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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 121 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
172.1.b.a	$172$	$1$	172.b	43.b	$2$	$1$	$1$	$0.086$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-q^{11}-q^{13}-q^{17}-q^{23}+\cdots$
387.1.b.a	$387$	$1$	387.b	43.b	$2$	$1$	$1$	$0.193$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-43}) $	$\Q(\sqrt{129}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-2q^{13}+q^{16}+q^{25}-2q^{31}+\cdots$
473.1.m.a	$473$	$1$	473.m	473.m	$10$	$4$	$1$	$0.236$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{10}q^{4}-\zeta_{10}^{3}q^{9}+q^{11}+(1-\zeta_{10}+\cdots)q^{13}+\cdots$
559.1.d.a	$559$	$1$	559.d	559.d	$2$	$1$	$1$	$0.279$	$\Q$	$D_{2}$	$\Q(\sqrt{-43}) $, $\Q(\sqrt{-559}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}+q^{13}+q^{16}+2q^{17}+\cdots$
559.1.o.a	$559$	$1$	559.o	559.o	$6$	$2$	$1$	$0.279$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+(1-\zeta_{6}^{2})q^{11}+\cdots$
559.1.s.a	$559$	$1$	559.s	559.s	$6$	$2$	$1$	$0.279$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}q^{4}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}-\zeta_{6}q^{13}+\cdots$
688.1.b.a	$688$	$1$	688.b	43.b	$2$	$1$	$1$	$0.343$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+q^{11}-q^{13}-q^{17}+q^{23}+\cdots$
731.1.c.b	$731$	$1$	731.c	731.c	$2$	$1$	$1$	$0.365$	$\Q$	$D_{2}$	$\Q(\sqrt{-43}) $, $\Q(\sqrt{-731}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}+2q^{13}+q^{16}-q^{17}+\cdots$
731.1.g.a	$731$	$1$	731.g	731.g	$4$	$2$	$1$	$0.365$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-iq^{9}+(-1-i)q^{11}+q^{13}+\cdots$
731.1.l.a	$731$	$1$	731.l	731.l	$8$	$4$	$1$	$0.365$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{2})q^{11}+\cdots$
989.1.q.a	$989$	$1$	989.q	989.q	$22$	$10$	$1$	$0.494$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{22}^{7}q^{4}-\zeta_{22}q^{9}+(-\zeta_{22}-\zeta_{22}^{3}+\cdots)q^{11}+\cdots$
1075.1.c.a	$1075$	$1$	1075.c	43.b	$2$	$1$	$1$	$0.536$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-q^{11}-q^{13}+q^{16}+2q^{17}+\cdots$
1075.1.c.b	$1075$	$1$	1075.c	43.b	$2$	$1$	$1$	$0.536$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-q^{11}+q^{13}+q^{16}-2q^{17}+\cdots$
1075.1.d.a	$1075$	$1$	1075.d	215.d	$2$	$2$	$2$	$0.536$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-q^{9}-q^{11}-iq^{13}+q^{16}+\cdots$
1333.1.o.a	$1333$	$1$	1333.o	1333.o	$6$	$2$	$1$	$0.665$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-\zeta_{6}q^{9}+\zeta_{6}q^{11}-\zeta_{6}q^{13}+\cdots$
1333.1.y.a	$1333$	$1$	1333.y	1333.y	$10$	$4$	$1$	$0.665$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{4}-\zeta_{10}^{3}q^{9}+(1+\zeta_{10}^{4}+\cdots)q^{11}+\cdots$
1333.1.br.a	$1333$	$1$	1333.br	1333.ar	$30$	$8$	$1$	$0.665$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{30}^{6}q^{4}+\zeta_{30}^{14}q^{9}+(\zeta_{30}^{10}+\zeta_{30}^{12}+\cdots)q^{11}+\cdots$
