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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 185 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
301.1.bc.a	$301$	$1$	301.bc	301.ac	$42$	$12$	$1$	$0.150$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$	$1$		$q+(\zeta_{42}^{16}+\zeta_{42}^{20})q^{2}+(-\zeta_{42}^{11}+\cdots)q^{4}+\cdots$
344.1.be.a	$344$	$1$	344.be	344.ae	$42$	$12$	$1$	$0.172$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$2$	$0$	$0$	$1$		$q-\zeta_{42}^{15}q^{2}+(\zeta_{42}^{8}-\zeta_{42}^{11})q^{3}+\cdots$
381.1.t.a	$381$	$1$	381.t	381.t	$42$	$12$	$1$	$0.190$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-5$	$1$		$q-\zeta_{42}^{11}q^{3}-\zeta_{42}^{9}q^{4}+(\zeta_{42}^{14}-\zeta_{42}^{17}+\cdots)q^{7}+\cdots$
431.1.b.c	$431$	$1$	431.b	431.b	$2$	$6$	$6$	$0.215$	$\Q(\zeta_{21})^+$	$D_{21}$	$\Q(\sqrt{-431}) $	None	✓	$2$	$0$	$-2$	$1$	$1$	$0$	$1$		$q+(-1-\beta _{3}+\beta _{5})q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}+\cdots$
503.1.b.c	$503$	$1$	503.b	503.b	$2$	$6$	$6$	$0.251$	$\Q(\zeta_{21})^+$	$D_{21}$	$\Q(\sqrt{-503}) $	None	✓	$2$	$0$	$-2$	$1$	$0$	$1$	$1$		$q+\beta _{3}q^{2}+\beta _{4}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots$
516.1.z.a	$516$	$1$	516.z	129.o	$42$	$12$	$1$	$0.258$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q-\zeta_{42}q^{3}+(\zeta_{42}^{10}+\zeta_{42}^{18})q^{7}+\zeta_{42}^{2}q^{9}+\cdots$
588.1.z.a	$588$	$1$	588.z	147.n	$42$	$12$	$1$	$0.293$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+\zeta_{42}^{10}q^{3}+\zeta_{42}^{8}q^{7}+\zeta_{42}^{20}q^{9}+\cdots$
639.1.g.b	$639$	$1$	639.g	639.g	$6$	$12$	$6$	$0.319$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$-1$	$1$	$2$	$0$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}-\zeta_{42}^{19}q^{3}+\cdots$
667.1.i.b	$667$	$1$	667.i	667.i	$14$	$12$	$2$	$0.333$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-5$	$2$	$0$	$0$	$1$		$q+(-\zeta_{42}+\zeta_{42}^{14})q^{2}+(\zeta_{42}^{16}-\zeta_{42}^{17}+\cdots)q^{3}+\cdots$
743.1.b.c	$743$	$1$	743.b	743.b	$2$	$6$	$6$	$0.371$	$\Q(\zeta_{21})^+$	$D_{21}$	$\Q(\sqrt{-743}) $	None	✓	$2$	$0$	$1$	$-2$	$0$	$0$	$1$		$q+\beta _{4}q^{2}+\beta _{3}q^{3}+(2-\beta _{1}+\beta _{3}-\beta _{5})q^{4}+\cdots$
817.1.bz.a	$817$	$1$	817.bz	817.az	$42$	$12$	$1$	$0.408$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-1$	$1$		$q+\zeta_{42}^{12}q^{4}+(\zeta_{42}^{10}-\zeta_{42}^{19})q^{5}+\cdots$
860.1.bq.a	$860$	$1$	860.bq	860.aq	$42$	$12$	$1$	$0.429$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-2$	$-8$	$1$	$2$	$1$		$q+\zeta_{42}^{12}q^{2}+(\zeta_{42}^{14}+\zeta_{42}^{18})q^{3}+\cdots$
860.1.bq.b	$860$	$1$	860.bq	860.aq	$42$	$12$	$1$	$0.429$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$2$	$8$	$1$	$-2$	$1$		$q-\zeta_{42}^{12}q^{2}+(-\zeta_{42}^{14}-\zeta_{42}^{18}+\cdots)q^{3}+\cdots$
863.1.b.c	$863$	$1$	863.b	863.b	$2$	$6$	$6$	$0.431$	$\Q(\zeta_{21})^+$	$D_{21}$	$\Q(\sqrt{-863}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
889.1.bo.a	$889$	$1$	889.bo	889.ao	$42$	$12$	$1$	$0.444$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-5$	$0$	$0$	$1$	$1$		$q+(\zeta_{42}^{14}+\zeta_{42}^{16})q^{2}+(-\zeta_{42}^{7}-\zeta_{42}^{9}+\cdots)q^{4}+\cdots$
903.1.cf.a	$903$	$1$	903.cf	903.bf	$42$	$12$	$1$	$0.451$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$1$	$1$		$q+\zeta_{42}^{18}q^{3}-\zeta_{42}^{13}q^{4}-\zeta_{42}^{19}q^{7}+\cdots$
903.1.cn.a	$903$	$1$	903.cn	903.bn	$42$	$12$	$1$	$0.451$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+\zeta_{42}^{8}q^{3}-\zeta_{42}^{19}q^{4}-\zeta_{42}^{11}q^{7}+\cdots$
