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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 15755 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
23.1.b.a	$23$	$1$	23.b	23.b	$2$	$1$	$1$	$0.011$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	✓	✓	✓	23.1.b.a	$2$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots$
31.1.b.a	$31$	$1$	31.b	31.b	$2$	$1$	$1$	$0.015$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	✓	✓	✓	31.1.b.a	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots$
39.1.d.a	$39$	$1$	39.d	39.d	$2$	$1$	$1$	$0.019$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	✓	✓	✓	39.1.d.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
44.1.d.a	$44$	$1$	44.d	11.b	$2$	$1$	$1$	$0.022$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	✓	✓	✓	44.1.d.a	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots$
47.1.b.a	$47$	$1$	47.b	47.b	$2$	$2$	$2$	$0.023$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-47}) $	None	✓	✓	✓	✓	47.1.b.a	$2$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
52.1.j.a	$52$	$1$	52.j	52.j	$6$	$2$	$1$	$0.026$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	52.1.j.a	$4$	$0$	$-1$	$0$	$-2$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
55.1.d.a	$55$	$1$	55.d	55.d	$2$	$1$	$1$	$0.027$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	✓	✓	✓	55.1.d.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots$
56.1.h.a	$56$	$1$	56.h	56.h	$2$	$1$	$1$	$0.028$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	✓	✓	✓	✓	56.1.h.a	$4$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots$
57.1.h.a	$57$	$1$	57.h	57.h	$6$	$2$	$1$	$0.028$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	57.1.h.a	$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots$
59.1.b.a	$59$	$1$	59.b	59.b	$2$	$1$	$1$	$0.029$	$\Q$	$D_{3}$	$\Q(\sqrt{-59}) $	None	✓	✓	✓	✓	59.1.b.a	$2$	$0$	$0$	$-1$	$-1$	$-1$		$1$		$q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots$
63.1.d.a	$63$	$1$	63.d	7.b	$2$	$1$	$1$	$0.031$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $	✓	✓	✓	✓	63.1.d.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots$
68.1.d.a	$68$	$1$	68.d	68.d	$2$	$1$	$1$	$0.034$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-17}) $	$\Q(\sqrt{17}) $	✓	✓	✓	✓	68.1.d.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots$
68.1.f.a	$68$	$1$	68.f	68.f	$4$	$2$	$1$	$0.034$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	68.1.f.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+i q^{2}-q^{4}+(-i-1)q^{5}-i q^{8}+\cdots$
71.1.b.a	$71$	$1$	71.b	71.b	$2$	$3$	$3$	$0.035$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-71}) $	None	✓	✓	✓	✓	71.1.b.a	$2$	$0$	$-1$	$-1$	$-1$	$0$		$1$		$q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
72.1.p.a	$72$	$1$	72.p	72.p	$6$	$2$	$1$	$0.036$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	72.1.p.a	$4$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
76.1.c.a	$76$	$1$	76.c	19.b	$2$	$1$	$1$	$0.038$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	✓	✓	✓	76.1.c.a	$2$	$0$	$0$	$0$	$-1$	$-1$		$1$		$q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
77.1.j.a	$77$	$1$	77.j	77.j	$10$	$4$	$1$	$0.038$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	77.1.j.a	$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
79.1.b.a	$79$	$1$	79.b	79.b	$2$	$2$	$2$	$0.039$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓	✓	✓	✓	79.1.b.a	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots$
80.1.h.a	$80$	$1$	80.h	20.d	$2$	$1$	$1$	$0.040$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	✓	✓	✓	80.1.h.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots$
83.1.b.a	$83$	$1$	83.b	83.b	$2$	$1$	$1$	$0.041$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	✓	✓	✓	83.1.b.a	$2$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$
84.1.p.a	$84$	$1$	84.p	21.h	$6$	$2$	$1$	$0.042$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	84.1.p.a	$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots$
87.1.d.a	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	✓			87.1.d.a	$2$	$0$	$-1$	$1$	$0$	$-1$		$1$		$q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots$
87.1.d.b	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	✓			87.1.d.a	$2$	$0$	$1$	$-1$	$0$	$-1$		$1$		$q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots$
88.1.l.a	$88$	$1$	88.l	88.l	$10$	$4$	$1$	$0.044$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	88.1.l.a	$4$	$0$	$-1$	$-2$	$0$	$0$		$1$		$q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
93.1.l.a	$93$	$1$	93.l	93.l	$10$	$4$	$1$	$0.046$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	93.1.l.a	$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
