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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 (50 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
311.1.b.a	$311$	$1$	311.b	311.b	$2$	$9$	$9$	$0.155$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-311}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
359.1.b.a	$359$	$1$	359.b	359.b	$2$	$9$	$9$	$0.179$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-359}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
687.1.p.a	$687$	$1$	687.p	687.p	$38$	$18$	$1$	$0.343$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{38}^{16}q^{3}+\zeta_{38}^{12}q^{4}+(\zeta_{38}^{2}-\zeta_{38}^{13}+\cdots)q^{7}+\cdots$
916.1.p.a	$916$	$1$	916.p	916.p	$38$	$18$	$1$	$0.457$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{38}^{17}q^{2}-\zeta_{38}^{15}q^{4}+(-\zeta_{38}^{3}+\cdots)q^{5}+\cdots$
919.1.b.a	$919$	$1$	919.b	919.b	$2$	$9$	$9$	$0.459$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-919}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
1063.1.b.a	$1063$	$1$	1063.b	1063.b	$2$	$9$	$9$	$0.531$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1063}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
1083.1.p.a	$1083$	$1$	1083.p	1083.p	$38$	$18$	$1$	$0.540$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{38}^{6}q^{3}+\zeta_{38}^{2}q^{4}+(\zeta_{38}^{6}-\zeta_{38}^{9}+\cdots)q^{7}+\cdots$
1199.1.d.a	$1199$	$1$	1199.d	1199.d	$2$	$9$	$9$	$0.598$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1199}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
1199.1.d.b	$1199$	$1$	1199.d	1199.d	$2$	$9$	$9$	$0.598$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1199}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
1337.1.s.a	$1337$	$1$	1337.s	1337.s	$38$	$18$	$1$	$0.667$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$18$	$1$		$q+(-\zeta_{38}^{7}-\zeta_{38}^{9})q^{2}+(\zeta_{38}^{14}+\zeta_{38}^{16}+\cdots)q^{4}+\cdots$
1371.1.t.a	$1371$	$1$	1371.t	1371.t	$38$	$18$	$1$	$0.684$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{38}^{8}q^{3}+\zeta_{38}^{6}q^{4}+(-\zeta_{38}+\zeta_{38}^{14}+\cdots)q^{7}+\cdots$
1535.1.d.a	$1535$	$1$	1535.d	1535.d	$2$	$9$	$9$	$0.766$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1535}) $	None	✓	$2$	$0$	$-1$	$-1$	$9$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
1535.1.d.b	$1535$	$1$	1535.d	1535.d	$2$	$9$	$9$	$0.766$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1535}) $	None	✓	$2$	$0$	$1$	$1$	$-9$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
1543.1.b.a	$1543$	$1$	1543.b	1543.b	$2$	$9$	$9$	$0.770$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1543}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
1671.1.d.a	$1671$	$1$	1671.d	1671.d	$2$	$9$	$9$	$0.834$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1671}) $	None	✓	$2$	$0$	$-1$	$9$	$-1$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
1671.1.d.b	$1671$	$1$	1671.d	1671.d	$2$	$9$	$9$	$0.834$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1671}) $	None	✓	$2$	$0$	$1$	$-9$	$1$	$-1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
1713.1.t.a	$1713$	$1$	1713.t	1713.t	$38$	$18$	$1$	$0.855$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{38}^{8}q^{3}+\zeta_{38}^{18}q^{4}+(\zeta_{38}^{4}+\zeta_{38}^{6}+\cdots)q^{7}+\cdots$
1828.1.s.a	$1828$	$1$	1828.s	1828.s	$38$	$18$	$1$	$0.912$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$17$	$0$	$1$		$q+\zeta_{38}^{6}q^{2}+\zeta_{38}^{12}q^{4}+(1-\zeta_{38}^{15}+\cdots)q^{5}+\cdots$
1831.1.b.a	$1831$	$1$	1831.b	1831.b	$2$	$9$	$9$	$0.914$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1831}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
2031.1.d.a	$2031$	$1$	2031.d	2031.d	$2$	$9$	$9$	$1.014$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-2031}) $	None	✓	$2$	$0$	$-1$	$9$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
2031.1.d.b	$2031$	$1$	2031.d	2031.d	$2$	$9$	$9$	$1.014$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-2031}) $	None	✓	$2$	$0$	$1$	$-9$	$1$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
2099.1.b.a	$2099$	$1$	2099.b	2099.b	$2$	$9$	$9$	$1.048$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-2099}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
2101.1.be.a	$2101$	$1$	2101.be	2101.ae	$38$	$18$	$1$	$1.049$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(-\zeta_{38}^{9}+\zeta_{38}^{12})q^{3}+\zeta_{38}^{6}q^{4}+\cdots$
2339.1.b.a	$2339$	$1$	2339.b	2339.b	$2$	$9$	$9$	$1.167$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-2339}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
2459.1.b.a	$2459$	$1$	2459.b	2459.b	$2$	$9$	$9$	$1.227$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-2459}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
