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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (47 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2856.1.bd.a	$2856$	$1$	2856.bd	2856.ad	$2$	$1$	$1$	$1.425$	$\Q$	$D_{3}$	$\Q(\sqrt{-714}) $	None	✓	✓			2856.1.bd.a	$2$	$0$	$-1$	$-1$	$-1$	$-1$		$1$		$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
2856.1.bd.b	$2856$	$1$	2856.bd	2856.ad	$2$	$1$	$1$	$1.425$	$\Q$	$D_{3}$	$\Q(\sqrt{-714}) $	None	✓	✓			2856.1.bd.a	$2$	$0$	$-1$	$-1$	$-1$	$1$		$1$		$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
2856.1.bd.c	$2856$	$1$	2856.bd	2856.ad	$2$	$1$	$1$	$1.425$	$\Q$	$D_{3}$	$\Q(\sqrt{-714}) $	None	✓	✓			2856.1.bd.a	$2$	$0$	$-1$	$1$	$1$	$-1$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
2856.1.bd.d	$2856$	$1$	2856.bd	2856.ad	$2$	$1$	$1$	$1.425$	$\Q$	$D_{3}$	$\Q(\sqrt{-714}) $	None	✓	✓			2856.1.bd.a	$2$	$0$	$-1$	$1$	$1$	$1$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
2856.1.bd.e	$2856$	$1$	2856.bd	2856.ad	$2$	$1$	$1$	$1.425$	$\Q$	$D_{3}$	$\Q(\sqrt{-714}) $	None	✓	✓			2856.1.bd.a	$2$	$0$	$1$	$-1$	$1$	$-1$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
2856.1.bd.f	$2856$	$1$	2856.bd	2856.ad	$2$	$1$	$1$	$1.425$	$\Q$	$D_{3}$	$\Q(\sqrt{-714}) $	None	✓	✓			2856.1.bd.a	$2$	$0$	$1$	$-1$	$1$	$1$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
2856.1.bd.g	$2856$	$1$	2856.bd	2856.ad	$2$	$1$	$1$	$1.425$	$\Q$	$D_{3}$	$\Q(\sqrt{-714}) $	None	✓	✓			2856.1.bd.a	$2$	$0$	$1$	$1$	$-1$	$-1$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
2856.1.bd.h	$2856$	$1$	2856.bd	2856.ad	$2$	$1$	$1$	$1.425$	$\Q$	$D_{3}$	$\Q(\sqrt{-714}) $	None	✓	✓			2856.1.bd.a	$2$	$0$	$1$	$1$	$-1$	$1$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
2856.1.bd.i	$2856$	$1$	2856.bd	2856.ad	$2$	$2$	$2$	$1.425$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{102}) $		✓			2856.1.bd.i	$8$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}-i q^{3}+q^{4}+i q^{6}+i q^{7}+\cdots$
2856.1.bd.j	$2856$	$1$	2856.bd	2856.ad	$2$	$2$	$2$	$1.425$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{102}) $		✓			2856.1.bd.i	$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}-i q^{3}+q^{4}-i q^{6}-i q^{7}+\cdots$
2856.1.bd.k	$2856$	$1$	2856.bd	2856.ad	$2$	$8$	$8$	$1.425$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		✓			2856.1.bd.k	$8$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{6}q^{2}-\zeta_{20}q^{3}-\zeta_{20}^{2}q^{4}+(\zeta_{20}^{3}+\cdots)q^{5}+\cdots$
2856.1.bd.l	$2856$	$1$	2856.bd	2856.ad	$2$	$8$	$8$	$1.425$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		✓			2856.1.bd.k	$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{4}q^{2}-\zeta_{20}q^{3}+\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{3}+\cdots)q^{5}+\cdots$
2856.1.bt.a	$2856$	$1$	2856.bt	2856.at	$4$	$4$	$2$	$1.425$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-42}) $	None		✓			2856.1.bt.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}-\zeta_{8}^{3}q^{6}+\cdots$
2856.1.bt.b	$2856$	$1$	2856.bt	2856.at	$4$	$4$	$2$	$1.425$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-42}) $	None		✓			2856.1.bt.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots$
2856.1.cb.a	$2856$	$1$	2856.cb	357.q	$6$	$8$	$4$	$1.425$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	2856.1.cb.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{10}q^{3}+(-\zeta_{24}^{5}-\zeta_{24}^{11})q^{5}+\cdots$
2856.1.dg.a	$2856$	$1$	2856.dg	2856.cg	$8$	$8$	$2$	$1.425$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-42}) $	None		✓			2856.1.dg.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{6}q^{2}+\zeta_{16}^{5}q^{3}-\zeta_{16}^{4}q^{4}+\cdots$
2856.1.dg.b	$2856$	$1$	2856.dg	2856.cg	$8$	$8$	$2$	$1.425$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-42}) $	None		✓			2856.1.dg.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{6}q^{2}+\zeta_{16}^{5}q^{3}-\zeta_{16}^{4}q^{4}+\cdots$
2856.2.a.a	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓			2856.2.a.a	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
2856.2.a.b	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓			2856.2.a.b	$1$	$1$	$0$	$-1$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
2856.2.a.c	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓			2856.2.a.c	$1$	$0$	$0$	$1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots$
2856.2.a.d	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓			2856.2.a.d	$1$	$0$	$0$	$1$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
2856.2.a.e	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓			2856.2.a.e	$1$	$0$	$0$	$1$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$
2856.2.a.f	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.f	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots$
2856.2.a.g	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.g	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots$
