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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 54 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
268.1.b.a	$268$	$1$	268.b	67.b	$2$	$1$	$1$	$0.134$	$\Q$	$D_{3}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}-q^{17}-q^{19}-q^{23}+q^{25}+\cdots$
603.1.b.a	$603$	$1$	603.b	67.b	$2$	$1$	$1$	$0.301$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-67}) $	$\Q(\sqrt{201}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{16}-2q^{19}+q^{25}-2q^{37}+\cdots$
1072.1.b.a	$1072$	$1$	1072.b	67.b	$2$	$1$	$1$	$0.535$	$\Q$	$D_{3}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}-q^{17}+q^{19}+q^{23}+q^{25}+\cdots$
1139.1.c.a	$1139$	$1$	1139.c	1139.c	$2$	$1$	$1$	$0.568$	$\Q$	$D_{2}$	$\Q(\sqrt{-67}) $, $\Q(\sqrt{-1139}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-q^{9}+q^{16}+q^{17}+2q^{19}+\cdots$
1139.1.g.a	$1139$	$1$	1139.g	1139.g	$4$	$2$	$1$	$0.568$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-iq^{9}+q^{16}+q^{17}+(-1-i+\cdots)q^{23}+\cdots$
1139.1.l.a	$1139$	$1$	1139.l	1139.l	$8$	$4$	$1$	$0.568$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{9}-q^{16}+q^{17}+\cdots$
1273.1.r.a	$1273$	$1$	1273.r	1273.r	$6$	$2$	$1$	$0.635$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{16}+\zeta_{6}q^{17}+\cdots$
1273.1.bf.a	$1273$	$1$	1273.bf	1273.af	$18$	$6$	$1$	$0.635$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{4}-\zeta_{18}^{7}q^{9}+\zeta_{18}^{8}q^{16}+\cdots$
1541.1.by.a	$1541$	$1$	1541.by	1541.ay	$22$	$10$	$1$	$0.769$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{22}^{6}q^{4}+\zeta_{22}^{4}q^{9}-\zeta_{22}q^{16}+\cdots$
1675.1.b.a	$1675$	$1$	1675.b	67.b	$2$	$1$	$1$	$0.836$	$\Q$	$D_{3}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}+q^{16}-q^{17}-q^{19}+2q^{23}+\cdots$
1675.1.b.b	$1675$	$1$	1675.b	67.b	$2$	$1$	$1$	$0.836$	$\Q$	$D_{3}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}+q^{16}+q^{17}-q^{19}-2q^{23}+\cdots$
1675.1.d.a	$1675$	$1$	1675.d	335.d	$2$	$2$	$2$	$0.836$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-q^{9}+q^{16}-iq^{17}+q^{19}+\cdots$
1943.1.d.a	$1943$	$1$	1943.d	1943.d	$2$	$1$	$1$	$0.970$	$\Q$	$D_{2}$	$\Q(\sqrt{-67}) $, $\Q(\sqrt{-1943}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-q^{9}+q^{16}+2q^{23}+q^{25}+\cdots$
1943.1.o.a	$1943$	$1$	1943.o	1943.o	$14$	$6$	$1$	$0.970$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{14}^{5}q^{4}-\zeta_{14}^{4}q^{9}-\zeta_{14}^{3}q^{16}+\cdots$
1943.1.q.a	$1943$	$1$	1943.q	1943.q	$14$	$6$	$1$	$0.970$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{14}^{3}q^{4}-\zeta_{14}q^{9}+\zeta_{14}^{6}q^{16}+\cdots$
2412.1.b.a	$2412$	$1$	2412.b	67.b	$2$	$1$	$1$	$1.204$	$\Q$	$D_{3}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{17}-q^{19}+q^{23}+q^{25}+q^{29}+\cdots$
2412.1.b.b	$2412$	$1$	2412.b	67.b	$2$	$2$	$2$	$1.204$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-67}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{17}+q^{19}+\beta q^{23}+q^{25}+\beta q^{29}+\cdots$