1548.1.c.a	$1548$	$1$	1548.c	43.b	$2$	$1$	$1$	$0.773$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{11}-q^{13}+q^{17}+q^{23}+q^{25}+\cdots$
1548.1.c.b	$1548$	$1$	1548.c	43.b	$2$	$2$	$2$	$0.773$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-43}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{11}+q^{13}+\beta q^{17}+\beta q^{23}+q^{25}+\cdots$
1763.1.c.b	$1763$	$1$	1763.c	1763.c	$2$	$1$	$1$	$0.880$	$\Q$	$D_{2}$	$\Q(\sqrt{-43}) $, $\Q(\sqrt{-1763}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}+q^{16}+2q^{23}+q^{25}+\cdots$
1763.1.g.a	$1763$	$1$	1763.g	1763.g	$4$	$2$	$1$	$0.880$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+iq^{9}+(-1-i)q^{11}+(1+i+\cdots)q^{13}+\cdots$
1763.1.p.a	$1763$	$1$	1763.p	1763.p	$10$	$4$	$1$	$0.880$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{10}^{4}q^{4}+q^{9}+(-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{11}+\cdots$
1763.1.q.a	$1763$	$1$	1763.q	1763.q	$10$	$4$	$1$	$0.880$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{4}-q^{9}+(-\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{11}+\cdots$
1763.1.x.a	$1763$	$1$	1763.x	1763.x	$20$	$8$	$1$	$0.880$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{20}^{6}q^{4}-\zeta_{20}^{5}q^{9}+(\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{11}+\cdots$
1892.1.y.a	$1892$	$1$	1892.y	473.m	$10$	$8$	$2$	$0.944$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{30}^{9}q^{9}-\zeta_{30}^{5}q^{11}+(-\zeta_{30}^{5}+\cdots)q^{13}+\cdots$
2021.1.t.a	$2021$	$1$	2021.t	2021.t	$46$	$22$	$1$	$1.009$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{46}^{2}q^{4}-\zeta_{46}^{15}q^{9}+(-\zeta_{46}^{13}+\cdots)q^{11}+\cdots$
2107.1.b.a	$2107$	$1$	2107.b	43.b	$2$	$1$	$1$	$1.052$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-43}) $	$\Q(\sqrt{301}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-2q^{11}+q^{16}+2q^{23}+\cdots$
2107.1.b.d	$2107$	$1$	2107.b	43.b	$2$	$2$	$2$	$1.052$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-43}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-\beta q^{13}+q^{16}+\beta q^{17}+\cdots$
2107.1.r.a	$2107$	$1$	2107.r	301.r	$6$	$2$	$1$	$1.052$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-43}) $	$\Q(\sqrt{301}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}-\zeta_{6}q^{16}+\cdots$
2107.1.r.b	$2107$	$1$	2107.r	301.r	$6$	$4$	$2$	$1.052$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-43}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-1-\beta _{2})q^{4}+\beta _{2}q^{9}-\beta _{3}q^{13}+\cdots$
2236.1.e.a	$2236$	$1$	2236.e	559.d	$2$	$2$	$2$	$1.116$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+\zeta_{6}^{2}q^{13}+\cdots$
2236.1.be.a	$2236$	$1$	2236.be	559.s	$6$	$2$	$1$	$1.116$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}+q^{13}+\zeta_{6}q^{17}+\cdots$
2236.1.be.b	$2236$	$1$	2236.be	559.s	$6$	$2$	$1$	$1.116$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{17}+\cdots$
2236.1.bn.a	$2236$	$1$	2236.bn	559.o	$6$	$2$	$1$	$1.116$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}q^{9}+(-1-\zeta_{6})q^{11}+\zeta_{6}^{2}q^{13}+\cdots$
