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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 174 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
896.1.h.a	$896$	$1$	896.h	56.h	$2$	$2$	$2$	$0.447$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-14}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta q^{3}-\beta q^{5}-q^{7}+q^{9}+\beta q^{13}+\cdots$
896.1.h.b	$896$	$1$	896.h	56.h	$2$	$2$	$2$	$0.447$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-14}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta q^{3}-\beta q^{5}+q^{7}+q^{9}+\beta q^{13}+\cdots$
896.1.l.a	$896$	$1$	896.l	112.l	$4$	$2$	$1$	$0.447$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{7}+iq^{9}+(-1+i)q^{11}-iq^{25}+\cdots$
896.1.l.b	$896$	$1$	896.l	112.l	$4$	$2$	$1$	$0.447$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{7}+iq^{9}+(1-i)q^{11}-iq^{25}+\cdots$
896.1.v.a	$896$	$1$	896.v	224.v	$8$	$4$	$1$	$0.447$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{2})q^{11}+\cdots$
896.1.bm.a	$896$	$1$	896.bm	896.am	$32$	$16$	$1$	$0.447$	$\Q(\zeta_{32})$	$D_{32}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{13}q^{2}-\zeta_{32}^{10}q^{4}-\zeta_{32}^{9}q^{7}+\cdots$
896.2.a.a	$896$	$2$	896.a	1.a	$1$	$1$	$1$	$7.155$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}-2q^{11}+4q^{13}-2q^{17}+\cdots$
896.2.a.b	$896$	$2$	896.a	1.a	$1$	$1$	$1$	$7.155$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}+2q^{11}-4q^{13}-2q^{17}+\cdots$
896.2.a.c	$896$	$2$	896.a	1.a	$1$	$1$	$1$	$7.155$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}-2q^{11}-4q^{13}-2q^{17}+\cdots$
896.2.a.d	$896$	$2$	896.a	1.a	$1$	$1$	$1$	$7.155$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}+2q^{11}+4q^{13}-2q^{17}+\cdots$
896.2.a.e	$896$	$2$	896.a	1.a	$1$	$2$	$2$	$7.155$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+\cdots$
896.2.a.f	$896$	$2$	896.a	1.a	$1$	$2$	$2$	$7.155$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots$
896.2.a.g	$896$	$2$	896.a	1.a	$1$	$2$	$2$	$7.155$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots$
896.2.a.h	$896$	$2$	896.a	1.a	$1$	$2$	$2$	$7.155$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots$
896.2.a.i	$896$	$2$	896.a	1.a	$1$	$3$	$3$	$7.155$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}-q^{7}+\cdots$
896.2.a.j	$896$	$2$	896.a	1.a	$1$	$3$	$3$	$7.155$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+q^{7}+\cdots$
896.2.a.k	$896$	$2$	896.a	1.a	$1$	$3$	$3$	$7.155$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+q^{7}+\cdots$
896.2.a.l	$896$	$2$	896.a	1.a	$1$	$3$	$3$	$7.155$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(1-\beta _{1})q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots$
896.2.b.a	$896$	$2$	896.b	8.b	$2$	$2$	$2$	$7.155$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{5}-q^{7}-q^{9}-iq^{13}+\cdots$
896.2.b.b	$896$	$2$	896.b	8.b	$2$	$2$	$2$	$7.155$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-q^{7}+3q^{9}-\beta q^{11}+\beta q^{13}+\cdots$
896.2.b.c	$896$	$2$	896.b	8.b	$2$	$2$	$2$	$7.155$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{5}+q^{7}-q^{9}+iq^{13}+\cdots$
896.2.b.d	$896$	$2$	896.b	8.b	$2$	$2$	$2$	$7.155$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+q^{7}+3q^{9}+\beta q^{11}+\beta q^{13}+\cdots$
896.2.b.e	$896$	$2$	896.b	8.b	$2$	$4$	$4$	$7.155$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}-q^{7}+(-3+\beta _{3})q^{9}+\cdots$
896.2.b.f	$896$	$2$	896.b	8.b	$2$	$4$	$4$	$7.155$	4.0.2048.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(-1-\beta _{3})q^{9}+\cdots$
896.2.b.g	$896$	$2$	896.b	8.b	$2$	$4$	$4$	$7.155$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{1}q^{5}+q^{7}+(-3+\beta _{3})q^{9}+\cdots$
896.2.b.h	$896$	$2$	896.b	8.b	$2$	$4$	$4$	$7.155$	4.0.2048.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(-1-\beta _{3})q^{9}+\cdots$
