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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 291 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
768.1.e.a	$768$	$1$	768.e	3.b	$2$	$1$	$1$	$0.383$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{9}+2q^{19}+q^{25}-q^{27}+\cdots$
768.1.e.b	$768$	$1$	768.e	3.b	$2$	$1$	$1$	$0.383$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{9}-2q^{19}+q^{25}+q^{27}+\cdots$
768.1.e.c	$768$	$1$	768.e	3.b	$2$	$2$	$2$	$0.383$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{3}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-q^{9}-iq^{11}+q^{25}+iq^{27}+\cdots$
768.1.i.a	$768$	$1$	768.i	48.i	$4$	$4$	$2$	$0.383$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{3}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
768.1.i.b	$768$	$1$	768.i	48.i	$4$	$4$	$2$	$0.383$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
768.2.a.a	$768$	$2$	768.a	1.a	$1$	$1$	$1$	$6.133$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+2q^{7}+q^{9}-4q^{13}+\cdots$
768.2.a.b	$768$	$2$	768.a	1.a	$1$	$1$	$1$	$6.133$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$
768.2.a.c	$768$	$2$	768.a	1.a	$1$	$1$	$1$	$6.133$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots$
768.2.a.d	$768$	$2$	768.a	1.a	$1$	$1$	$1$	$6.133$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-2q^{7}+q^{9}+4q^{13}+\cdots$
768.2.a.e	$768$	$2$	768.a	1.a	$1$	$1$	$1$	$6.133$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{13}+\cdots$
768.2.a.f	$768$	$2$	768.a	1.a	$1$	$1$	$1$	$6.133$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$
768.2.a.g	$768$	$2$	768.a	1.a	$1$	$1$	$1$	$6.133$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
768.2.a.h	$768$	$2$	768.a	1.a	$1$	$1$	$1$	$6.133$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{13}+\cdots$
768.2.a.i	$768$	$2$	768.a	1.a	$1$	$2$	$2$	$6.133$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-\beta q^{7}+q^{9}-4q^{11}+\cdots$
768.2.a.j	$768$	$2$	768.a	1.a	$1$	$2$	$2$	$6.133$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots$
768.2.a.k	$768$	$2$	768.a	1.a	$1$	$2$	$2$	$6.133$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots$
768.2.a.l	$768$	$2$	768.a	1.a	$1$	$2$	$2$	$6.133$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+4q^{11}+\cdots$
768.2.c.a	$768$	$2$	768.c	12.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta )q^{3}+2\beta q^{5}-2\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
768.2.c.b	$768$	$2$	768.c	12.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta )q^{3}+2\beta q^{5}-2\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
768.2.c.c	$768$	$2$	768.c	12.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-\beta )q^{3}+(-1+2\beta )q^{9}+6q^{11}+\cdots$
768.2.c.d	$768$	$2$	768.c	12.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(1+\beta )q^{3}+(-1+2\beta )q^{9}-6q^{11}+\cdots$
768.2.c.e	$768$	$2$	768.c	12.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta )q^{3}+2\beta q^{5}+2\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
768.2.c.f	$768$	$2$	768.c	12.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta )q^{3}+2\beta q^{5}+2\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
768.2.c.g	$768$	$2$	768.c	12.b	$2$	$4$	$4$	$6.133$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}-3q^{9}+\zeta_{12}^{3}q^{13}+\cdots$
768.2.c.h	$768$	$2$	768.c	12.b	$2$	$4$	$4$	$6.133$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\zeta_{8}^{2}q^{3}+(1+\zeta_{8}^{3})q^{9}+(\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
768.2.c.i	$768$	$2$	768.c	12.b	$2$	$4$	$4$	$6.133$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+3q^{9}+\cdots$
