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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 95 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				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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1815.1.g.a	$1815$	$1$	1815.g	15.d	$2$	$1$	$1$	$0.906$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$		$1$		$q-q^{2}-q^{3}-q^{5}+q^{6}+q^{8}+q^{9}+\cdots$
1815.1.g.b	$1815$	$1$	1815.g	15.d	$2$	$1$	$1$	$0.906$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-q^{2}+q^{3}+q^{5}-q^{6}+q^{8}+q^{9}+\cdots$
1815.1.g.c	$1815$	$1$	1815.g	15.d	$2$	$1$	$1$	$0.906$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{165}) $	✓	$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-q^{3}-q^{4}+q^{5}+q^{9}+q^{12}-q^{15}+\cdots$
1815.1.g.d	$1815$	$1$	1815.g	15.d	$2$	$1$	$1$	$0.906$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{165}) $	✓	$4$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+q^{3}-q^{4}-q^{5}+q^{9}-q^{12}-q^{15}+\cdots$
1815.1.g.e	$1815$	$1$	1815.g	15.d	$2$	$1$	$1$	$0.906$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+q^{2}-q^{3}-q^{5}-q^{6}-q^{8}+q^{9}+\cdots$
1815.1.g.f	$1815$	$1$	1815.g	15.d	$2$	$1$	$1$	$0.906$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$1$	$1$	$0$		$1$		$q+q^{2}+q^{3}+q^{5}+q^{6}-q^{8}+q^{9}+\cdots$
1815.1.g.g	$1815$	$1$	1815.g	15.d	$2$	$2$	$2$	$0.906$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None	✓	$4$	$0$	$0$	$-2$	$2$	$0$		$1$		$q-\beta q^{2}-q^{3}+2q^{4}+q^{5}+\beta q^{6}-\beta q^{8}+\cdots$
1815.1.g.h	$1815$	$1$	1815.g	15.d	$2$	$2$	$2$	$0.906$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None	✓	$4$	$0$	$0$	$2$	$-2$	$0$		$1$		$q-\beta q^{2}+q^{3}+2q^{4}-q^{5}-\beta q^{6}-\beta q^{8}+\cdots$
1815.1.o.a	$1815$	$1$	1815.o	165.o	$10$	$4$	$1$	$0.906$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$-1$	$-1$	$-1$	$0$		$1$		$q-\zeta_{10}^{3}q^{2}+\zeta_{10}^{4}q^{3}+\zeta_{10}^{2}q^{5}+\cdots$
1815.1.o.b	$1815$	$1$	1815.o	165.o	$10$	$4$	$1$	$0.906$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}^{2}q^{5}+\cdots$
1815.1.o.c	$1815$	$1$	1815.o	165.o	$10$	$4$	$1$	$0.906$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{165}) $		$16$	$0$	$0$	$-1$	$1$	$0$		$1$		$q+\zeta_{10}^{4}q^{3}+\zeta_{10}q^{4}-\zeta_{10}^{2}q^{5}-\zeta_{10}^{3}q^{9}+\cdots$
1815.1.o.d	$1815$	$1$	1815.o	165.o	$10$	$4$	$1$	$0.906$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{165}) $		$16$	$0$	$0$	$1$	$-1$	$0$		$1$		$q-\zeta_{10}^{4}q^{3}+\zeta_{10}q^{4}+\zeta_{10}^{2}q^{5}-\zeta_{10}^{3}q^{9}+\cdots$
1815.1.o.e	$1815$	$1$	1815.o	165.o	$10$	$4$	$1$	$0.906$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+\zeta_{10}^{3}q^{2}+\zeta_{10}^{4}q^{3}+\zeta_{10}^{2}q^{5}+\cdots$
1815.1.o.f	$1815$	$1$	1815.o	165.o	$10$	$4$	$1$	$0.906$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$1$	$1$	$1$	$0$		$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}^{2}q^{5}+\cdots$
1815.1.o.g	$1815$	$1$	1815.o	165.o	$10$	$8$	$2$	$0.906$	8.0.324000000.3	$D_{6}$	$\Q(\sqrt{-15}) $	None		$16$	$0$	$0$	$-2$	$2$	$0$		$1$		$q-\beta _{7}q^{2}+\beta _{6}q^{3}+2\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
1815.1.o.h	$1815$	$1$	1815.o	165.o	$10$	$8$	$2$	$0.906$	8.0.324000000.3	$D_{6}$	$\Q(\sqrt{-15}) $	None		$16$	$0$	$0$	$2$	$-2$	$0$		$1$		$q-\beta _{7}q^{2}-\beta _{6}q^{3}+2\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
1815.1.v.a	$1815$	$1$	1815.v	165.u	$20$	$8$	$1$	$0.906$	$\Q(\zeta_{20})$	$D_{4}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{3}q^{4}+\zeta_{20}q^{5}-\zeta_{20}^{4}q^{9}+\cdots$
1815.1.v.b	$1815$	$1$	1815.v	165.u	$20$	$8$	$1$	$0.906$	$\Q(\zeta_{20})$	$D_{4}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{20}^{2}q^{3}+\zeta_{20}^{3}q^{4}-\zeta_{20}q^{5}+\zeta_{20}^{4}q^{9}+\cdots$
1815.2.a.a	$1815$	$2$	1815.a	1.a	$1$	$1$	$1$	$14.493$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
1815.2.a.b	$1815$	$2$	1815.a	1.a	$1$	$1$	$1$	$14.493$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-2q^{12}+\cdots$
1815.2.a.c	$1815$	$2$	1815.a	1.a	$1$	$1$	$1$	$14.493$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-2q^{12}+\cdots$
1815.2.a.d	$1815$	$2$	1815.a	1.a	$1$	$1$	$1$	$14.493$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots$
1815.2.a.e	$1815$	$2$	1815.a	1.a	$1$	$1$	$1$	$14.493$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
