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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 19306 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	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	$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$
103.1.b.a	$103$	$1$	103.b	103.b	$2$	$2$	$2$	$0.051$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-103}) $	None	✓	✓	✓	✓	103.1.b.a	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots$
104.1.h.a	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓	✓			104.1.h.a	$2$	$0$	$-1$	$-1$	$1$	$1$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
104.1.h.b	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓	✓			104.1.h.a	$2$	$0$	$1$	$-1$	$-1$	$-1$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
107.1.b.a	$107$	$1$	107.b	107.b	$2$	$1$	$1$	$0.053$	$\Q$	$D_{3}$	$\Q(\sqrt{-107}) $	None	✓	✓	✓	✓	107.1.b.a	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots$
108.1.c.a	$108$	$1$	108.c	3.b	$2$	$1$	$1$	$0.054$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	✓	✓	✓	108.1.c.a	$2$	$0$	$0$	$0$	$0$	$-1$	$1$		$q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots$
111.1.d.a	$111$	$1$	111.d	111.d	$2$	$1$	$1$	$0.055$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $	✓	✓			111.1.d.a	$4$	$0$	$0$	$1$	$0$	$-2$	$1$		$q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots$
111.1.d.b	$111$	$1$	111.d	111.d	$2$	$2$	$2$	$0.055$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-111}) $	None	✓	✓	✓		111.1.d.b	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots$
111.1.h.a	$111$	$1$	111.h	111.h	$6$	$2$	$1$	$0.055$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	111.1.h.a	$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
111.1.i.a	$111$	$1$	111.i	111.i	$6$	$2$	$1$	$0.055$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	111.1.i.a	$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
112.1.l.a	$112$	$1$	112.l	112.l	$4$	$2$	$1$	$0.056$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	112.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+i q^{2}-q^{4}+i q^{7}-i q^{8}-i q^{9}+\cdots$
116.1.d.a	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	✓			116.1.d.a	$2$	$0$	$-1$	$1$	$-1$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
116.1.d.b	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	✓			116.1.d.a	$2$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
116.1.j.a	$116$	$1$	116.j	116.j	$14$	$6$	$1$	$0.058$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	116.1.j.a	$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
117.1.j.a	$117$	$1$	117.j	13.d	$4$	$2$	$1$	$0.058$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	117.1.j.a	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+i q^{4}+(-i-1)q^{7}-i q^{13}-q^{16}+\cdots$
119.1.d.a	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	✓			119.1.d.a	$2$	$0$	$-1$	$-1$	$-1$	$2$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
119.1.d.b	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	✓			119.1.d.a	$2$	$0$	$-1$	$1$	$1$	$-2$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots$
120.1.i.a	$120$	$1$	120.i	120.i	$2$	$2$	$2$	$0.060$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $		✓	✓	✓	120.1.i.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-i q^{2}-i q^{3}-q^{4}+i q^{5}-q^{6}+\cdots$
124.1.i.a	$124$	$1$	124.i	124.i	$6$	$4$	$2$	$0.062$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	124.1.i.a	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
127.1.b.a	$127$	$1$	127.b	127.b	$2$	$2$	$2$	$0.063$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-127}) $	None	✓	✓	✓	✓	127.1.b.a	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots$
128.1.d.a	$128$	$1$	128.d	8.d	$2$	$1$	$1$	$0.064$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	✓	✓	✓	✓	128.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots$
129.1.l.a	$129$	$1$	129.l	129.l	$14$	$6$	$1$	$0.064$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	129.1.l.a	$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$

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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.