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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 51 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
183.1.d.a	$183$	$1$	183.d	183.d	$2$	$1$	$1$	$0.091$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-183}) $	$\Q(\sqrt{61}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}-2q^{13}+q^{16}+\cdots$
183.1.d.b	$183$	$1$	183.d	183.d	$2$	$2$	$2$	$0.091$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}+\beta q^{11}+\cdots$
1464.1.k.e	$1464$	$1$	1464.k	1464.k	$2$	$8$	$8$	$0.731$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{4}q^{3}+\zeta_{16}^{2}q^{4}-\zeta_{16}^{5}q^{6}+\cdots$
1647.1.d.a	$1647$	$1$	1647.d	183.d	$2$	$1$	$1$	$0.822$	$\Q$	$D_{3}$	$\Q(\sqrt{-183}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{8}-q^{11}+2q^{13}-q^{16}+\cdots$
1647.1.d.b	$1647$	$1$	1647.d	183.d	$2$	$1$	$1$	$0.822$	$\Q$	$D_{3}$	$\Q(\sqrt{-183}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}-q^{8}+q^{11}+2q^{13}-q^{16}+\cdots$
1647.1.d.c	$1647$	$1$	1647.d	183.d	$2$	$2$	$2$	$0.822$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{2}+2q^{4}-\beta q^{8}-\beta q^{11}-2q^{13}+\cdots$
1647.1.d.d	$1647$	$1$	1647.d	183.d	$2$	$4$	$4$	$0.822$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2\beta _{1}-\beta _{3})q^{8}+\cdots$
2013.1.bm.a	$2013$	$1$	2013.bm	2013.am	$10$	$4$	$1$	$1.005$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$-3$	$-1$	$0$	$0$	$1$		$q+(-1+\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2013.1.bm.b	$2013$	$1$	2013.bm	2013.am	$10$	$4$	$1$	$1.005$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$3$	$-1$	$0$	$0$	$1$		$q+(1-\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2013.1.bm.c	$2013$	$1$	2013.bm	2013.am	$10$	$8$	$2$	$1.005$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\zeta_{20}^{8}q^{3}+(-1+\cdots)q^{4}+\cdots$
2013.1.bm.d	$2013$	$1$	2013.bm	2013.am	$10$	$16$	$4$	$1.005$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}-\zeta_{40}^{16}q^{3}+\cdots$
2196.1.h.a	$2196$	$1$	2196.h	244.c	$2$	$1$	$1$	$1.096$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+2q^{11}+2q^{13}+\cdots$
2196.1.h.c	$2196$	$1$	2196.h	244.c	$2$	$1$	$1$	$1.096$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-2q^{11}+2q^{13}+\cdots$
2196.1.h.f	$2196$	$1$	2196.h	244.c	$2$	$2$	$2$	$1.096$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-183}) $	$\Q(\sqrt{183}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{13}+q^{16}+\cdots$
2196.1.h.h	$2196$	$1$	2196.h	244.c	$2$	$4$	$4$	$1.096$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+(-\zeta_{8}+\cdots)q^{11}+\cdots$
2379.1.e.e	$2379$	$1$	2379.e	2379.e	$2$	$1$	$1$	$1.187$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-2379}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
2379.1.e.f	$2379$	$1$	2379.e	2379.e	$2$	$1$	$1$	$1.187$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-2379}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
2379.1.e.g	$2379$	$1$	2379.e	2379.e	$2$	$2$	$2$	$1.187$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-183}) $	$\Q(\sqrt{793}) $		$8$	$0$	$0$	$2$	$0$	$0$	$2$		$q-iq^{2}+q^{3}-3q^{4}-2iq^{6}+4iq^{8}+\cdots$
2379.1.e.h	$2379$	$1$	2379.e	2379.e	$2$	$4$	$4$	$1.187$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$-4$	$0$	$0$	$2$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-q^{3}-q^{4}+(-\zeta_{8}+\cdots)q^{6}+\cdots$
2379.1.be.a	$2379$	$1$	2379.be	2379.ae	$6$	$2$	$1$	$1.187$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{6}-q^{8}+\cdots$
2379.1.be.d	$2379$	$1$	2379.be	2379.ae	$6$	$2$	$1$	$1.187$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{6}+q^{8}+\cdots$
2379.1.be.e	$2379$	$1$	2379.be	2379.ae	$6$	$4$	$2$	$1.187$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$	$3$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots$
2379.1.be.f	$2379$	$1$	2379.be	2379.ae	$6$	$8$	$4$	$1.187$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{2}+\zeta_{24}^{4}q^{3}+\cdots$
2379.1.bw.a	$2379$	$1$	2379.bw	2379.aw	$6$	$2$	$1$	$1.187$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$-3$	$-1$	$0$	$0$	$1$		$q+(-1+\zeta_{6}^{2})q^{2}-\zeta_{6}q^{3}+(1-\zeta_{6}+\cdots)q^{4}+\cdots$
2379.1.bw.d	$2379$	$1$	2379.bw	2379.aw	$6$	$2$	$1$	$1.187$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$3$	$-1$	$0$	$0$	$1$		$q+(1-\zeta_{6}^{2})q^{2}-\zeta_{6}q^{3}+(1-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
2379.1.bw.e	$2379$	$1$	2379.bw	2379.aw	$6$	$4$	$2$	$1.187$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}-\zeta_{12}^{5}q^{6}+\zeta_{12}^{3}q^{8}+\cdots$
2379.1.bw.f	$2379$	$1$	2379.bw	2379.aw	$6$	$8$	$4$	$1.187$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}-\zeta_{24}^{8}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