95.1.d.a	$95$	$1$	95.d	95.d	$2$	$1$	$1$	$0.047$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓	✓			95.1.d.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots$
95.1.d.b	$95$	$1$	95.d	95.d	$2$	$2$	$2$	$0.047$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	✓	✓	✓		95.1.d.b	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
99.1.h.a	$99$	$1$	99.h	99.h	$6$	$2$	$1$	$0.049$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	99.1.h.a	$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots$
100.1.j.a	$100$	$1$	100.j	100.j	$10$	$4$	$1$	$0.050$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	100.1.j.a	$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$
11.2.a.a	$11$	$2$	11.a	1.a	$1$	$1$	$1$	$0.088$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	11.2.a.a	$1$	$0$	$-2$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots$
13.2.e.a	$13$	$2$	13.e	13.e	$6$	$2$	$1$	$0.104$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓	✓	✓	13.2.e.a	$2$	$0$	$-3$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
14.2.a.a	$14$	$2$	14.a	1.a	$1$	$1$	$1$	$0.112$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	14.2.a.a	$1$	$0$	$-1$	$-2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots$
15.2.a.a	$15$	$2$	15.a	1.a	$1$	$1$	$1$	$0.120$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	15.2.a.a	$1$	$0$	$-1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots$
16.2.e.a	$16$	$2$	16.e	16.e	$4$	$2$	$1$	$0.128$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓	✓	✓	16.2.e.a	$2$	$0$	$-2$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+(i-1)q^{3}+2 i q^{4}+\cdots$
17.2.a.a	$17$	$2$	17.a	1.a	$1$	$1$	$1$	$0.136$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	17.2.a.a	$1$	$0$	$-1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots$
17.2.d.a	$17$	$2$	17.d	17.d	$8$	$4$	$1$	$0.136$	$\Q(\zeta_{8})$	$_{}$	None	None		✓	✓	✓	17.2.d.a	$2$	$0$	$-4$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$
18.2.c.a	$18$	$2$	18.c	9.c	$3$	$2$	$1$	$0.144$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓	✓	✓	18.2.c.a	$2$	$0$	$-1$	$-3$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
19.2.a.a	$19$	$2$	19.a	1.a	$1$	$1$	$1$	$0.152$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	19.2.a.a	$1$	$0$	$0$	$-2$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots$
19.2.e.a	$19$	$2$	19.e	19.e	$9$	$6$	$1$	$0.152$	$\Q(\zeta_{18})$	$_{}$	None	None		✓	✓	✓	19.2.e.a	$2$	$0$	$-6$	$-3$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots$
20.2.a.a	$20$	$2$	20.a	1.a	$1$	$1$	$1$	$0.160$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	20.2.a.a	$1$	$0$	$0$	$-2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots$
20.2.e.a	$20$	$2$	20.e	20.e	$4$	$2$	$1$	$0.160$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	20.2.e.a	$4$	$0$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(i-2)q^{5}+\cdots$
21.2.a.a	$21$	$2$	21.a	1.a	$1$	$1$	$1$	$0.168$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	21.2.a.a	$1$	$0$	$-1$	$1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
21.2.e.a	$21$	$2$	21.e	7.c	$3$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓	✓	✓	21.2.e.a	$2$	$0$	$-2$	$-1$	$2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots$
21.2.g.a	$21$	$2$	21.g	21.g	$6$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	21.2.g.a	$4$	$0$	$0$	$-3$	$0$	$1$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots$
22.2.c.a	$22$	$2$	22.c	11.c	$5$	$4$	$1$	$0.176$	$\Q(\zeta_{10})$	$_{}$	None	None		✓	✓	✓	22.2.c.a	$2$	$0$	$-1$	$-4$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
23.2.a.a	$23$	$2$	23.a	1.a	$1$	$2$	$2$	$0.184$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	23.2.a.a	$1$	$0$	$-1$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
23.2.c.a	$23$	$2$	23.c	23.c	$11$	$10$	$1$	$0.184$	$\Q(\zeta_{22})$	$_{}$	None	None		✓	✓	✓	23.2.c.a	$2$	$0$	$-7$	$-7$	$-3$	$-5$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
24.2.a.a	$24$	$2$	24.a	1.a	$1$	$1$	$1$	$0.192$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	24.2.a.a	$1$	$0$	$0$	$-1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
24.2.d.a	$24$	$2$	24.d	8.b	$2$	$2$	$2$	$0.192$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓	✓	✓	24.2.d.a	$2$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i-1)q^{2}+i q^{3}-2 i q^{4}-2 i q^{5}+\cdots$
24.2.f.a	$24$	$2$	24.f	24.f	$2$	$2$	$2$	$0.192$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	24.2.f.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots$

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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.