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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 112 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
1024.1.c.a	$1024$	$1$	1024.c	4.b	$2$	$2$	$2$	$0.511$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}+q^{9}+\beta q^{13}+q^{25}+\beta q^{29}+\cdots$
1024.1.d.a	$1024$	$1$	1024.d	8.d	$2$	$2$	$2$	$0.511$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}-q^{9}-\beta q^{13}-q^{25}-\beta q^{29}+\cdots$
1024.1.f.a	$1024$	$1$	1024.f	16.f	$4$	$2$	$1$	$0.511$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-1-i)q^{3}+iq^{9}+(1-i)q^{11}+\cdots$
1024.1.f.b	$1024$	$1$	1024.f	16.f	$4$	$2$	$1$	$0.511$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{9}+q^{17}-iq^{25}+iq^{41}-q^{49}+\cdots$
1024.1.f.c	$1024$	$1$	1024.f	16.f	$4$	$2$	$1$	$0.511$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(1+i)q^{3}+iq^{9}+(-1+i)q^{11}+\cdots$
1024.2.a.a	$1024$	$2$	1024.a	1.a	$1$	$2$	$2$	$8.177$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+\beta q^{5}-4q^{7}+5q^{9}+2\beta q^{11}+\cdots$
1024.2.a.b	$1024$	$2$	1024.a	1.a	$1$	$2$	$2$	$8.177$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}-2q^{7}-q^{9}-\beta q^{11}+\cdots$
1024.2.a.c	$1024$	$2$	1024.a	1.a	$1$	$2$	$2$	$8.177$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{5}-3q^{9}-5\beta q^{13}-8q^{17}-3q^{25}+\cdots$
1024.2.a.d	$1024$	$2$	1024.a	1.a	$1$	$2$	$2$	$8.177$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+3\beta q^{5}-3q^{9}+\beta q^{13}+8q^{17}+13q^{25}+\cdots$
1024.2.a.e	$1024$	$2$	1024.a	1.a	$1$	$2$	$2$	$8.177$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{5}+2q^{7}-q^{9}-\beta q^{11}+\cdots$
1024.2.a.f	$1024$	$2$	1024.a	1.a	$1$	$2$	$2$	$8.177$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}-\beta q^{5}+4q^{7}+5q^{9}+2\beta q^{11}+\cdots$
1024.2.a.g	$1024$	$2$	1024.a	1.a	$1$	$4$	$4$	$8.177$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+\cdots$
1024.2.a.h	$1024$	$2$	1024.a	1.a	$1$	$4$	$4$	$8.177$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-8$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-2-\beta _{2})q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots$
1024.2.a.i	$1024$	$2$	1024.a	1.a	$1$	$4$	$4$	$8.177$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$8$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
1024.2.a.j	$1024$	$2$	1024.a	1.a	$1$	$4$	$4$	$8.177$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+\cdots$
1024.2.b.a	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{3}+\beta q^{5}-4q^{7}-5q^{9}-2\beta q^{11}+\cdots$
1024.2.b.b	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-\beta q^{5}-2q^{7}+q^{9}+\beta q^{11}+\cdots$
1024.2.b.c	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{5}+3q^{9}-5\beta q^{13}-8q^{17}+3q^{25}+\cdots$
1024.2.b.d	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3\beta q^{5}+3q^{9}+\beta q^{13}+8q^{17}-13q^{25}+\cdots$
1024.2.b.e	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+\beta q^{5}+2q^{7}+q^{9}+\beta q^{11}+\cdots$
1024.2.b.f	$1024$	$2$	1024.b	8.b	$2$	$2$	$2$	$8.177$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{3}-\beta q^{5}+4q^{7}-5q^{9}-2\beta q^{11}+\cdots$