931.1.bq.a	$931$	$1$	931.bq	931.aq	$42$	$12$	$1$	$0.465$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-\zeta_{42}^{17}q^{4}+(-\zeta_{42}^{5}+\zeta_{42}^{18})q^{5}+\cdots$
980.1.bq.a	$980$	$1$	980.bq	980.aq	$42$	$12$	$1$	$0.489$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$8$	$1$	$-1$	$1$		$q-\zeta_{42}^{4}q^{2}+(\zeta_{42}^{3}+\zeta_{42}^{7})q^{3}+\zeta_{42}^{8}q^{4}+\cdots$
980.1.bq.b	$980$	$1$	980.bq	980.aq	$42$	$12$	$1$	$0.489$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$-8$	$1$	$1$	$1$		$q+\zeta_{42}^{4}q^{2}+(-\zeta_{42}^{3}-\zeta_{42}^{7})q^{3}+\cdots$
1004.1.d.b	$1004$	$1$	1004.d	251.b	$2$	$6$	$6$	$0.501$	$\Q(\zeta_{21})^+$	$D_{21}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$-2$	$1$	$1$	$1$		$q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1137.1.t.a	$1137$	$1$	1137.t	1137.t	$42$	$12$	$1$	$0.567$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q+\zeta_{42}^{4}q^{3}+\zeta_{42}^{16}q^{4}+(\zeta_{42}^{4}-\zeta_{42}^{19}+\cdots)q^{7}+\cdots$
1161.1.by.a	$1161$	$1$	1161.by	129.o	$42$	$12$	$1$	$0.579$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{42}^{12}q^{4}+(-\zeta_{42}^{11}-\zeta_{42}^{17}+\cdots)q^{7}+\cdots$
1176.1.ck.a	$1176$	$1$	1176.ck	1176.bk	$42$	$12$	$1$	$0.587$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$1$	$1$	$1$		$q+\zeta_{42}^{13}q^{2}+\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots$
1176.1.ck.b	$1176$	$1$	1176.ck	1176.bk	$42$	$12$	$1$	$0.587$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$-1$	$1$	$1$		$q-\zeta_{42}^{13}q^{2}-\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots$
1323.1.br.a	$1323$	$1$	1323.br	147.n	$42$	$12$	$1$	$0.660$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{42}^{13}q^{4}-\zeta_{42}^{3}q^{7}+(-\zeta_{42}-\zeta_{42}^{5}+\cdots)q^{13}+\cdots$
1348.1.z.a	$1348$	$1$	1348.z	1348.z	$42$	$12$	$1$	$0.673$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$10$	$0$	$1$		$q+\zeta_{42}^{20}q^{2}-\zeta_{42}^{19}q^{4}+(1+\zeta_{42}^{6}+\cdots)q^{5}+\cdots$
1349.1.g.b	$1349$	$1$	1349.g	1349.g	$6$	$12$	$6$	$0.673$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{42}^{8}+\zeta_{42}^{20})q^{2}+(-\zeta_{42}^{3}+\zeta_{42}^{4}+\cdots)q^{3}+\cdots$
1376.1.by.a	$1376$	$1$	1376.by	344.ae	$42$	$12$	$1$	$0.687$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(\zeta_{42}^{5}+\zeta_{42}^{17})q^{3}+(-\zeta_{42}+\zeta_{42}^{10}+\cdots)q^{9}+\cdots$
1477.1.cf.a	$1477$	$1$	1477.cf	1477.bf	$42$	$12$	$1$	$0.737$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-5$	$0$	$0$	$1$	$1$		$q+(\zeta_{42}^{14}-\zeta_{42}^{17})q^{2}+(-\zeta_{42}^{7}+\zeta_{42}^{10}+\cdots)q^{4}+\cdots$
1505.1.x.c	$1505$	$1$	1505.x	1505.x	$6$	$12$	$6$	$0.751$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-215}) $	None		$4$	$0$	$-1$	$2$	$-6$	$1$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}+(-\zeta_{42}-\zeta_{42}^{13}+\cdots)q^{3}+\cdots$
1505.1.x.d	$1505$	$1$	1505.x	1505.x	$6$	$12$	$6$	$0.751$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-215}) $	None		$4$	$0$	$1$	$-2$	$6$	$-1$	$1$		$q+(\zeta_{42}^{3}-\zeta_{42}^{4})q^{2}+(\zeta_{42}+\zeta_{42}^{13}+\cdots)q^{3}+\cdots$
1508.1.cj.a	$1508$	$1$	1508.cj	1508.bj	$42$	$12$	$1$	$0.753$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q+\zeta_{42}^{2}q^{2}+\zeta_{42}^{4}q^{4}+(\zeta_{42}^{8}+\zeta_{42}^{10}+\cdots)q^{5}+\cdots$
1508.1.cj.b	$1508$	$1$	1508.cj	1508.bj	$42$	$12$	$1$	$0.753$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q+\zeta_{42}^{2}q^{2}+\zeta_{42}^{4}q^{4}+(-\zeta_{42}-\zeta_{42}^{17}+\cdots)q^{5}+\cdots$
