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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 121 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
833.1.h.a	$833$	$1$	833.h	119.h	$6$	$4$	$2$	$0.416$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}+\cdots$
833.1.h.b	$833$	$1$	833.h	119.h	$6$	$4$	$2$	$0.416$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$1$	$1$	$0$		$1$		$q+(\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+\cdots$
833.2.a.a	$833$	$2$	833.a	1.a	$1$	$1$	$1$	$6.652$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots$
833.2.a.b	$833$	$2$	833.a	1.a	$1$	$3$	$3$	$6.652$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
833.2.a.c	$833$	$2$	833.a	1.a	$1$	$3$	$3$	$6.652$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
833.2.a.d	$833$	$2$	833.a	1.a	$1$	$4$	$4$	$6.652$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
833.2.a.e	$833$	$2$	833.a	1.a	$1$	$4$	$4$	$6.652$	4.4.9301.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
833.2.a.f	$833$	$2$	833.a	1.a	$1$	$4$	$4$	$6.652$	4.4.1957.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$4$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
833.2.a.g	$833$	$2$	833.a	1.a	$1$	$5$	$5$	$6.652$	5.5.453749.1	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(2-\beta _{3})q^{4}+\cdots$
833.2.a.h	$833$	$2$	833.a	1.a	$1$	$7$	$7$	$6.652$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
833.2.a.i	$833$	$2$	833.a	1.a	$1$	$7$	$7$	$6.652$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
833.2.a.j	$833$	$2$	833.a	1.a	$1$	$8$	$8$	$6.652$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-8$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
833.2.a.k	$833$	$2$	833.a	1.a	$1$	$8$	$8$	$6.652$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$8$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
833.2.b.a	$833$	$2$	833.b	17.b	$2$	$10$	$10$	$6.652$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-\beta _{1}-\beta _{2})q^{4}+\cdots$
833.2.b.b	$833$	$2$	833.b	17.b	$2$	$10$	$10$	$6.652$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(2+\beta _{8})q^{4}-\beta _{5}q^{5}+\cdots$
833.2.b.c	$833$	$2$	833.b	17.b	$2$	$10$	$10$	$6.652$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+\beta _{2}q^{5}+\cdots$
833.2.b.d	$833$	$2$	833.b	17.b	$2$	$10$	$10$	$6.652$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1+\beta _{9})q^{4}+\beta _{2}q^{5}+\cdots$
833.2.b.e	$833$	$2$	833.b	17.b	$2$	$16$	$16$	$6.652$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}-\beta _{1}q^{3}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}+\cdots$
833.2.e.a	$833$	$2$	833.e	7.c	$3$	$2$	$1$	$6.652$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-2\zeta_{6}q^{5}+3q^{8}+\cdots$
833.2.e.b	$833$	$2$	833.e	7.c	$3$	$2$	$1$	$6.652$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+2\zeta_{6}q^{5}+3q^{8}+\cdots$
833.2.e.c	$833$	$2$	833.e	7.c	$3$	$6$	$3$	$6.652$	6.0.64827.1	$_{}$	None	None		$2$	$0$	$1$	$1$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
833.2.e.d	$833$	$2$	833.e	7.c	$3$	$8$	$4$	$6.652$	8.0.310217769.2	$_{}$	None	None		$2$	$0$	$1$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}-\beta _{6})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
833.2.e.e	$833$	$2$	833.e	7.c	$3$	$8$	$4$	$6.652$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{3}+\beta _{7})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
833.2.e.f	$833$	$2$	833.e	7.c	$3$	$8$	$4$	$6.652$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(1+\beta _{3}-\beta _{7})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
833.2.e.g	$833$	$2$	833.e	7.c	$3$	$8$	$4$	$6.652$	8.0.310217769.2	$_{}$	None	None		$2$	$0$	$1$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}-\beta _{6})q^{2}+(\beta _{2}-\beta _{4}+\beta _{5})q^{3}+\cdots$
833.2.e.h	$833$	$2$	833.e	7.c	$3$	$10$	$5$	$6.652$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(\beta _{3}-\beta _{7}-\beta _{8})q^{3}+(\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots$
