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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 235 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
912.1.b.a	$912$	$1$	912.b	228.b	$2$	$1$	$1$	$0.455$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-57}) $	$\Q(\sqrt{19}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{9}+q^{19}+q^{25}-q^{27}+2q^{31}+\cdots$
912.1.b.b	$912$	$1$	912.b	228.b	$2$	$1$	$1$	$0.455$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-57}) $	$\Q(\sqrt{19}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{9}-q^{19}+q^{25}+q^{27}-2q^{31}+\cdots$
912.1.bj.a	$912$	$1$	912.bj	228.n	$6$	$2$	$1$	$0.455$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
912.1.bj.b	$912$	$1$	912.bj	228.n	$6$	$2$	$1$	$0.455$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+\zeta_{6}q^{3}+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
912.1.bl.a	$912$	$1$	912.bl	57.h	$6$	$2$	$1$	$0.455$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q+\zeta_{6}q^{3}+q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
912.1.cb.a	$912$	$1$	912.cb	57.l	$18$	$6$	$1$	$0.455$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{8}q^{3}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{7}+\cdots$
912.1.ce.a	$912$	$1$	912.ce	228.u	$18$	$6$	$1$	$0.455$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{8}q^{3}+(\zeta_{18}^{2}-\zeta_{18}^{4})q^{7}-\zeta_{18}^{7}q^{9}+\cdots$
912.1.ce.b	$912$	$1$	912.ce	228.u	$18$	$6$	$1$	$0.455$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{3}+(-\zeta_{18}^{2}+\zeta_{18}^{4})q^{7}+\cdots$
912.2.a.a	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+3q^{7}+q^{9}+q^{11}-2q^{13}+\cdots$
912.2.a.b	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots$
912.2.a.c	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}-4q^{13}+6q^{17}+\cdots$
912.2.a.d	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-3q^{7}+q^{9}+3q^{11}-6q^{13}+\cdots$
912.2.a.e	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots$
912.2.a.f	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-q^{7}+q^{9}+5q^{11}-6q^{13}+\cdots$
912.2.a.g	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+5q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
912.2.a.h	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-4q^{11}-2q^{17}+\cdots$
912.2.a.i	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+3q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots$
912.2.a.j	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots$
912.2.a.k	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
912.2.a.l	$912$	$2$	912.a	1.a	$1$	$1$	$1$	$7.282$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
912.2.a.m	$912$	$2$	912.a	1.a	$1$	$2$	$2$	$7.282$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots$
912.2.a.n	$912$	$2$	912.a	1.a	$1$	$2$	$2$	$7.282$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots$
912.2.a.o	$912$	$2$	912.a	1.a	$1$	$2$	$2$	$7.282$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}+(2-\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
912.2.d.a	$912$	$2$	912.d	12.b	$2$	$12$	$12$	$7.282$	12.0.$\cdots$.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{3}+(-\beta _{2}+\beta _{3}+\beta _{10})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
912.2.d.b	$912$	$2$	912.d	12.b	$2$	$24$	$24$	$7.282$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
912.2.f.a	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-q^{7}+\cdots$
912.2.f.b	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta )q^{3}+\beta q^{5}+4q^{7}+(-1+\cdots)q^{9}+\cdots$
912.2.f.c	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\zeta_{6}q^{3}-4q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots$
912.2.f.d	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta )q^{3}+\beta q^{5}+4q^{7}+(-1-2\beta )q^{9}+\cdots$
912.2.f.e	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}+\cdots$
912.2.f.f	$912$	$2$	912.f	57.d	$2$	$4$	$4$	$7.282$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2})q^{3}-\beta _{3}q^{5}-q^{7}+(-2+\cdots)q^{9}+\cdots$
912.2.f.g	$912$	$2$	912.f	57.d	$2$	$4$	$4$	$7.282$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{2}q^{5}+q^{7}+(2-\beta _{2})q^{9}+\cdots$
912.2.f.h	$912$	$2$	912.f	57.d	$2$	$10$	$10$	$7.282$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots$
912.2.f.i	$912$	$2$	912.f	57.d	$2$	$10$	$10$	$7.282$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$1$	$0$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots$
912.2.k.a	$912$	$2$	912.k	76.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-2q^{5}+2\beta q^{7}+q^{9}-\beta q^{11}+\cdots$
912.2.k.b	$912$	$2$	912.k	76.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots$
912.2.k.c	$912$	$2$	912.k	76.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+3q^{5}+\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots$
912.2.k.d	$912$	$2$	912.k	76.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-2q^{5}-2\beta q^{7}+q^{9}+\beta q^{11}+\cdots$
912.2.k.e	$912$	$2$	912.k	76.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-2\zeta_{6}q^{7}+q^{9}-2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots$
912.2.k.f	$912$	$2$	912.k	76.d	$2$	$2$	$2$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+3q^{5}-\zeta_{6}q^{7}+q^{9}+3\zeta_{6}q^{11}+\cdots$
912.2.k.g	$912$	$2$	912.k	76.d	$2$	$4$	$4$	$7.282$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots$
912.2.k.h	$912$	$2$	912.k	76.d	$2$	$4$	$4$	$7.282$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots$
912.2.q.a	$912$	$2$	912.q	19.c	$3$	$2$	$1$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-q^{7}-\zeta_{6}q^{9}+2q^{11}+\cdots$
912.2.q.b	$912$	$2$	912.q	19.c	$3$	$2$	$1$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-q^{7}-\zeta_{6}q^{9}+2q^{11}+\cdots$
912.2.q.c	$912$	$2$	912.q	19.c	$3$	$2$	$1$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$2$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}+5q^{7}+\cdots$
912.2.q.d	$912$	$2$	912.q	19.c	$3$	$2$	$1$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$4$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+3q^{7}+\cdots$
912.2.q.e	$912$	$2$	912.q	19.c	$3$	$2$	$1$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-2$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}+3q^{7}+\cdots$
912.2.q.f	$912$	$2$	912.q	19.c	$3$	$2$	$1$	$7.282$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$1$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-3q^{7}-\zeta_{6}q^{9}-2q^{11}+\cdots$
912.2.q.g	$912$	$2$	912.q	19.c	$3$	$4$	$2$	$7.282$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		$2$	$1$	$0$	$-2$	$-2$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
912.2.q.h	$912$	$2$	912.q	19.c	$3$	$4$	$2$	$7.282$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots$

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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.