta_{54}^{20})q^{2}-\zeta_{54}^{5}q^{3}+\cdots$
648.1.bf.a	$648$	$1$	648.bf	648.af	$54$	$18$	$1$	$0.323$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{7}q^{2}-\zeta_{54}^{19}q^{3}+\zeta_{54}^{14}q^{4}+\cdots$
763.1.bz.a	$763$	$1$	763.bz	763.az	$54$	$18$	$1$	$0.381$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{54}^{2}+\zeta_{54}^{22})q^{2}+(\zeta_{54}^{4}-\zeta_{54}^{17}+\cdots)q^{4}+\cdots$
891.1.w.a	$891$	$1$	891.w	891.w	$54$	$18$	$1$	$0.445$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{13}q^{3}+\zeta_{54}^{10}q^{4}+(\zeta_{54}^{6}+\zeta_{54}^{8}+\cdots)q^{5}+\cdots$
983.1.b.c	$983$	$1$	983.b	983.b	$2$	$9$	$9$	$0.491$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-983}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
1121.1.l.a	$1121$	$1$	1121.l	1121.l	$18$	$18$	$3$	$0.559$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{7}-\zeta_{54}^{17})q^{3}+\zeta_{54}^{6}q^{4}+\cdots$
1141.1.bm.a	$1141$	$1$	1141.bm	1141.am	$54$	$18$	$1$	$0.569$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{54}^{6}+\zeta_{54}^{14})q^{2}+(-\zeta_{54}+\zeta_{54}^{12}+\cdots)q^{4}+\cdots$
1231.1.b.c	$1231$	$1$	1231.b	1231.b	$2$	$9$	$9$	$0.614$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-1231}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1304.1.bf.a	$1304$	$1$	1304.bf	1304.af	$54$	$18$	$1$	$0.651$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{17}q^{2}+(-\zeta_{54}^{11}-\zeta_{54}^{21}+\cdots)q^{3}+\cdots$
1308.1.br.a	$1308$	$1$	1308.br	327.v	$54$	$18$	$1$	$0.653$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{54}^{22}q^{3}+(-\zeta_{54}^{5}+\zeta_{54}^{6})q^{7}+\cdots$
1393.1.n.a	$1393$	$1$	1393.n	1393.n	$6$	$18$	$9$	$0.695$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-199}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{2}+(\zeta_{54}^{10}+\zeta_{54}^{18}+\cdots)q^{4}+\cdots$
1399.1.b.d	$1399$	$1$	1399.b	1399.b	$2$	$9$	$9$	$0.698$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-1399}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
1461.1.o.a	$1461$	$1$	1461.o	1461.o	$54$	$18$	$1$	$0.729$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{17}q^{3}-\zeta_{54}^{19}q^{4}+(\zeta_{54}^{2}+\zeta_{54}^{10}+\cdots)q^{7}+\cdots$
1593.1.l.a	$1593$	$1$	1593.l	1593.l	$18$	$18$	$3$	$0.795$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{17}q^{3}-\zeta_{54}^{15}q^{4}+(\zeta_{54}^{8}-\zeta_{54}^{13}+\cdots)q^{5}+\cdots$
1607.1.b.c	$1607$	$1$	1607.b	1607.b	$2$	$9$	$9$	$0.802$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-1607}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{6}q^{2}-\beta _{1}q^{3}+(1+\beta _{3}-\beta _{6})q^{4}+\cdots$
1620.1.bp.a	$1620$	$1$	1620.bp	1620.ap	$54$	$18$	$1$	$0.808$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{54}^{25}q^{2}-\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots$
1620.1.bp.b	$1620$	$1$	1620.bp	1620.ap	$54$	$18$	$1$	$0.808$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{25}q^{2}+\zeta_{54}^{26}q^{3}-\zeta_{54}^{23}q^{4}+\cdots$