2519.1.z.a	$2519$	$1$	2519.z	2519.z	$38$	$18$	$1$	$1.257$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(-\zeta_{38}^{7}-\zeta_{38}^{15})q^{3}-\zeta_{38}^{13}q^{4}+\cdots$
2591.1.b.b	$2591$	$1$	2591.b	2591.b	$2$	$9$	$9$	$1.293$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-2591}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
2799.1.d.a	$2799$	$1$	2799.d	311.b	$2$	$9$	$9$	$1.397$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-311}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
2879.1.b.b	$2879$	$1$	2879.b	2879.b	$2$	$9$	$9$	$1.437$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-2879}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
2888.1.bb.a	$2888$	$1$	2888.bb	2888.ab	$38$	$18$	$1$	$1.441$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$17$	$0$	$0$	$1$		$q-\zeta_{38}^{3}q^{2}+(1-\zeta_{38}^{17})q^{3}+\zeta_{38}^{6}q^{4}+\cdots$
3044.1.q.a	$3044$	$1$	3044.q	3044.q	$38$	$18$	$1$	$1.519$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$17$	$0$	$1$		$q+\zeta_{38}^{14}q^{2}-\zeta_{38}^{9}q^{4}+(1+\zeta_{38}^{6}+\cdots)q^{5}+\cdots$
3047.1.d.a	$3047$	$1$	3047.d	3047.d	$2$	$9$	$9$	$1.521$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3047}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
3047.1.d.b	$3047$	$1$	3047.d	3047.d	$2$	$9$	$9$	$1.521$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3047}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
3071.1.d.c	$3071$	$1$	3071.d	3071.d	$2$	$9$	$9$	$1.533$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3071}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
3071.1.d.d	$3071$	$1$	3071.d	3071.d	$2$	$9$	$9$	$1.533$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3071}) $	None	✓	$2$	$0$	$1$	$-1$	$1$	$-1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
3199.1.br.a	$3199$	$1$	3199.br	3199.ar	$38$	$18$	$1$	$1.597$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(\zeta_{38}^{12}-\zeta_{38}^{13})q^{2}+(-\zeta_{38}^{5}+\zeta_{38}^{6}+\cdots)q^{4}+\cdots$
3231.1.d.a	$3231$	$1$	3231.d	359.b	$2$	$9$	$9$	$1.612$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-359}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
3343.1.b.a	$3343$	$1$	3343.b	3343.b	$2$	$9$	$9$	$1.668$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3343}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
3352.1.s.a	$3352$	$1$	3352.s	3352.s	$38$	$18$	$1$	$1.673$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{38}^{11}q^{2}+(\zeta_{38}^{6}-\zeta_{38}^{9})q^{3}-\zeta_{38}^{3}q^{4}+\cdots$
3407.1.b.c	$3407$	$1$	3407.b	3407.b	$2$	$9$	$9$	$1.700$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3407}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+\beta _{6}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
3415.1.d.a	$3415$	$1$	3415.d	3415.d	$2$	$9$	$9$	$1.704$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3415}) $	None	✓	$2$	$0$	$-1$	$0$	$9$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
3415.1.d.b	$3415$	$1$	3415.d	3415.d	$2$	$9$	$9$	$1.704$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3415}) $	None	✓	$2$	$0$	$1$	$0$	$-9$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
3435.1.bq.a	$3435$	$1$	3435.bq	3435.aq	$38$	$18$	$1$	$1.714$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(-\zeta_{38}^{7}-\zeta_{38}^{17})q^{2}-\zeta_{38}^{13}q^{3}+\cdots$
3435.1.bq.b	$3435$	$1$	3435.bq	3435.aq	$38$	$18$	$1$	$1.714$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(\zeta_{38}^{7}+\zeta_{38}^{17})q^{2}+\zeta_{38}^{13}q^{3}+\cdots$
3463.1.b.a	$3463$	$1$	3463.b	3463.b	$2$	$9$	$9$	$1.728$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3463}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
3467.1.b.a	$3467$	$1$	3467.b	3467.b	$2$	$9$	$9$	$1.730$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3467}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
3607.1.b.a	$3607$	$1$	3607.b	3607.b	$2$	$9$	$9$	$1.800$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-3607}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
3629.1.x.a	$3629$	$1$	3629.x	3629.x	$38$	$18$	$1$	$1.811$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{38}^{7}q^{4}+(\zeta_{38}^{6}+\zeta_{38}^{8})q^{5}+(-\zeta_{38}^{5}+\cdots)q^{7}+\cdots$
3656.1.bj.a	$3656$	$1$	3656.bj	3656.aj	$38$	$18$	$1$	$1.825$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{38}^{8}q^{2}+(\zeta_{38}^{14}+\zeta_{38}^{16})q^{3}+\cdots$
3997.1.bp.a	$3997$	$1$	3997.bp	3997.ap	$38$	$18$	$1$	$1.995$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{38}^{3}+\zeta_{38}^{8})q^{2}+(\zeta_{38}^{6}-\zeta_{38}^{11}+\cdots)q^{4}+\cdots$

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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.