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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 75 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
2312.1.e.a	$2312$	$1$	2312.e	136.e	$2$	$2$	$2$	$1.154$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}-q^{9}+\cdots$
2312.1.e.b	$2312$	$1$	2312.e	136.e	$2$	$4$	$4$	$1.154$	4.0.2048.2	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{8}+\cdots$
2312.1.f.a	$2312$	$1$	2312.f	8.d	$2$	$1$	$1$	$1.154$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-34}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}-q^{9}+q^{16}-q^{18}+\cdots$
2312.1.f.b	$2312$	$1$	2312.f	8.d	$2$	$2$	$2$	$1.154$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+q^{8}+q^{9}+\cdots$
2312.1.f.c	$2312$	$1$	2312.f	8.d	$2$	$4$	$4$	$1.154$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-2}) $	None	✓	$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{8}+\cdots$
2312.1.j.a	$2312$	$1$	2312.j	136.j	$4$	$2$	$1$	$1.154$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-34}) $	$\Q(\sqrt{17}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-q^{4}-iq^{8}+iq^{9}+q^{16}+\cdots$
2312.1.j.b	$2312$	$1$	2312.j	136.j	$4$	$2$	$1$	$1.154$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+iq^{2}+(1-i)q^{3}-q^{4}+(1+i)q^{6}+\cdots$
2312.1.j.c	$2312$	$1$	2312.j	136.j	$4$	$8$	$4$	$1.154$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$		$q+\zeta_{16}^{4}q^{2}+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}-q^{4}+\cdots$
2312.1.p.a	$2312$	$1$	2312.p	136.p	$8$	$4$	$1$	$1.154$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}+(-1-\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
2312.1.p.b	$2312$	$1$	2312.p	136.p	$8$	$4$	$1$	$1.154$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
2312.1.p.c	$2312$	$1$	2312.p	136.p	$8$	$4$	$1$	$1.154$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-34}) $	$\Q(\sqrt{17}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots$
2312.1.p.d	$2312$	$1$	2312.p	136.p	$8$	$4$	$1$	$1.154$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots$
2312.1.p.e	$2312$	$1$	2312.p	136.p	$8$	$8$	$2$	$1.154$	$\Q(\zeta_{16})$	$D_{4}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+\zeta_{16}^{6}q^{2}+(-\zeta_{16}^{3}-\zeta_{16}^{7})q^{3}+\cdots$
2312.1.q.a	$2312$	$1$	2312.q	136.q	$16$	$16$	$2$	$1.154$	$\Q(\zeta_{32})$	$D_{4}$	None	$\Q(\sqrt{34}) $		$32$	$0$	$0$	$0$	$0$	$0$		$2^{4}$		$q-\zeta_{32}^{2}q^{2}+(-\zeta_{32}^{3}-\zeta_{32}^{11})q^{3}+\cdots$
2312.1.x.a	$2312$	$1$	2312.x	2312.x	$34$	$16$	$1$	$1.154$	$\Q(\zeta_{34})$	$D_{17}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$		$1$		$q-\zeta_{34}q^{2}+(-\zeta_{34}^{5}-\zeta_{34}^{7})q^{3}+\zeta_{34}^{2}q^{4}+\cdots$
2312.1.y.a	$2312$	$1$	2312.y	2312.y	$34$	$16$	$1$	$1.154$	$\Q(\zeta_{34})$	$D_{34}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\zeta_{34}^{5}q^{2}+(\zeta_{34}+\zeta_{34}^{8})q^{3}+\zeta_{34}^{10}q^{4}+\cdots$
2312.1.be.a	$2312$	$1$	2312.be	2312.ae	$68$	$32$	$1$	$1.154$	$\Q(\zeta_{68})$	$D_{68}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{68}^{13}q^{2}+(\zeta_{68}^{14}+\zeta_{68}^{23})q^{3}+\cdots$
2312.1.bg.a	$2312$	$1$	2312.bg	2312.ag	$136$	$64$	$1$	$1.154$	$\Q(\zeta_{136})$	$D_{136}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{136}^{35}q^{2}+(\zeta_{136}^{7}-\zeta_{136}^{22})q^{3}+\cdots$
2312.2.a.a	$2312$	$2$	2312.a	1.a	$1$	$1$	$1$	$18.461$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-2q^{11}-6q^{13}+4q^{19}+\cdots$
2312.2.a.b	$2312$	$2$	2312.a	1.a	$1$	$1$	$1$	$18.461$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
2312.2.a.c	$2312$	$2$	2312.a	1.a	$1$	$1$	$1$	$18.461$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
2312.2.a.d	$2312$	$2$	2312.a	1.a	$1$	$1$	$1$	$18.461$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots$
2312.2.a.e	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+\beta q^{5}+\beta q^{7}+(1+3\beta )q^{9}+\cdots$