1815.2.a.f	$1815$	$2$	1815.a	1.a	$1$	$2$	$2$	$14.493$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$-2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots$
1815.2.a.g	$1815$	$2$	1815.a	1.a	$1$	$2$	$2$	$14.493$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}-\beta q^{7}+q^{9}+2q^{12}+\cdots$
1815.2.a.h	$1815$	$2$	1815.a	1.a	$1$	$2$	$2$	$14.493$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{8}+\cdots$
1815.2.a.i	$1815$	$2$	1815.a	1.a	$1$	$2$	$2$	$14.493$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}-2q^{7}+\cdots$
1815.2.a.j	$1815$	$2$	1815.a	1.a	$1$	$2$	$2$	$14.493$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$-2$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$
1815.2.a.k	$1815$	$2$	1815.a	1.a	$1$	$2$	$2$	$14.493$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots$
1815.2.a.l	$1815$	$2$	1815.a	1.a	$1$	$3$	$3$	$14.493$	3.3.469.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
1815.2.a.m	$1815$	$2$	1815.a	1.a	$1$	$3$	$3$	$14.493$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
1815.2.a.n	$1815$	$2$	1815.a	1.a	$1$	$3$	$3$	$14.493$	3.3.469.1	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1815.2.a.o	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	4.4.725.1	$_{}$	None	None	✓	$1$	$1$	$-5$	$4$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1}+\beta _{2})q^{2}+q^{3}+(3-\beta _{1}+\cdots)q^{4}+\cdots$
1815.2.a.p	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	4.4.725.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$4$	$4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1815.2.a.q	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	$\Q(\zeta_{15})^+$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-4$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+q^{5}+\cdots$
1815.2.a.r	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	4.4.5725.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$-4$	$-4$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots$
1815.2.a.s	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	4.4.8112.1	$_{}$	None	None	✓	$2$	$0$	$0$	$-4$	$4$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(2-\beta _{3})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots$
1815.2.a.t	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	$\Q(\sqrt{3}, \sqrt{7})$	$_{}$	None	None	✓	$2$	$0$	$0$	$4$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+q^{3}-\beta _{2}q^{4}-q^{5}+\beta _{3}q^{6}+\cdots$
1815.2.a.u	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	$\Q(\zeta_{15})^+$	$_{}$	None	None	✓	$1$	$0$	$1$	$-4$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{2}-\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+q^{5}+\cdots$
1815.2.a.v	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	4.4.5725.1	$_{}$	None	None	✓	$1$	$1$	$1$	$-4$	$-4$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots$
1815.2.a.w	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	4.4.725.1	$_{}$	None	None	✓	$1$	$0$	$3$	$4$	$4$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots$
1815.2.a.x	$1815$	$2$	1815.a	1.a	$1$	$4$	$4$	$14.493$	4.4.725.1	$_{}$	None	None	✓	$1$	$0$	$5$	$4$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1}-\beta _{2})q^{2}+q^{3}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots$
1815.2.a.y	$1815$	$2$	1815.a	1.a	$1$	$6$	$6$	$14.493$	6.6.437199552.1	$_{}$	None	None	✓	$2$	$0$	$0$	$-6$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
1815.2.c.a	$1815$	$2$	1815.c	5.b	$2$	$2$	$2$	$14.493$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}+q^{4}+(-1-2i)q^{5}+\cdots$
1815.2.c.b	$1815$	$2$	1815.c	5.b	$2$	$2$	$2$	$14.493$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots$
1815.2.c.c	$1815$	$2$	1815.c	5.b	$2$	$4$	$4$	$14.493$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}-3q^{4}+(-1-2\beta _{1}+\cdots)q^{5}+\cdots$
1815.2.c.d	$1815$	$2$	1815.c	5.b	$2$	$6$	$6$	$14.493$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots$
1815.2.c.e	$1815$	$2$	1815.c	5.b	$2$	$6$	$6$	$14.493$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots$
1815.2.c.f	$1815$	$2$	1815.c	5.b	$2$	$8$	$8$	$14.493$	8.0.49787136.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$16$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+(2-\beta _{3}+\cdots)q^{5}+\cdots$
1815.2.c.g	$1815$	$2$	1815.c	5.b	$2$	$8$	$8$	$14.493$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+\zeta_{24}^{3}q^{3}+(-1+\cdots)q^{5}+\cdots$

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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.