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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 76 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
2156.1.h.a	$2156$	$1$	2156.h	11.b	$2$	$1$	$1$	$1.076$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{5}+q^{11}+q^{15}-q^{23}-q^{27}+\cdots$
2156.1.h.b	$2156$	$1$	2156.h	11.b	$2$	$2$	$2$	$1.076$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}+\beta q^{5}+2q^{9}+q^{11}-3q^{15}+\cdots$
2156.1.h.c	$2156$	$1$	2156.h	11.b	$2$	$4$	$4$	$1.076$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-11}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{2})q^{9}-q^{11}+\cdots$
2156.1.k.a	$2156$	$1$	2156.k	77.h	$6$	$2$	$1$	$1.076$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{11}+q^{15}+\cdots$
2156.1.k.b	$2156$	$1$	2156.k	77.h	$6$	$2$	$1$	$1.076$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{11}+q^{15}+\cdots$
2156.1.k.c	$2156$	$1$	2156.k	77.h	$6$	$4$	$2$	$1.076$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(\zeta_{12}^{3}+\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
2156.1.k.d	$2156$	$1$	2156.k	77.h	$6$	$8$	$4$	$1.076$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$		$q+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+(\zeta_{24}^{7}+\zeta_{24}^{9}+\cdots)q^{5}+\cdots$
2156.1.m.a	$2156$	$1$	2156.m	308.m	$6$	$2$	$1$	$1.076$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-77}) $	$\Q(\sqrt{11}) $		$8$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}-\zeta_{6}^{2}q^{9}+\cdots$
2156.1.m.b	$2156$	$1$	2156.m	308.m	$6$	$2$	$1$	$1.076$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-77}) $	$\Q(\sqrt{11}) $		$8$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}^{2}q^{9}+\cdots$
2156.1.v.a	$2156$	$1$	2156.v	44.h	$10$	$4$	$1$	$1.076$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{8}+\cdots$
2156.1.v.b	$2156$	$1$	2156.v	44.h	$10$	$4$	$1$	$1.076$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+\zeta_{10}q^{8}-\zeta_{10}^{3}q^{9}+\cdots$
2156.1.bk.a	$2156$	$1$	2156.bk	308.ab	$30$	$8$	$1$	$1.076$	$\Q(\zeta_{15})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{30}q^{2}+\zeta_{30}^{2}q^{4}+\zeta_{30}^{3}q^{8}+\zeta_{30}^{4}q^{9}+\cdots$
2156.1.bk.b	$2156$	$1$	2156.bk	308.ab	$30$	$8$	$1$	$1.076$	$\Q(\zeta_{15})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{30}^{7}q^{2}+\zeta_{30}^{14}q^{4}-\zeta_{30}^{6}q^{8}+\cdots$
2156.1.bm.a	$2156$	$1$	2156.bm	308.ad	$30$	$8$	$1$	$1.076$	$\Q(\zeta_{15})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}-\zeta_{30}^{12}q^{8}+\cdots$
2156.1.bm.b	$2156$	$1$	2156.bm	308.ad	$30$	$8$	$1$	$1.076$	$\Q(\zeta_{15})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}+\zeta_{30}^{6}q^{8}+\cdots$
2156.2.a.a	$2156$	$2$	2156.a	1.a	$1$	$1$	$1$	$17.216$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{9}-q^{11}+4q^{13}+\cdots$
2156.2.a.b	$2156$	$2$	2156.a	1.a	$1$	$1$	$1$	$17.216$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+q^{11}+4q^{13}+\cdots$
2156.2.a.c	$2156$	$2$	2156.a	1.a	$1$	$2$	$2$	$17.216$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}+3q^{9}-q^{11}+(-2+\cdots)q^{13}+\cdots$
2156.2.a.d	$2156$	$2$	2156.a	1.a	$1$	$2$	$2$	$17.216$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-3q^{9}+q^{11}-3\beta q^{13}-\beta q^{17}+\cdots$
2156.2.a.e	$2156$	$2$	2156.a	1.a	$1$	$2$	$2$	$17.216$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{9}-q^{11}-\beta q^{13}-5\beta q^{17}+\cdots$
2156.2.a.f	$2156$	$2$	2156.a	1.a	$1$	$2$	$2$	$17.216$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+\beta q^{5}+5q^{9}-q^{11}-\beta q^{13}+\cdots$
2156.2.a.g	$2156$	$2$	2156.a	1.a	$1$	$3$	$3$	$17.216$	3.3.257.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(1+\cdots)q^{9}+\cdots$
2156.2.a.h	$2156$	$2$	2156.a	1.a	$1$	$3$	$3$	$17.216$	3.3.321.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1}-2\beta _{2})q^{9}+\cdots$
2156.2.a.i	$2156$	$2$	2156.a	1.a	$1$	$3$	$3$	$17.216$	3.3.321.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
2156.2.a.j	$2156$	$2$	2156.a	1.a	$1$	$3$	$3$	$17.216$	3.3.1016.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
2156.2.a.k	$2156$	$2$	2156.a	1.a	$1$	$3$	$3$	$17.216$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