896.2.e.a	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1-\zeta_{12}^{3})q^{5}+\cdots$
896.2.e.b	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1-\zeta_{12}^{3})q^{5}+\cdots$
896.2.e.c	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-2-\beta _{2})q^{7}+q^{9}+\cdots$
896.2.e.d	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(2+\beta _{2})q^{7}+q^{9}+\cdots$
896.2.e.e	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(1+\zeta_{12}^{3})q^{5}+\cdots$
896.2.e.f	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(1+\zeta_{12}^{3})q^{5}+\cdots$
896.2.e.g	$896$	$2$	896.e	56.e	$2$	$8$	$8$	$7.155$	8.0.2517630976.5	$_{}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots$
896.2.f.a	$896$	$2$	896.f	28.d	$2$	$8$	$8$	$7.155$	8.0.40960000.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+\beta _{1}q^{5}+(\beta _{4}+\beta _{7})q^{7}+\beta _{2}q^{9}+\cdots$
896.2.f.b	$896$	$2$	896.f	28.d	$2$	$8$	$8$	$7.155$	8.0.40960000.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}-\beta _{1}q^{5}+(-\beta _{4}-\beta _{7})q^{7}+\cdots$
896.2.f.c	$896$	$2$	896.f	28.d	$2$	$8$	$8$	$7.155$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$
896.2.f.d	$896$	$2$	896.f	28.d	$2$	$8$	$8$	$7.155$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{1}q^{5}+(\beta _{2}-\beta _{4}-\beta _{5})q^{7}+\cdots$
896.2.i.a	$896$	$2$	896.i	7.c	$3$	$8$	$4$	$7.155$	8.0.3010058496.1	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{3}+(-\beta _{5}+\beta _{6}+\beta _{7})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
896.2.i.b	$896$	$2$	896.i	7.c	$3$	$8$	$4$	$7.155$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{6})q^{3}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
896.2.i.c	$896$	$2$	896.i	7.c	$3$	$8$	$4$	$7.155$	8.0.3010058496.1	$_{}$	None	None		$2$	$0$	$0$	$-2$	$2$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{3}+(\beta _{5}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
896.2.i.d	$896$	$2$	896.i	7.c	$3$	$8$	$4$	$7.155$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{6})q^{3}+(1-\beta _{4}-\beta _{5}-\beta _{7})q^{5}+\cdots$
896.2.i.e	$896$	$2$	896.i	7.c	$3$	$8$	$4$	$7.155$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{6})q^{3}+(-1+\beta _{4}+\beta _{5}+\beta _{7})q^{5}+\cdots$
896.2.i.f	$896$	$2$	896.i	7.c	$3$	$8$	$4$	$7.155$	8.0.3010058496.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{3}+(-\beta _{5}+\beta _{6}+\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
896.2.i.g	$896$	$2$	896.i	7.c	$3$	$8$	$4$	$7.155$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{6})q^{3}+(1-\beta _{4}-\beta _{5}-\beta _{7})q^{5}+\cdots$
896.2.i.h	$896$	$2$	896.i	7.c	$3$	$8$	$4$	$7.155$	8.0.3010058496.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{3}+(\beta _{5}-\beta _{6}-\beta _{7})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
896.2.j.a	$896$	$2$	896.j	112.j	$4$	$4$	$2$	$7.155$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots$
896.2.j.b	$896$	$2$	896.j	112.j	$4$	$4$	$2$	$7.155$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}-3\beta _{1}q^{9}+\cdots$
896.2.j.c	$896$	$2$	896.j	112.j	$4$	$4$	$2$	$7.155$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{2}q^{7}+3\beta _{1}q^{9}+(-2+2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
896.2.j.d	$896$	$2$	896.j	112.j	$4$	$4$	$2$	$7.155$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{2}q^{7}+3\beta _{1}q^{9}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
896.2.j.e	$896$	$2$	896.j	112.j	$4$	$4$	$2$	$7.155$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{2}-\beta _{3})q^{5}+(1-\beta _{2})q^{7}-3\beta _{1}q^{9}+\cdots$

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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.