2479.1.d.b	$2479$	$1$	2479.d	2479.d	$2$	$1$	$1$	$1.237$	$\Q$	$D_{2}$	$\Q(\sqrt{-67}) $, $\Q(\sqrt{-2479}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+q^{9}+q^{16}-q^{25}-q^{36}+q^{37}+\cdots$
2479.1.n.a	$2479$	$1$	2479.n	2479.n	$6$	$2$	$1$	$1.237$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{16}+(-1+\cdots)q^{19}+\cdots$
2479.1.t.a	$2479$	$1$	2479.t	2479.t	$6$	$2$	$1$	$1.237$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{9}-\zeta_{6}q^{16}-\zeta_{6}q^{17}+\cdots$
2479.1.bi.a	$2479$	$1$	2479.bi	2479.ai	$18$	$6$	$1$	$1.237$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{8}q^{4}-\zeta_{18}q^{9}-\zeta_{18}^{7}q^{16}+\cdots$
2479.1.bq.a	$2479$	$1$	2479.bq	2479.aq	$18$	$6$	$1$	$1.237$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{4}+\zeta_{18}^{4}q^{9}-\zeta_{18}q^{16}+\cdots$
3149.1.q.a	$3149$	$1$	3149.q	3149.q	$46$	$22$	$1$	$1.572$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{46}^{6}q^{4}+\zeta_{46}^{22}q^{9}+\zeta_{46}^{12}q^{16}+\cdots$
3283.1.b.a	$3283$	$1$	3283.b	67.b	$2$	$1$	$1$	$1.638$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-67}) $	$\Q(\sqrt{469}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}+q^{16}-2q^{23}+q^{25}+\cdots$
3283.1.b.c	$3283$	$1$	3283.b	67.b	$2$	$2$	$2$	$1.638$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-67}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}+q^{16}-\beta q^{17}+\beta q^{19}+\cdots$
3283.1.r.b	$3283$	$1$	3283.r	469.r	$6$	$2$	$1$	$1.638$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-67}) $	$\Q(\sqrt{469}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{23}+\cdots$
3283.1.r.d	$3283$	$1$	3283.r	469.r	$6$	$4$	$2$	$1.638$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-67}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{2}q^{4}+(-1-\beta _{2})q^{9}+(-1-\beta _{2}+\cdots)q^{16}+\cdots$
67.3.b.a	$67$	$3$	67.b	67.b	$2$	$1$	$1$	$1.826$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+9q^{9}+2^{4}q^{16}-33q^{17}+\cdots$
3953.1.q.a	$3953$	$1$	3953.q	3953.q	$58$	$28$	$1$	$1.973$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{58}^{19}q^{4}+\zeta_{58}^{22}q^{9}-\zeta_{58}^{9}q^{16}+\cdots$
603.2.d.a	$603$	$2$	603.d	201.d	$2$	$4$	$4$	$4.815$	$\Q(\sqrt{-2}, \sqrt{67})$	$_{}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+4q^{16}+\beta _{1}q^{17}+\beta _{3}q^{19}+\cdots$
67.5.b.a	$67$	$5$	67.b	67.b	$2$	$1$	$1$	$6.926$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+3^{4}q^{9}+2^{8}q^{16}+511q^{17}+\cdots$
268.3.b.a	$268$	$3$	268.b	67.b	$2$	$2$	$2$	$7.302$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{9}+(17-\beta )q^{17}+(13+3\beta )q^{19}+\cdots$
1072.2.g.a	$1072$	$2$	1072.g	268.d	$2$	$2$	$2$	$8.560$	$\Q(\sqrt{-67}) $	$_{}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{9}-q^{17}-\beta q^{19}-\beta q^{23}+5q^{25}+\cdots$