2928.1.e.a	$2928$	$1$	2928.e	183.d	$2$	$1$	$1$	$1.461$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-183}) $	$\Q(\sqrt{61}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{9}-2q^{13}+2q^{19}+q^{25}+\cdots$
2928.1.e.b	$2928$	$1$	2928.e	183.d	$2$	$2$	$2$	$1.461$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+q^{3}+q^{9}-\beta q^{11}+\beta q^{17}+\beta q^{23}+\cdots$
2928.1.bj.a	$2928$	$1$	2928.bj	2928.aj	$4$	$16$	$8$	$1.461$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{12}q^{3}+\zeta_{32}^{6}q^{4}+\cdots$
3111.1.h.e	$3111$	$1$	3111.h	3111.h	$2$	$8$	$8$	$1.553$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{2}-\zeta_{16}^{4}q^{3}+(1+\cdots)q^{4}+\cdots$
3111.1.k.a	$3111$	$1$	3111.k	3111.k	$4$	$16$	$8$	$1.553$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{32}^{7}-\zeta_{32}^{9})q^{2}+\zeta_{32}^{12}q^{3}+\cdots$
3111.1.bi.a	$3111$	$1$	3111.bi	3111.ai	$8$	$32$	$8$	$1.553$	$\Q(\zeta_{64})$	$D_{32}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{64}^{19}+\zeta_{64}^{29})q^{2}+\zeta_{64}^{4}q^{3}+\cdots$
3477.1.y.a	$3477$	$1$	3477.y	3477.y	$6$	$2$	$1$	$1.735$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{6}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
3477.1.y.d	$3477$	$1$	3477.y	3477.y	$6$	$2$	$1$	$1.735$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{6}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
3477.1.y.e	$3477$	$1$	3477.y	3477.y	$6$	$4$	$2$	$1.735$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$	$3$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}+\zeta_{12}^{4}q^{3}+\cdots$
3477.1.y.f	$3477$	$1$	3477.y	3477.y	$6$	$8$	$4$	$1.735$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}-\zeta_{24}^{8}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
3477.1.dh.a	$3477$	$1$	3477.dh	3477.ch	$18$	$6$	$1$	$1.735$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$-6$	$0$	$0$	$0$	$1$		$q+(-1+\zeta_{18})q^{2}+\zeta_{18}^{2}q^{3}+(1-\zeta_{18}+\cdots)q^{4}+\cdots$
3477.1.dh.b	$3477$	$1$	3477.dh	3477.ch	$18$	$6$	$1$	$1.735$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$6$	$0$	$0$	$0$	$1$		$q+(1-\zeta_{18})q^{2}+\zeta_{18}^{2}q^{3}+(1-\zeta_{18}+\cdots)q^{4}+\cdots$
3477.1.dh.c	$3477$	$1$	3477.dh	3477.ch	$18$	$12$	$2$	$1.735$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$3$		$q+(\zeta_{36}^{9}+\zeta_{36}^{11})q^{2}+\zeta_{36}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots$
3477.1.dh.d	$3477$	$1$	3477.dh	3477.ch	$18$	$24$	$4$	$1.735$	$\Q(\zeta_{72})$	$D_{36}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{72}-\zeta_{72}^{27})q^{2}+\zeta_{72}^{20}q^{3}+(\zeta_{72}^{2}+\cdots)q^{4}+\cdots$
549.2.c.f	$549$	$2$	549.c	61.b	$2$	$8$	$8$	$4.384$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3}+\cdots)q^{8}+\cdots$
183.3.d.a	$183$	$3$	183.d	183.d	$2$	$4$	$4$	$4.986$	4.4.178608.1	$_{}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$-12$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}-3q^{3}+(4-\beta _{3})q^{4}+3\beta _{2}q^{6}+\cdots$
183.3.d.b	$183$	$3$	183.d	183.d	$2$	$4$	$4$	$4.986$	4.4.140544.1	$_{}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$12$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots$
732.2.e.a	$732$	$2$	732.e	732.e	$2$	$16$	$16$	$5.845$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{11}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{7}q^{2}-\beta _{4}q^{3}+\beta _{6}q^{4}+\beta _{3}q^{6}+\cdots$
1647.2.c.h	$1647$	$2$	1647.c	61.b	$2$	$8$	$8$	$13.151$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{2}+(-2-\beta _{4})q^{4}+(\beta _{1}-2\beta _{3}+\cdots)q^{8}+\cdots$
1647.2.c.i	$1647$	$2$	1647.c	61.b	$2$	$8$	$8$	$13.151$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{2}+(-2-\beta _{2}+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{8}+\cdots$
183.5.d.a	$183$	$5$	183.d	183.d	$2$	$2$	$2$	$18.917$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$18$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+9q^{3}-13q^{4}+9\beta q^{6}-29\beta q^{8}+\cdots$
183.5.d.b	$183$	$5$	183.d	183.d	$2$	$2$	$2$	$18.917$	$\Q(\sqrt{61}) $	$_{}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$18$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}+9q^{3}+45q^{4}-9\beta q^{6}-29\beta q^{8}+\cdots$
183.5.d.c	$183$	$5$	183.d	183.d	$2$	$4$	$4$	$18.917$	$\Q(\sqrt{6}, \sqrt{122})$	$_{}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$-36$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-9q^{3}+(2^{4}+\beta _{3})q^{4}-9\beta _{1}q^{6}+\cdots$

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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.