2156.2.a.l	$2156$	$2$	2156.a	1.a	$1$	$4$	$4$	$17.216$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(2\beta _{1}+\beta _{3})q^{5}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
2156.2.a.m	$2156$	$2$	2156.a	1.a	$1$	$4$	$4$	$17.216$	4.4.301088.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(4+\beta _{3})q^{9}+q^{11}+\cdots$
2156.2.c.a	$2156$	$2$	2156.c	77.b	$2$	$8$	$8$	$17.216$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
2156.2.c.b	$2156$	$2$	2156.c	77.b	$2$	$16$	$16$	$17.216$	16.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 7^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{5}q^{3}+\beta _{11}q^{5}+(-3+\beta _{6})q^{9}+\cdots$
2156.2.c.c	$2156$	$2$	2156.c	77.b	$2$	$16$	$16$	$17.216$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{5}q^{9}-\beta _{11}q^{11}+\cdots$
2156.2.i.a	$2156$	$2$	2156.i	7.c	$3$	$2$	$1$	$17.216$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$
2156.2.i.b	$2156$	$2$	2156.i	7.c	$3$	$2$	$1$	$17.216$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$
2156.2.i.c	$2156$	$2$	2156.i	7.c	$3$	$2$	$1$	$17.216$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots$
2156.2.i.d	$2156$	$2$	2156.i	7.c	$3$	$2$	$1$	$17.216$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-1+\cdots)q^{11}+\cdots$
2156.2.i.e	$2156$	$2$	2156.i	7.c	$3$	$4$	$2$	$17.216$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{3}+(-2+2\beta _{1})q^{5}+(-3+3\beta _{1}+\cdots)q^{9}+\cdots$
2156.2.i.f	$2156$	$2$	2156.i	7.c	$3$	$4$	$2$	$17.216$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots$
2156.2.i.g	$2156$	$2$	2156.i	7.c	$3$	$4$	$2$	$17.216$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{9}+(1+\beta _{2})q^{11}-\beta _{3}q^{13}+\cdots$
2156.2.i.h	$2156$	$2$	2156.i	7.c	$3$	$4$	$2$	$17.216$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{5}+(3+3\beta _{2})q^{9}+\beta _{2}q^{11}+3\beta _{3}q^{13}+\cdots$
2156.2.i.i	$2156$	$2$	2156.i	7.c	$3$	$4$	$2$	$17.216$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{3}+(2-2\beta _{1})q^{5}+(-3+3\beta _{1}+\cdots)q^{9}+\cdots$
2156.2.i.j	$2156$	$2$	2156.i	7.c	$3$	$6$	$3$	$17.216$	6.0.1783323.2	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4}-\beta _{5})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
2156.2.i.k	$2156$	$2$	2156.i	7.c	$3$	$6$	$3$	$17.216$	6.0.27870912.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5})q^{5}+(-1+\cdots)q^{9}+\cdots$
2156.2.i.l	$2156$	$2$	2156.i	7.c	$3$	$6$	$3$	$17.216$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$0$	$1$	$-2$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{5})q^{5}+\cdots$
2156.2.i.m	$2156$	$2$	2156.i	7.c	$3$	$6$	$3$	$17.216$	6.0.27870912.1	$_{}$	None	None		$2$	$0$	$0$	$1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{3}+\beta _{5})q^{5}+\cdots$
2156.2.i.n	$2156$	$2$	2156.i	7.c	$3$	$8$	$4$	$17.216$	8.0.$\cdots$.14	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+\beta _{7}q^{5}+(4\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{9}+\cdots$
2156.2.i.o	$2156$	$2$	2156.i	7.c	$3$	$8$	$4$	$17.216$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{24}^{7}q^{3}+(-\zeta_{24}^{3}-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{5}+\cdots$
2156.2.q.a	$2156$	$2$	2156.q	77.i	$6$	$8$	$4$	$17.216$	8.0.796594176.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{3}+(-2\beta _{3}-2\beta _{5})q^{5}+(-1+\cdots)q^{9}+\cdots$
2156.2.q.b	$2156$	$2$	2156.q	77.i	$6$	$8$	$4$	$17.216$	8.0.3317760000.3	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{6}q^{3}+\beta _{1}q^{5}+2\beta _{3}q^{9}+(1-\beta _{3}+\cdots)q^{11}+\cdots$
2156.2.q.c	$2156$	$2$	2156.q	77.i	$6$	$16$	$8$	$17.216$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-6$	$0$		$7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{7}q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots$
2156.2.q.d	$2156$	$2$	2156.q	77.i	$6$	$16$	$8$	$17.216$	16.0.$\cdots$.5	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}+\beta _{5})q^{3}-\beta _{5}q^{5}+(-1-\beta _{6}+\cdots)q^{9}+\cdots$

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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.