833.2.e.i	$833$	$2$	833.e	7.c	$3$	$10$	$5$	$6.652$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(-\beta _{3}+\beta _{7}+\beta _{8})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots$
833.2.e.j	$833$	$2$	833.e	7.c	$3$	$14$	$7$	$6.652$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$1$	$2$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2})q^{2}-\beta _{13}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$
833.2.e.k	$833$	$2$	833.e	7.c	$3$	$16$	$8$	$6.652$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$-8$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{6}+\beta _{10}+\beta _{14}+\cdots)q^{3}+\cdots$
833.2.e.l	$833$	$2$	833.e	7.c	$3$	$16$	$8$	$6.652$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$8$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(1+\beta _{6}-\beta _{10}-\beta _{14})q^{3}+\cdots$
833.2.g.a	$833$	$2$	833.g	17.c	$4$	$2$	$1$	$6.652$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{2}+(-2-2i)q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
833.2.g.b	$833$	$2$	833.g	17.c	$4$	$2$	$1$	$6.652$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{2}+(2+2i)q^{3}+q^{4}+(1+i)q^{5}+\cdots$
833.2.g.c	$833$	$2$	833.g	17.c	$4$	$4$	$2$	$6.652$	$\Q(i, \sqrt{11})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
833.2.g.d	$833$	$2$	833.g	17.c	$4$	$4$	$2$	$6.652$	$\Q(i, \sqrt{11})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
833.2.g.e	$833$	$2$	833.g	17.c	$4$	$16$	$8$	$6.652$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{8}-\beta _{13})q^{2}+\beta _{9}q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots$
833.2.g.f	$833$	$2$	833.g	17.c	$4$	$16$	$8$	$6.652$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
833.2.g.g	$833$	$2$	833.g	17.c	$4$	$16$	$8$	$6.652$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
833.2.g.h	$833$	$2$	833.g	17.c	$4$	$20$	$10$	$6.652$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$4$	$8$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{14}q^{3}+(-2+\beta _{17}+\beta _{18}+\cdots)q^{4}+\cdots$
833.2.g.i	$833$	$2$	833.g	17.c	$4$	$32$	$16$	$6.652$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
833.2.j.a	$833$	$2$	833.j	119.j	$6$	$20$	$10$	$6.652$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{15}q^{2}-\beta _{1}q^{3}+(-1+\beta _{11}+\beta _{14}+\cdots)q^{4}+\cdots$
833.2.j.b	$833$	$2$	833.j	119.j	$6$	$20$	$10$	$6.652$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-\beta _{12}q^{2}+\beta _{1}q^{3}+(\beta _{3}+\beta _{6}+2\beta _{8}+\cdots)q^{4}+\cdots$
833.2.j.c	$833$	$2$	833.j	119.j	$6$	$20$	$10$	$6.652$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}+\beta _{3})q^{2}+\beta _{13}q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
833.2.j.d	$833$	$2$	833.j	119.j	$6$	$20$	$10$	$6.652$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}+\beta _{3})q^{2}-\beta _{13}q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
833.2.j.e	$833$	$2$	833.j	119.j	$6$	$32$	$16$	$6.652$		$_{}$	None	None		$8$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
833.2.k.a	$833$	$2$	833.k	49.e	$7$	$6$	$1$	$6.652$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$-3$	$5$	$-4$	$7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
833.2.k.b	$833$	$2$	833.k	49.e	$7$	$216$	$36$	$6.652$		$_{}$	None	None		$2$	$0$	$2$	$-2$	$-2$	$-4$			$\mathrm{SU}(2)[C_{7}]$
833.2.k.c	$833$	$2$	833.k	49.e	$7$	$234$	$39$	$6.652$		$_{}$	None	None		$2$	$0$	$1$	$-7$	$2$	$-13$			$\mathrm{SU}(2)[C_{7}]$
833.2.l.a	$833$	$2$	833.l	17.d	$8$	$4$	$1$	$6.652$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$-4$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
833.2.l.b	$833$	$2$	833.l	17.d	$8$	$32$	$8$	$6.652$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
833.2.l.c	$833$	$2$	833.l	17.d	$8$	$32$	$8$	$6.652$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$

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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.