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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 160 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
792.1.e.a	$792$	$1$	792.e	88.b	$2$	$1$	$1$	$0.395$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}-q^{22}+\cdots$
792.1.e.b	$792$	$1$	792.e	88.b	$2$	$1$	$1$	$0.395$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}-q^{11}+q^{16}-q^{22}+\cdots$
792.1.s.a	$792$	$1$	792.s	792.s	$6$	$2$	$1$	$0.395$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
792.1.s.b	$792$	$1$	792.s	792.s	$6$	$2$	$1$	$0.395$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
792.1.bs.a	$792$	$1$	792.bs	88.p	$10$	$4$	$1$	$0.395$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}+\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
792.1.bs.b	$792$	$1$	792.bs	88.p	$10$	$4$	$1$	$0.395$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
792.1.bu.a	$792$	$1$	792.bu	88.l	$10$	$4$	$1$	$0.395$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{3}q^{8}+\zeta_{10}^{3}q^{11}+\cdots$
792.1.bx.a	$792$	$1$	792.bx	792.ax	$30$	$8$	$1$	$0.395$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{11}q^{3}-\zeta_{30}^{13}q^{4}+\cdots$
792.1.bx.b	$792$	$1$	792.bx	792.ax	$30$	$8$	$1$	$0.395$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q+\zeta_{30}^{14}q^{2}+\zeta_{30}^{8}q^{3}-\zeta_{30}^{13}q^{4}+\cdots$
792.1.cl.a	$792$	$1$	792.cl	792.bl	$30$	$8$	$1$	$0.395$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q+\zeta_{30}^{7}q^{2}-\zeta_{30}^{4}q^{3}+\zeta_{30}^{14}q^{4}+\cdots$
792.1.cl.b	$792$	$1$	792.cl	792.bl	$30$	$8$	$1$	$0.395$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q-\zeta_{30}^{7}q^{2}+\zeta_{30}^{13}q^{3}+\zeta_{30}^{14}q^{4}+\cdots$
792.2.a.a	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots$
792.2.a.b	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{11}+2q^{13}-6q^{17}-4q^{23}+\cdots$
792.2.a.c	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-q^{11}-6q^{13}+6q^{17}-2q^{19}+\cdots$
792.2.a.d	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{11}-6q^{13}-6q^{17}-2q^{19}+\cdots$
792.2.a.e	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-q^{11}+2q^{17}+8q^{19}+2q^{23}+\cdots$
792.2.a.f	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}+q^{11}+6q^{13}-6q^{17}+\cdots$
792.2.a.g	$792$	$2$	792.a	1.a	$1$	$1$	$1$	$6.324$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-2q^{7}+q^{11}+6q^{17}+4q^{19}+\cdots$
792.2.a.h	$792$	$2$	792.a	1.a	$1$	$2$	$2$	$6.324$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(-2+2\beta )q^{7}+q^{11}+\cdots$
792.2.a.i	$792$	$2$	792.a	1.a	$1$	$2$	$2$	$6.324$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(2-\beta )q^{7}-q^{11}+(2+\beta )q^{13}+\cdots$
792.2.a.j	$792$	$2$	792.a	1.a	$1$	$2$	$2$	$6.324$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(2+\beta )q^{7}+q^{11}+(2-\beta )q^{13}+\cdots$
792.2.b.a	$792$	$2$	792.b	33.d	$2$	$6$	$6$	$6.324$	6.0.12781568.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}-\beta _{4})q^{11}+\cdots$
792.2.b.b	$792$	$2$	792.b	33.d	$2$	$6$	$6$	$6.324$	6.0.12781568.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots$
792.2.f.a	$792$	$2$	792.f	8.b	$2$	$2$	$2$	$6.324$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-i)q^{2}+2iq^{4}+4q^{7}+(2-2i)q^{8}+\cdots$
792.2.f.b	$792$	$2$	792.f	8.b	$2$	$2$	$2$	$6.324$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}+2iq^{4}+(-2+2i)q^{8}+\cdots$
792.2.f.c	$792$	$2$	792.f	8.b	$2$	$2$	$2$	$6.324$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}+2iq^{4}+4iq^{5}+4q^{7}+\cdots$
792.2.f.d	$792$	$2$	792.f	8.b	$2$	$4$	$4$	$6.324$	$\Q(i, \sqrt{7})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}+(-1-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