1635.1.cl.a	$1635$	$1$	1635.cl	1635.bl	$54$	$18$	$1$	$0.816$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{10}-\zeta_{54}^{14})q^{2}+\zeta_{54}^{19}q^{3}+\cdots$
1635.1.cl.b	$1635$	$1$	1635.cl	1635.bl	$54$	$18$	$1$	$0.816$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{54}^{10}+\zeta_{54}^{14})q^{2}-\zeta_{54}^{19}q^{3}+\cdots$
1676.1.d.a	$1676$	$1$	1676.d	419.b	$2$	$9$	$9$	$0.836$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-419}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+(\beta _{3}-\beta _{6})q^{5}-\beta _{5}q^{7}+(1+\cdots)q^{9}+\cdots$
1679.1.r.a	$1679$	$1$	1679.r	1679.r	$18$	$18$	$3$	$0.838$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{17}-\zeta_{54}^{25})q^{2}+(\zeta_{54}^{20}+\cdots)q^{3}+\cdots$
1732.1.bb.a	$1732$	$1$	1732.bb	1732.ab	$54$	$18$	$1$	$0.864$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{54}^{24}q^{2}-\zeta_{54}^{21}q^{4}+(\zeta_{54}^{6}-\zeta_{54}^{23}+\cdots)q^{5}+\cdots$
1759.1.b.c	$1759$	$1$	1759.b	1759.b	$2$	$9$	$9$	$0.878$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-1759}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{6}q^{2}+(1+\beta _{3}-\beta _{6})q^{4}-\beta _{1}q^{5}+\cdots$
1793.1.w.a	$1793$	$1$	1793.w	1793.w	$54$	$18$	$1$	$0.895$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-9$	$0$	$1$		$q+(-\zeta_{54}+\zeta_{54}^{6})q^{3}+\zeta_{54}^{26}q^{4}+\cdots$
1863.1.k.a	$1863$	$1$	1863.k	621.k	$18$	$18$	$3$	$0.930$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+(\zeta_{54}-\zeta_{54}^{20})q^{2}+(\zeta_{54}^{2}-\zeta_{54}^{13}+\cdots)q^{4}+\cdots$
1879.1.b.d	$1879$	$1$	1879.b	1879.b	$2$	$9$	$9$	$0.938$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-1879}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{3}-\beta _{6})q^{2}+(1-\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots$
1944.1.bf.a	$1944$	$1$	1944.bf	648.af	$54$	$18$	$1$	$0.970$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{54}^{7}q^{2}+\zeta_{54}^{14}q^{4}+\zeta_{54}^{21}q^{8}+\cdots$
1964.1.d.a	$1964$	$1$	1964.d	491.b	$2$	$9$	$9$	$0.980$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-491}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+\beta _{6}q^{5}+(1+\beta _{2})q^{9}+\beta _{4}q^{11}+\cdots$
1999.1.b.c	$1999$	$1$	1999.b	1999.b	$2$	$9$	$9$	$0.998$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-1999}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{3}-\beta _{6})q^{2}+(1-\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots$
2033.1.l.a	$2033$	$1$	2033.l	2033.l	$18$	$18$	$3$	$1.015$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}+\zeta_{54}^{20})q^{3}+\zeta_{54}^{12}q^{4}+\cdots$
2164.1.be.a	$2164$	$1$	2164.be	2164.ae	$54$	$18$	$1$	$1.080$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{25}q^{2}-\zeta_{54}^{23}q^{4}+(-\zeta_{54}^{17}+\cdots)q^{5}+\cdots$
2180.1.cj.a	$2180$	$1$	2180.cj	2180.bj	$54$	$18$	$1$	$1.088$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$-9$	$0$	$0$	$1$		$q-\zeta_{54}^{15}q^{2}+(-\zeta_{54}^{9}+\zeta_{54}^{16})q^{3}+\cdots$