1072.2.g.c	$1072$	$2$	1072.g	268.d	$2$	$4$	$4$	$8.560$	$\Q(\sqrt{-3}, \sqrt{-67})$	$_{}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{9}+(1-\beta _{2})q^{17}+(-2\beta _{1}-\beta _{3})q^{19}+\cdots$
67.7.b.a	$67$	$7$	67.b	67.b	$2$	$1$	$1$	$15.414$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{6}q^{4}+3^{6}q^{9}+2^{12}q^{16}-7326q^{17}+\cdots$
603.3.b.a	$603$	$3$	603.b	67.b	$2$	$1$	$1$	$16.431$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+2^{4}q^{16}+33q^{17}-29q^{19}+\cdots$
603.3.b.b	$603$	$3$	603.b	67.b	$2$	$2$	$2$	$16.431$	$\Q(\sqrt{67}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+2^{4}q^{16}+\beta q^{17}+29q^{19}+\cdots$
2412.2.g.a	$2412$	$2$	2412.g	201.d	$2$	$8$	$8$	$19.260$	8.0.$\cdots$.23	$_{}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{17}+\beta _{1}q^{19}+\beta _{5}q^{23}-5q^{25}+\cdots$
67.9.b.a	$67$	$9$	67.b	67.b	$2$	$1$	$1$	$27.294$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{4}+3^{8}q^{9}+2^{16}q^{16}+94079q^{17}+\cdots$
268.5.b.a	$268$	$5$	268.b	67.b	$2$	$2$	$2$	$27.703$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+3^{4}q^{9}+(-250+11\beta )q^{17}+(-74+\cdots)q^{19}+\cdots$
1072.3.b.a	$1072$	$3$	1072.b	67.b	$2$	$1$	$1$	$29.210$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{9}-33q^{17}+29q^{19}+21q^{23}+\cdots$
1072.3.b.b	$1072$	$3$	1072.b	67.b	$2$	$2$	$2$	$29.210$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{9}+(2^{4}+\beta )q^{17}+(-2^{4}+3\beta )q^{19}+\cdots$
603.4.d.a	$603$	$4$	603.d	201.d	$2$	$4$	$4$	$35.578$	$\Q(\sqrt{-2}, \sqrt{67})$	$_{}$	$\Q(\sqrt{-67}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-8q^{4}+2^{6}q^{16}+(8\beta _{1}-\beta _{2})q^{17}+\cdots$
4489.2.a.b	$4489$	$2$	4489.a	1.a	$1$	$1$	$1$	$35.845$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-3q^{9}+4q^{16}-q^{17}+3q^{19}+\cdots$
67.11.b.a	$67$	$11$	67.b	67.b	$2$	$1$	$1$	$42.569$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{10}q^{4}+3^{10}q^{9}+2^{20}q^{16}-987393q^{17}+\cdots$
67.13.b.a	$67$	$13$	67.b	67.b	$2$	$1$	$1$	$61.238$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{12}q^{4}+3^{12}q^{9}+2^{24}q^{16}+5395138q^{17}+\cdots$
268.7.b.a	$268$	$7$	268.b	67.b	$2$	$2$	$2$	$61.654$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 5$	$\mathrm{U}(1)[D_{2}]$	$q+3^{6}q^{9}+(3663-20\beta )q^{17}+(-3509+\cdots)q^{19}+\cdots$
2412.3.b.a	$2412$	$3$	2412.b	67.b	$2$	$2$	$2$	$65.722$	$\Q(\sqrt{201}) $	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-17+\beta )q^{17}+(13+3\beta )q^{19}+(-13+\cdots)q^{23}+\cdots$
2412.3.b.c	$2412$	$3$	2412.b	67.b	$2$	$4$	$4$	$65.722$	$\Q(\sqrt{3}, \sqrt{67})$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}+2\beta _{2})q^{17}+(-15-\beta _{3})q^{19}+\cdots$
67.15.b.a	$67$	$15$	67.b	67.b	$2$	$1$	$1$	$83.300$	$\Q$	$_{}$	$\Q(\sqrt{-67}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{14}q^{4}+3^{14}q^{9}+2^{28}q^{16}+107317023q^{17}+\cdots$

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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.