792.2.f.e	$792$	$2$	792.f	8.b	$2$	$4$	$4$	$6.324$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{3}q^{2}+2q^{4}+2\zeta_{8}^{2}q^{5}+(-2+\cdots)q^{7}+\cdots$
792.2.f.f	$792$	$2$	792.f	8.b	$2$	$6$	$6$	$6.324$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{5})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
792.2.f.g	$792$	$2$	792.f	8.b	$2$	$10$	$10$	$6.324$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+(-\beta _{2}-\beta _{6}+\beta _{9})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
792.2.f.h	$792$	$2$	792.f	8.b	$2$	$20$	$20$	$6.324$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{12}q^{2}+\beta _{11}q^{4}+(-\beta _{2}+\beta _{8})q^{5}+\cdots$
792.2.h.a	$792$	$2$	792.h	88.g	$2$	$2$	$2$	$6.324$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$0$	$-1$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}+(-2+\beta )q^{4}-4q^{7}+(2+\beta )q^{8}+\cdots$
792.2.h.b	$792$	$2$	792.h	88.g	$2$	$2$	$2$	$6.324$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-2q^{4}-2\beta q^{8}+(3-\beta )q^{11}+\cdots$
792.2.h.c	$792$	$2$	792.h	88.g	$2$	$2$	$2$	$6.324$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-2+\beta )q^{4}+4q^{7}+(-2+\cdots)q^{8}+\cdots$
792.2.h.d	$792$	$2$	792.h	88.g	$2$	$4$	$4$	$6.324$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(1-\beta _{3})q^{4}+(2\beta _{1}+\cdots)q^{7}+\cdots$
792.2.h.e	$792$	$2$	792.h	88.g	$2$	$4$	$4$	$6.324$	$\Q(\sqrt{2}, \sqrt{-7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+2q^{4}+\beta _{2}q^{5}-\beta _{1}q^{7}-2\beta _{1}q^{8}+\cdots$
792.2.h.f	$792$	$2$	792.h	88.g	$2$	$8$	$8$	$6.324$	8.0.$\cdots$.5	$_{}$	$\Q(\sqrt{-66}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}-2q^{4}-\beta _{1}q^{5}+\beta _{2}q^{7}+2\beta _{3}q^{8}+\cdots$
792.2.h.g	$792$	$2$	792.h	88.g	$2$	$8$	$8$	$6.324$	8.0.$\cdots$.6	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{7}q^{5}+(\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots$
792.2.h.h	$792$	$2$	792.h	88.g	$2$	$12$	$12$	$6.324$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{4}+\beta _{7}q^{5}-\beta _{5}q^{7}+\cdots$
792.2.h.i	$792$	$2$	792.h	88.g	$2$	$16$	$16$	$6.324$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(1-\beta _{6})q^{4}-\beta _{1}q^{5}+\beta _{12}q^{7}+\cdots$
792.2.k.a	$792$	$2$	792.k	24.f	$2$	$40$	$40$	$6.324$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
792.2.m.a	$792$	$2$	792.m	264.m	$2$	$4$	$4$	$6.324$	$\Q(\sqrt{-2}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-2q^{4}-2\beta _{2}q^{8}+\beta _{3}q^{11}+\cdots$
792.2.m.b	$792$	$2$	792.m	264.m	$2$	$4$	$4$	$6.324$	$\Q(\sqrt{-2}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}-2q^{4}+2\beta _{2}q^{8}-\beta _{3}q^{11}+\cdots$
792.2.m.c	$792$	$2$	792.m	264.m	$2$	$40$	$40$	$6.324$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
792.2.q.a	$792$	$2$	792.q	9.c	$3$	$2$	$1$	$6.324$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots$
792.2.q.b	$792$	$2$	792.q	9.c	$3$	$2$	$1$	$6.324$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$
792.2.q.c	$792$	$2$	792.q	9.c	$3$	$2$	$1$	$6.324$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots$
792.2.q.d	$792$	$2$	792.q	9.c	$3$	$4$	$2$	$6.324$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{5}+(-1+\zeta_{12}+\cdots)q^{7}+\cdots$
792.2.q.e	$792$	$2$	792.q	9.c	$3$	$6$	$3$	$6.324$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$0$	$-4$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{2}+\beta _{3}-\beta _{5})q^{3}+(-1-\beta _{3}+2\beta _{5})q^{5}+\cdots$
792.2.q.f	$792$	$2$	792.q	9.c	$3$	$12$	$6$	$6.324$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$1$	$-4$	$-5$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{10}q^{3}+(-\beta _{4}-\beta _{6}+\beta _{8})q^{5}+(-1+\cdots)q^{7}+\cdots$

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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.