2312.2.a.f	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-3\beta )q^{5}+(-3+\beta )q^{7}+\cdots$
2312.2.a.g	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{5}+\beta q^{7}-3q^{9}-2\beta q^{11}+2q^{13}+\cdots$
2312.2.a.h	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-3\beta q^{5}-3\beta q^{7}-q^{9}-\beta q^{11}+\cdots$
2312.2.a.i	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}+\beta q^{7}-q^{9}-\beta q^{11}+\cdots$
2312.2.a.j	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}+2\beta q^{7}-q^{9}-\beta q^{11}+\cdots$
2312.2.a.k	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+\beta q^{5}-2\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots$
2312.2.a.l	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+3\beta )q^{5}+(3-\beta )q^{7}+\cdots$
2312.2.a.m	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-4$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-2q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
2312.2.a.n	$2312$	$2$	2312.a	1.a	$1$	$2$	$2$	$18.461$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}-\beta q^{7}+(1+3\beta )q^{9}+\cdots$
2312.2.a.o	$2312$	$2$	2312.a	1.a	$1$	$3$	$3$	$18.461$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-6$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-2\beta _{1}+\beta _{2})q^{3}+(-2-\beta _{1}+\cdots)q^{5}+\cdots$
2312.2.a.p	$2312$	$2$	2312.a	1.a	$1$	$3$	$3$	$18.461$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$6$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(2+\beta _{1}-\beta _{2})q^{5}+\cdots$
2312.2.a.q	$2312$	$2$	2312.a	1.a	$1$	$3$	$3$	$18.461$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-2-\beta _{1}+\beta _{2})q^{5}+\cdots$
2312.2.a.r	$2312$	$2$	2312.a	1.a	$1$	$3$	$3$	$18.461$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$6$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+2\beta _{1}-\beta _{2})q^{3}+(2+\beta _{1})q^{5}+(2+\cdots)q^{7}+\cdots$
2312.2.a.s	$2312$	$2$	2312.a	1.a	$1$	$4$	$4$	$18.461$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-2\beta _{1}-\beta _{3})q^{7}+\cdots$
2312.2.a.t	$2312$	$2$	2312.a	1.a	$1$	$4$	$4$	$18.461$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{3})q^{3}+(-2\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
2312.2.a.u	$2312$	$2$	2312.a	1.a	$1$	$6$	$6$	$18.461$	6.6.3418281.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-6$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$
2312.2.a.v	$2312$	$2$	2312.a	1.a	$1$	$6$	$6$	$18.461$	6.6.3418281.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
2312.2.a.w	$2312$	$2$	2312.a	1.a	$1$	$12$	$12$	$18.461$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{10}q^{5}+\beta _{6}q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots$
2312.2.b.a	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{3}+\beta q^{5}+2\beta q^{7}-5q^{9}+2\beta q^{11}+\cdots$
2312.2.b.b	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-q^{9}-iq^{11}-6q^{13}-4q^{19}+\cdots$
2312.2.b.c	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{5}-iq^{7}-q^{9}-3iq^{11}+\cdots$
2312.2.b.d	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+2\beta q^{5}-2\beta q^{7}+q^{9}+\beta q^{11}+\cdots$
2312.2.b.e	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{11}+\cdots$
2312.2.b.f	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-3\beta q^{5}+3\beta q^{7}+q^{9}+\beta q^{11}+\cdots$
2312.2.b.g	$2312$	$2$	2312.b	17.b	$2$	$4$	$4$	$18.461$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(-3+\beta _{3})q^{9}+\cdots$
2312.2.b.h	$2312$	$2$	2312.b	17.b	$2$	$4$	$4$	$18.461$	$\Q(i, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{3}-\beta _{1}q^{5}+\beta _{1}q^{7}+(-4+\cdots)q^{9}+\cdots$
2312.2.b.i	$2312$	$2$	2312.b	17.b	$2$	$4$	$4$	$18.461$	4.0.2048.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}+(\beta _{1}-2\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$

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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.