2236.1.bn.b	$2236$	$1$	2236.bn	559.o	$6$	$2$	$1$	$1.116$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}q^{9}+q^{13}+\zeta_{6}q^{17}-\zeta_{6}^{2}q^{23}+\cdots$
2279.1.d.a	$2279$	$1$	2279.d	2279.d	$2$	$1$	$1$	$1.137$	$\Q$	$D_{2}$	$\Q(\sqrt{-43}) $, $\Q(\sqrt{-2279}) $	$\Q(\sqrt{53}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-q^{9}+2q^{11}-2q^{13}+q^{16}+\cdots$
2279.1.s.a	$2279$	$1$	2279.s	2279.s	$26$	$12$	$1$	$1.137$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{26}^{3}q^{4}-\zeta_{26}^{12}q^{9}+(\zeta_{26}^{2}-\zeta_{26}^{3}+\cdots)q^{11}+\cdots$
2279.1.u.a	$2279$	$1$	2279.u	2279.u	$26$	$12$	$1$	$1.137$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{26}^{8}q^{4}+\zeta_{26}^{6}q^{9}+(-\zeta_{26}+\zeta_{26}^{8}+\cdots)q^{11}+\cdots$
43.3.b.a	$43$	$3$	43.b	43.b	$2$	$1$	$1$	$1.172$	$\Q$	$_{}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+9q^{9}-21q^{11}-17q^{13}+\cdots$
2537.1.t.a	$2537$	$1$	2537.t	2537.t	$58$	$28$	$1$	$1.266$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{58}^{17}q^{4}-\zeta_{58}^{9}q^{9}+(-\zeta_{58}^{21}+\cdots)q^{11}+\cdots$
2752.1.b.a	$2752$	$1$	2752.b	43.b	$2$	$1$	$1$	$1.373$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-q^{11}+q^{13}-q^{17}+q^{23}+\cdots$
2752.1.b.b	$2752$	$1$	2752.b	43.b	$2$	$1$	$1$	$1.373$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+q^{11}+q^{13}-q^{17}-q^{23}+\cdots$
2752.1.h.a	$2752$	$1$	2752.h	344.h	$2$	$2$	$2$	$1.373$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-43}) $	$\Q(\sqrt{86}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{9}-iq^{11}-q^{17}-q^{25}-q^{41}+\cdots$
2752.1.h.b	$2752$	$1$	2752.h	344.h	$2$	$4$	$4$	$1.373$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-43}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{2}$		$q-q^{9}-\zeta_{12}^{3}q^{11}+(-\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{13}+\cdots$
2881.1.n.a	$2881$	$1$	2881.n	2881.n	$6$	$2$	$1$	$1.438$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}+q^{9}-\zeta_{6}^{2}q^{11}+\zeta_{6}q^{13}+\cdots$
2881.1.be.a	$2881$	$1$	2881.be	2881.ae	$22$	$10$	$1$	$1.438$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{22}^{8}q^{4}+\zeta_{22}^{4}q^{9}+(\zeta_{22}^{2}+\zeta_{22}^{8}+\cdots)q^{11}+\cdots$
2881.1.cc.a	$2881$	$1$	2881.cc	2881.bc	$66$	$20$	$1$	$1.438$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{66}^{14}q^{4}+\zeta_{66}^{18}q^{9}+(-\zeta_{66}^{9}+\cdots)q^{11}+\cdots$
2924.1.h.a	$2924$	$1$	2924.h	731.c	$2$	$2$	$2$	$1.459$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{9}+(\zeta_{6}+\zeta_{6}^{2})q^{11}-q^{13}+\zeta_{6}q^{17}+\cdots$
2924.1.k.a	$2924$	$1$	2924.k	731.g	$4$	$4$	$2$	$1.459$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{3}q^{9}+(-\zeta_{12}+\zeta_{12}^{2})q^{11}+\cdots$
2924.1.w.a	$2924$	$1$	2924.w	731.l	$8$	$8$	$2$	$1.459$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{3}q^{9}+(\zeta_{24}^{10}+\zeta_{24}^{11})q^{11}+\cdots$

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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.