2180.1.cj.b	$2180$	$1$	2180.cj	2180.bj	$54$	$18$	$1$	$1.088$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$9$	$0$	$0$	$1$		$q+\zeta_{54}^{15}q^{2}+(\zeta_{54}^{9}-\zeta_{54}^{16})q^{3}+\cdots$
2204.1.bk.a	$2204$	$1$	2204.bk	2204.ak	$18$	$18$	$3$	$1.100$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+\zeta_{54}^{6}q^{2}+(-\zeta_{54}+\zeta_{54}^{20})q^{3}+\cdots$
2204.1.bk.b	$2204$	$1$	2204.bk	2204.ak	$18$	$18$	$3$	$1.100$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q-\zeta_{54}^{6}q^{2}+(\zeta_{54}-\zeta_{54}^{20})q^{3}+\zeta_{54}^{12}q^{4}+\cdots$
2241.1.k.a	$2241$	$1$	2241.k	2241.k	$18$	$18$	$3$	$1.118$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{17}q^{3}-\zeta_{54}^{21}q^{4}+(\zeta_{54}^{4}+\zeta_{54}^{8}+\cdots)q^{7}+\cdots$
2252.1.d.a	$2252$	$1$	2252.d	563.b	$2$	$9$	$9$	$1.124$	$\Q(\zeta_{54})^+$	$D_{27}$	$\Q(\sqrt{-563}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+\beta _{4}q^{7}+(1+\beta _{2})q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots$
2289.1.en.a	$2289$	$1$	2289.en	2289.dn	$54$	$18$	$1$	$1.142$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{13}q^{3}+\zeta_{54}^{24}q^{4}+\zeta_{54}^{24}q^{7}+\cdots$
2289.1.ep.a	$2289$	$1$	2289.ep	2289.dp	$54$	$18$	$1$	$1.142$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{5}q^{3}-\zeta_{54}^{21}q^{4}+\zeta_{54}^{22}q^{7}+\cdots$
2345.1.x.a	$2345$	$1$	2345.x	2345.x	$6$	$18$	$9$	$1.170$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-335}) $	None		$4$	$0$	$0$	$0$	$-9$	$0$	$1$		$q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{2}+(-\zeta_{54}^{11}+\cdots)q^{3}+\cdots$
2345.1.x.b	$2345$	$1$	2345.x	2345.x	$6$	$18$	$9$	$1.170$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-335}) $	None		$4$	$0$	$0$	$0$	$9$	$0$	$1$		$q+(\zeta_{54}^{5}+\zeta_{54}^{13})q^{2}+(\zeta_{54}^{11}+\zeta_{54}^{25}+\cdots)q^{3}+\cdots$
2433.1.y.a	$2433$	$1$	2433.y	2433.y	$54$	$18$	$1$	$1.214$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{54}^{20}q^{3}+\zeta_{54}^{6}q^{4}-\zeta_{54}^{24}q^{7}+\cdots$
2569.1.n.a	$2569$	$1$	2569.n	2569.n	$6$	$18$	$9$	$1.282$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-367}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{2}+(\zeta_{54}^{10}+\zeta_{54}^{18}+\cdots)q^{4}+\cdots$
2587.1.n.a	$2587$	$1$	2587.n	2587.n	$6$	$18$	$9$	$1.291$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-199}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{2}+(\zeta_{54}^{10}+\zeta_{54}^{18}+\cdots)q^{4}+\cdots$
2592.1.bz.a	$2592$	$1$	2592.bz	648.af	$54$	$18$	$1$	$1.294$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{26}q^{3}-\zeta_{54}^{25}q^{9}+(\zeta_{54}^{3}+\zeta_{54}^{13}+\cdots)q^{11}+\cdots$
2653.1.ck.a	$2653$	$1$	2653.ck	2653.bk	$54$	$18$	$1$	$1.324$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{54}^{16}+\zeta_{54}^{24})q^{2}+(-\zeta_{54}^{5}-\zeta_{54}^{13}+\cdots)q^{4}+\cdots$
2673.1.w.a	$2673$	$1$	2673.w	891.w	$54$	$18$	$1$	$1.334$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{23}q^{4}+(\zeta_{54}^{3}+\zeta_{54}^{13})q^{5}+\cdots$

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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.