768.2.c.j	$768$	$2$	768.c	12.b	$2$	$4$	$4$	$6.133$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}-\beta _{1}q^{5}-\beta _{3}q^{7}+3q^{9}-2\beta _{2}q^{11}+\cdots$
768.2.d.a	$768$	$2$	768.d	8.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots$
768.2.d.b	$768$	$2$	768.d	8.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-2q^{7}-q^{9}-4iq^{11}-6iq^{13}+\cdots$
768.2.d.c	$768$	$2$	768.d	8.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+4iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots$
768.2.d.d	$768$	$2$	768.d	8.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2iq^{5}-q^{9}+4iq^{11}-2iq^{13}+\cdots$
768.2.d.e	$768$	$2$	768.d	8.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+2iq^{5}-q^{9}-4iq^{11}-2iq^{13}+\cdots$
768.2.d.f	$768$	$2$	768.d	8.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+4iq^{5}+2q^{7}-q^{9}+4iq^{11}+\cdots$
768.2.d.g	$768$	$2$	768.d	8.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+2q^{7}-q^{9}+4iq^{11}-6iq^{13}+\cdots$
768.2.d.h	$768$	$2$	768.d	8.b	$2$	$2$	$2$	$6.133$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+2iq^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots$
768.2.f.a	$768$	$2$	768.f	24.f	$2$	$4$	$4$	$6.133$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{8}^{2})q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}q^{7}+\cdots$
768.2.f.b	$768$	$2$	768.f	24.f	$2$	$4$	$4$	$6.133$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{3}+(-2-\beta _{1}+\beta _{3})q^{5}+\cdots$
768.2.f.c	$768$	$2$	768.f	24.f	$2$	$4$	$4$	$6.133$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{3}+(2+\beta _{1}-\beta _{3})q^{5}+\cdots$
768.2.f.d	$768$	$2$	768.f	24.f	$2$	$4$	$4$	$6.133$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{7}+3q^{9}+\zeta_{12}^{3}q^{13}+\cdots$
768.2.f.e	$768$	$2$	768.f	24.f	$2$	$4$	$4$	$6.133$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{3}+(-2-\beta _{1}+\beta _{3})q^{5}+\cdots$
768.2.f.f	$768$	$2$	768.f	24.f	$2$	$4$	$4$	$6.133$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}+(2+\beta _{1}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
768.2.f.g	$768$	$2$	768.f	24.f	$2$	$4$	$4$	$6.133$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{8}^{2})q^{3}-\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+(-1+\cdots)q^{9}+\cdots$
768.2.j.a	$768$	$2$	768.j	16.e	$4$	$4$	$2$	$6.133$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$1$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}q^{3}+(-2+2\zeta_{8}^{2})q^{5}+(3\zeta_{8}+3\zeta_{8}^{3})q^{7}+\cdots$
768.2.j.b	$768$	$2$	768.j	16.e	$4$	$4$	$2$	$6.133$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{3}q^{3}+(\zeta_{8}+\zeta_{8}^{3})q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
768.2.j.c	$768$	$2$	768.j	16.e	$4$	$4$	$2$	$6.133$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{3}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
768.2.j.d	$768$	$2$	768.j	16.e	$4$	$4$	$2$	$6.133$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}+(2-2\zeta_{8}^{2})q^{5}+(3\zeta_{8}+3\zeta_{8}^{3})q^{7}+\cdots$
768.2.j.e	$768$	$2$	768.j	16.e	$4$	$8$	$4$	$6.133$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{24}q^{3}+(-1+\zeta_{24}^{2}-\zeta_{24}^{6})q^{5}+\cdots$
768.2.j.f	$768$	$2$	768.j	16.e	$4$	$8$	$4$	$6.133$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{24}q^{3}+(1-\zeta_{24}^{2}+\zeta_{24}^{6})q^{5}+\cdots$
768.2.k.a	$768$	$2$	768.k	48.k	$4$	$4$	$2$	$6.133$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$1$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{5}+\cdots$
768.2.k.b	$768$	$2$	768.k	48.k	$4$	$4$	$2$	$6.133$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{5}+\cdots$

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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.