1519.1.ba.b	$1519$	$1$	1519.ba	1519.aa	$14$	$12$	$2$	$0.758$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$2$	$1$	$1$		$q+(\zeta_{42}^{8}+\zeta_{42}^{10})q^{2}+(\zeta_{42}^{16}+\zeta_{42}^{18}+\cdots)q^{4}+\cdots$
1561.1.n.c	$1561$	$1$	1561.n	1561.n	$6$	$12$	$6$	$0.779$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-223}) $	None		$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}+(\zeta_{42}^{6}-\zeta_{42}^{7}+\cdots)q^{4}+\cdots$
1633.1.l.b	$1633$	$1$	1633.l	1633.l	$14$	$12$	$2$	$0.815$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$2$	$0$	$0$	$1$		$q+\zeta_{42}^{3}q^{2}+(\zeta_{42}^{16}-\zeta_{42}^{17})q^{3}+\cdots$
1677.1.cz.a	$1677$	$1$	1677.cz	1677.bz	$42$	$12$	$1$	$0.837$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-2$	$1$	$5$	$0$	$1$		$q+(-\zeta_{42}^{10}-\zeta_{42}^{20})q^{2}-\zeta_{42}^{13}q^{3}+\cdots$
1677.1.cz.b	$1677$	$1$	1677.cz	1677.bz	$42$	$12$	$1$	$0.837$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$2$	$1$	$-5$	$0$	$1$		$q+(\zeta_{42}^{10}+\zeta_{42}^{20})q^{2}-\zeta_{42}^{13}q^{3}+\cdots$
1677.1.dd.a	$1677$	$1$	1677.dd	1677.cd	$42$	$12$	$1$	$0.837$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q+\zeta_{42}^{8}q^{3}-\zeta_{42}^{5}q^{4}+(\zeta_{42}^{4}+\zeta_{42}^{10}+\cdots)q^{7}+\cdots$
1677.1.dh.a	$1677$	$1$	1677.dh	1677.ch	$42$	$12$	$1$	$0.837$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$-4$	$1$		$q-\zeta_{42}^{9}q^{3}+\zeta_{42}^{10}q^{4}+(\zeta_{42}^{6}-\zeta_{42}^{15}+\cdots)q^{7}+\cdots$
1684.1.bf.a	$1684$	$1$	1684.bf	1684.af	$42$	$12$	$1$	$0.840$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q-\zeta_{42}q^{2}+\zeta_{42}^{2}q^{4}+(-\zeta_{42}-\zeta_{42}^{9}+\cdots)q^{5}+\cdots$
1688.1.bv.a	$1688$	$1$	1688.bv	1688.av	$42$	$12$	$1$	$0.842$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$2$	$0$	$0$	$1$		$q+\zeta_{42}^{2}q^{2}+(\zeta_{42}^{8}-\zeta_{42}^{17})q^{3}+\zeta_{42}^{4}q^{4}+\cdots$
1711.1.i.b	$1711$	$1$	1711.i	1711.i	$14$	$12$	$2$	$0.854$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-5$	$2$	$2$	$1$		$q+(-\zeta_{42}^{5}-\zeta_{42}^{7})q^{3}-\zeta_{42}^{15}q^{4}+\cdots$
1757.1.h.b	$1757$	$1$	1757.h	1757.h	$6$	$12$	$6$	$0.877$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$-1$	$-1$	$-2$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{3}+\zeta_{42}^{14}q^{4}+\cdots$
1868.1.d.b	$1868$	$1$	1868.d	467.b	$2$	$6$	$6$	$0.932$	$\Q(\zeta_{21})^+$	$D_{21}$	$\Q(\sqrt{-467}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$	$1$		$q+\beta _{4}q^{3}+(-\beta _{2}+\beta _{5})q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
1893.1.bc.a	$1893$	$1$	1893.bc	1893.ac	$42$	$12$	$1$	$0.945$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{42}^{13}q^{3}-\zeta_{42}^{7}q^{4}+(\zeta_{42}^{2}+\zeta_{42}^{20}+\cdots)q^{7}+\cdots$
1911.1.dd.a	$1911$	$1$	1911.dd	1911.cd	$42$	$12$	$1$	$0.954$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$1$	$1$		$q+\zeta_{42}^{6}q^{3}-\zeta_{42}^{11}q^{4}+\zeta_{42}^{16}q^{7}+\cdots$
1911.1.dx.a	$1911$	$1$	1911.dx	1911.cx	$42$	$12$	$1$	$0.954$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+\zeta_{42}^{20}q^{3}+\zeta_{42}^{18}q^{4}+\zeta_{42}^{2}q^{7}+\cdots$
1917.1.g.b	$1917$	$1$	1917.g	639.g	$6$	$12$	$6$	$0.957$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$	$3^{3}$		$q+(\zeta_{42}^{3}-\zeta_{42}^{4})q^{2}+(\zeta_{42}^{6}-\zeta_{42}^{7}+\cdots)q^{4}+\cdots$

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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.