2856.2.a.h	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓			2856.2.a.h	$1$	$0$	$0$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}-3q^{11}-q^{13}+\cdots$
2856.2.a.i	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓			2856.2.a.i	$1$	$0$	$0$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots$
2856.2.a.j	$2856$	$2$	2856.a	1.a	$1$	$1$	$1$	$22.805$	$\Q$	$_{}$	None	None	✓	✓			2856.2.a.j	$1$	$0$	$0$	$1$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-q^{7}+q^{9}+5q^{11}-3q^{13}+\cdots$
2856.2.a.k	$2856$	$2$	2856.a	1.a	$1$	$2$	$2$	$22.805$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.k	$1$	$1$	$0$	$-2$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots$
2856.2.a.l	$2856$	$2$	2856.a	1.a	$1$	$2$	$2$	$22.805$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.l	$1$	$0$	$0$	$-2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}+(1-2\beta )q^{11}+\cdots$
2856.2.a.m	$2856$	$2$	2856.a	1.a	$1$	$2$	$2$	$22.805$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			2856.2.a.m	$1$	$0$	$0$	$2$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots$
2856.2.a.n	$2856$	$2$	2856.a	1.a	$1$	$2$	$2$	$22.805$	$\Q(\sqrt{15}) $	$_{}$	None	None	✓	✓			2856.2.a.n	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}-q^{7}+q^{9}-5q^{11}+(2+\cdots)q^{13}+\cdots$
2856.2.a.o	$2856$	$2$	2856.a	1.a	$1$	$2$	$2$	$22.805$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.o	$1$	$1$	$0$	$2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(-3-2\beta )q^{11}+\cdots$
2856.2.a.p	$2856$	$2$	2856.a	1.a	$1$	$2$	$2$	$22.805$	$\Q(\sqrt{201}) $	$_{}$	None	None	✓	✓	✓		2856.2.a.p	$1$	$0$	$0$	$2$	$6$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
2856.2.a.q	$2856$	$2$	2856.a	1.a	$1$	$3$	$3$	$22.805$	3.3.568.1	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.q	$1$	$1$	$0$	$-3$	$-4$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
2856.2.a.r	$2856$	$2$	2856.a	1.a	$1$	$3$	$3$	$22.805$	3.3.961.1	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.r	$1$	$0$	$0$	$-3$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
2856.2.a.s	$2856$	$2$	2856.a	1.a	$1$	$3$	$3$	$22.805$	3.3.316.1	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.s	$1$	$1$	$0$	$3$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1})q^{5}-q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots$
2856.2.a.t	$2856$	$2$	2856.a	1.a	$1$	$4$	$4$	$22.805$	4.4.81416.1	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.t	$1$	$0$	$0$	$-4$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(1-\beta _{3})q^{11}+\cdots$
2856.2.a.u	$2856$	$2$	2856.a	1.a	$1$	$4$	$4$	$22.805$	4.4.7232.1	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.u	$1$	$1$	$0$	$-4$	$2$	$-4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{3}q^{5}-q^{7}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots$
2856.2.a.v	$2856$	$2$	2856.a	1.a	$1$	$4$	$4$	$22.805$	4.4.183064.1	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.v	$1$	$0$	$0$	$-4$	$5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}-q^{7}+q^{9}+\beta _{2}q^{11}+\cdots$
2856.2.a.w	$2856$	$2$	2856.a	1.a	$1$	$5$	$5$	$22.805$	5.5.14050576.1	$_{}$	None	None	✓	✓	✓	✓	2856.2.a.w	$1$	$0$	$0$	$5$	$1$	$5$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(\beta _{2}+\beta _{4})q^{11}+\cdots$
2856.2.h.a	$2856$	$2$	2856.h	17.b	$2$	$2$	$2$	$22.805$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2856.2.h.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+2 i q^{5}+i q^{7}-q^{9}+2 i q^{11}+\cdots$
2856.2.h.b	$2856$	$2$	2856.h	17.b	$2$	$2$	$2$	$22.805$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2856.2.h.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+i q^{5}-i q^{7}-q^{9}+i q^{11}+\cdots$
2856.2.h.c	$2856$	$2$	2856.h	17.b	$2$	$2$	$2$	$22.805$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			2856.2.h.c	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+4 i q^{5}+i q^{7}-q^{9}-4 i q^{11}+\cdots$
2856.2.h.d	$2856$	$2$	2856.h	17.b	$2$	$10$	$10$	$22.805$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓			2856.2.h.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(\beta _{2}+\beta _{8})q^{5}-\beta _{2}q^{7}-q^{9}+\cdots$
2856.2.h.e	$2856$	$2$	2856.h	17.b	$2$	$12$	$12$	$22.805$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2856.2.h.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}-q^{9}+\cdots$
2856.2.h.f	$2856$	$2$	2856.h	17.b	$2$	$12$	$12$	$22.805$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2856.2.h.f	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+\beta _{1}q^{5}-\beta _{5}q^{7}-q^{9}+(-\beta _{5}+\cdots)q^{11}+\cdots$
2856.2.h.g	$2856$	$2$	2856.h	17.b	$2$	$12$	$12$	$22.805$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			2856.2.h.g	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{3}+(-\beta _{4}+\beta _{8})q^{5}-\beta _{8}q^{7}+\cdots$

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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.