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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 69 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
107.1.b.a	$107$	$1$	107.b	107.b	$2$	$1$	$1$	$0.053$	$\Q$	$D_{3}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots$
428.1.d.a	$428$	$1$	428.d	107.b	$2$	$3$	$3$	$0.214$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}-\beta _{2})q^{11}+\cdots$
963.1.b.a	$963$	$1$	963.b	107.b	$2$	$1$	$1$	$0.481$	$\Q$	$D_{3}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{11}-q^{13}+q^{16}-q^{19}+\cdots$
963.1.h.a	$963$	$1$	963.h	963.h	$6$	$2$	$1$	$0.481$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots$
963.1.h.b	$963$	$1$	963.h	963.h	$6$	$2$	$1$	$0.481$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{9}+\zeta_{6}q^{11}+\cdots$
963.1.h.c	$963$	$1$	963.h	963.h	$6$	$2$	$1$	$0.481$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+q^{3}+\zeta_{6}^{2}q^{4}+q^{9}+\zeta_{6}q^{11}+\zeta_{6}^{2}q^{12}+\cdots$
1177.1.h.a	$1177$	$1$	1177.h	1177.h	$10$	$4$	$1$	$0.587$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
1177.1.h.b	$1177$	$1$	1177.h	1177.h	$10$	$8$	$2$	$0.587$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{4})q^{3}+\zeta_{30}^{12}q^{4}+(\zeta_{30}^{4}+\cdots)q^{9}+\cdots$
1391.1.d.a	$1391$	$1$	1391.d	1391.d	$2$	$1$	$1$	$0.694$	$\Q$	$D_{2}$	$\Q(\sqrt{-107}) $, $\Q(\sqrt{-1391}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+2q^{3}-q^{4}+3q^{9}-2q^{12}-q^{13}+\cdots$
1391.1.d.b	$1391$	$1$	1391.d	1391.d	$2$	$2$	$2$	$0.694$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-q^{3}-q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+q^{12}+\cdots$
1391.1.h.a	$1391$	$1$	1391.h	1391.h	$6$	$6$	$3$	$0.694$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}+\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{9}+\cdots$
1391.1.i.a	$1391$	$1$	1391.i	1391.i	$6$	$6$	$3$	$0.694$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{9}+\cdots$
1712.1.g.a	$1712$	$1$	1712.g	107.b	$2$	$1$	$1$	$0.854$	$\Q$	$D_{3}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{11}-q^{13}+q^{19}+q^{23}+\cdots$
1712.1.g.b	$1712$	$1$	1712.g	107.b	$2$	$3$	$3$	$0.854$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(-\beta _{1}+\beta _{2})q^{11}+\cdots$
2033.1.g.b	$2033$	$1$	2033.g	2033.g	$6$	$6$	$3$	$1.015$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{9}+\cdots$
2033.1.l.a	$2033$	$1$	2033.l	2033.l	$18$	$18$	$3$	$1.015$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}+\zeta_{54}^{20})q^{3}+\zeta_{54}^{12}q^{4}+\cdots$
2461.1.h.a	$2461$	$1$	2461.h	2461.h	$22$	$10$	$1$	$1.228$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(-\zeta_{22}^{7}+\zeta_{22}^{8})q^{3}+\zeta_{22}^{6}q^{4}+\cdots$
2461.1.h.b	$2461$	$1$	2461.h	2461.h	$22$	$20$	$2$	$1.228$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(\zeta_{66}^{26}-\zeta_{66}^{31})q^{3}-\zeta_{66}^{3}q^{4}+\cdots$
2675.1.c.a	$2675$	$1$	2675.c	107.b	$2$	$1$	$1$	$1.335$	$\Q$	$D_{3}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}-q^{11}+q^{12}+q^{13}+q^{16}+\cdots$
2675.1.c.b	$2675$	$1$	2675.c	107.b	$2$	$3$	$3$	$1.335$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-\beta _{1}q^{11}+\cdots$
2675.1.c.c	$2675$	$1$	2675.c	107.b	$2$	$3$	$3$	$1.335$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-\beta _{1}q^{11}+\cdots$
2675.1.d.a	$2675$	$1$	2675.d	535.d	$2$	$2$	$2$	$1.335$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{4}-q^{11}+iq^{12}-iq^{13}+\cdots$
2675.1.d.b	$2675$	$1$	2675.d	535.d	$2$	$6$	$6$	$1.335$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}-q^{4}+(-1+\beta _{2})q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots$
2889.1.h.a	$2889$	$1$	2889.h	963.h	$6$	$2$	$1$	$1.442$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{11}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots$
2889.1.h.b	$2889$	$1$	2889.h	963.h	$6$	$2$	$1$	$1.442$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{11}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots$
2889.1.h.c	$2889$	$1$	2889.h	963.h	$6$	$2$	$1$	$1.442$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{11}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots$
2889.1.k.a	$2889$	$1$	2889.k	2889.k	$18$	$6$	$1$	$1.442$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{3}-\zeta_{18}^{5}q^{4}-\zeta_{18}^{3}q^{9}+\cdots$
2889.1.k.b	$2889$	$1$	2889.k	2889.k	$18$	$6$	$1$	$1.442$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{3}-\zeta_{18}^{5}q^{4}+\zeta_{18}^{6}q^{9}+\cdots$
2889.1.k.c	$2889$	$1$	2889.k	2889.k	$18$	$6$	$1$	$1.442$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$6$	$0$	$0$	$1$		$q+q^{3}-\zeta_{18}^{5}q^{4}+q^{9}+(-\zeta_{18}^{5}+\zeta_{18}^{6}+\cdots)q^{11}+\cdots$
3103.1.d.a	$3103$	$1$	3103.d	3103.d	$2$	$1$	$1$	$1.549$	$\Q$	$D_{2}$	$\Q(\sqrt{-107}) $, $\Q(\sqrt{-3103}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}-2q^{13}+q^{16}+2q^{23}+\cdots$
3103.1.d.c	$3103$	$1$	3103.d	3103.d	$2$	$2$	$2$	$1.549$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-q^{4}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots$
3103.1.h.a	$3103$	$1$	3103.h	3103.h	$14$	$6$	$1$	$1.549$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$7$	$0$	$0$	$1$		$q+(1-\zeta_{14}^{6})q^{3}-\zeta_{14}^{4}q^{4}+(1-\zeta_{14}^{5}+\cdots)q^{9}+\cdots$
3103.1.h.b	$3103$	$1$	3103.h	3103.h	$14$	$12$	$2$	$1.549$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-7$	$0$	$0$	$1$		$q+(\zeta_{42}^{5}-\zeta_{42}^{7})q^{3}+\zeta_{42}^{15}q^{4}+(\zeta_{42}^{10}+\cdots)q^{9}+\cdots$
3103.1.i.a	$3103$	$1$	3103.i	3103.i	$14$	$6$	$1$	$1.549$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$5$	$0$	$0$	$1$		$q+(1-\zeta_{14})q^{3}-\zeta_{14}^{3}q^{4}+(1-\zeta_{14}+\cdots)q^{9}+\cdots$
3103.1.i.b	$3103$	$1$	3103.i	3103.i	$14$	$12$	$2$	$1.549$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-5$	$0$	$0$	$7$		$q+(\zeta_{42}^{14}+\zeta_{42}^{16})q^{3}+\zeta_{42}^{6}q^{4}+\cdots$
3531.1.e.a	$3531$	$1$	3531.e	3531.e	$2$	$1$	$1$	$1.762$	$\Q$	$D_{2}$	$\Q(\sqrt{-107}) $, $\Q(\sqrt{-3531}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}-q^{11}+q^{12}+q^{16}+\cdots$
3531.1.e.b	$3531$	$1$	3531.e	3531.e	$2$	$1$	$1$	$1.762$	$\Q$	$D_{2}$	$\Q(\sqrt{-107}) $, $\Q(\sqrt{-3531}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{11}+q^{12}+q^{16}+\cdots$
3531.1.e.e	$3531$	$1$	3531.e	3531.e	$2$	$2$	$2$	$1.762$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}+\cdots$
3531.1.e.f	$3531$	$1$	3531.e	3531.e	$2$	$2$	$2$	$1.762$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}q^{3}+q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
3531.1.m.a	$3531$	$1$	3531.m	3531.m	$10$	$4$	$1$	$1.762$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\zeta_{10}q^{3}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{9}+\zeta_{10}^{2}q^{11}+\cdots$
3531.1.m.b	$3531$	$1$	3531.m	3531.m	$10$	$4$	$1$	$1.762$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{9}-\zeta_{10}^{2}q^{11}+\cdots$
3531.1.m.c	$3531$	$1$	3531.m	3531.m	$10$	$8$	$2$	$1.762$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{30}^{11}q^{3}-\zeta_{30}^{3}q^{4}-\zeta_{30}^{7}q^{9}+\cdots$
3531.1.m.d	$3531$	$1$	3531.m	3531.m	$10$	$8$	$2$	$1.762$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{30}^{8}q^{3}-\zeta_{30}^{3}q^{4}-\zeta_{30}q^{9}-\zeta_{30}^{11}q^{11}+\cdots$
3852.1.c.a	$3852$	$1$	3852.c	107.b	$2$	$3$	$3$	$1.922$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{11}-\beta _{1}q^{13}+(\beta _{1}-\beta _{2})q^{19}+\cdots$
3852.1.p.a	$3852$	$1$	3852.p	963.h	$6$	$6$	$3$	$1.922$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}-\zeta_{18}^{7}q^{9}+(-\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{11}+\cdots$
3852.1.p.b	$3852$	$1$	3852.p	963.h	$6$	$6$	$3$	$1.922$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{4}q^{3}+\zeta_{18}^{8}q^{9}+(-\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{11}+\cdots$
3959.1.d.a	$3959$	$1$	3959.d	3959.d	$2$	$1$	$1$	$1.976$	$\Q$	$D_{2}$	$\Q(\sqrt{-107}) $, $\Q(\sqrt{-3959}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}-q^{4}+3q^{9}+2q^{11}+2q^{12}+\cdots$
3959.1.d.b	$3959$	$1$	3959.d	3959.d	$2$	$2$	$2$	$1.976$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+q^{3}-q^{4}-q^{11}-q^{12}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots$
3959.1.h.a	$3959$	$1$	3959.h	3959.h	$6$	$6$	$3$	$1.976$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\zeta_{18}^{3}q^{4}+\cdots$
3959.1.j.a	$3959$	$1$	3959.j	3959.j	$6$	$6$	$3$	$1.976$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}+\zeta_{18}^{6}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{9}+\cdots$

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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.