1024.2.b.g	$1024$	$2$	1024.b	8.b	$2$	$8$	$8$	$8.177$	$\Q(\zeta_{16})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{16}^{2}q^{3}+\zeta_{16}q^{5}-\zeta_{16}^{3}q^{7}+(-1+\cdots)q^{9}+\cdots$
1024.2.b.h	$1024$	$2$	1024.b	8.b	$2$	$8$	$8$	$8.177$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{24}q^{3}+\zeta_{24}^{5}q^{5}+\zeta_{24}^{4}q^{7}+(-1+\cdots)q^{9}+\cdots$
1024.2.e.a	$1024$	$2$	1024.e	16.e	$4$	$2$	$1$	$8.177$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$1$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-2+2i)q^{3}-5iq^{9}+(2+2i)q^{11}+\cdots$
1024.2.e.b	$1024$	$2$	1024.e	16.e	$4$	$2$	$1$	$8.177$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{3}+(-2-2i)q^{5}-4iq^{7}+\cdots$
1024.2.e.c	$1024$	$2$	1024.e	16.e	$4$	$2$	$1$	$8.177$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{3}+(2+2i)q^{5}+4iq^{7}+\cdots$
1024.2.e.d	$1024$	$2$	1024.e	16.e	$4$	$2$	$1$	$8.177$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{3}+(-2-2i)q^{5}+4iq^{7}+\cdots$
1024.2.e.e	$1024$	$2$	1024.e	16.e	$4$	$2$	$1$	$8.177$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{3}+(2+2i)q^{5}-4iq^{7}+iq^{9}+\cdots$
1024.2.e.f	$1024$	$2$	1024.e	16.e	$4$	$2$	$1$	$8.177$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(2-2i)q^{3}-5iq^{9}+(-2-2i)q^{11}+\cdots$
1024.2.e.g	$1024$	$2$	1024.e	16.e	$4$	$4$	$2$	$8.177$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(-2\zeta_{8}+3\zeta_{8}^{2}+\cdots)q^{9}+\cdots$
1024.2.e.h	$1024$	$2$	1024.e	16.e	$4$	$4$	$2$	$8.177$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots$
1024.2.e.i	$1024$	$2$	1024.e	16.e	$4$	$4$	$2$	$8.177$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+4\zeta_{8}^{2}q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
1024.2.e.j	$1024$	$2$	1024.e	16.e	$4$	$4$	$2$	$8.177$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q-\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{9}-3\zeta_{8}^{3}q^{13}-2q^{17}+\cdots$
1024.2.e.k	$1024$	$2$	1024.e	16.e	$4$	$4$	$2$	$8.177$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{4}]$	$q+\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{9}-\zeta_{8}^{3}q^{13}+2q^{17}+\cdots$
1024.2.e.l	$1024$	$2$	1024.e	16.e	$4$	$4$	$2$	$8.177$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}-3\zeta_{8}^{3}q^{11}+6q^{17}+\cdots$
1024.2.e.m	$1024$	$2$	1024.e	16.e	$4$	$4$	$2$	$8.177$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}-4\zeta_{8}^{2}q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
1024.2.e.n	$1024$	$2$	1024.e	16.e	$4$	$4$	$2$	$8.177$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots$
1024.2.e.o	$1024$	$2$	1024.e	16.e	$4$	$4$	$2$	$8.177$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}+(2\zeta_{8}+3\zeta_{8}^{2}+\cdots)q^{9}+\cdots$
1024.2.e.p	$1024$	$2$	1024.e	16.e	$4$	$8$	$4$	$8.177$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{24}^{7}q^{3}+\zeta_{24}q^{5}-\zeta_{24}^{6}q^{7}-3\zeta_{24}^{2}q^{9}+\cdots$
1024.2.g.a	$1024$	$2$	1024.g	32.g	$8$	$16$	$4$	$8.177$	$\Q(\zeta_{48})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{48}^{15}q^{3}+(-1+\zeta_{48}^{3}-\zeta_{48}^{8}+\cdots)q^{5}+\cdots$
1024.2.g.b	$1024$	$2$	1024.g	32.g	$8$	$16$	$4$	$8.177$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{2}q^{3}+(\beta _{3}+\beta _{10})q^{5}+(-\beta _{4}-\beta _{9}+\cdots)q^{7}+\cdots$
1024.2.g.c	$1024$	$2$	1024.g	32.g	$8$	$16$	$4$	$8.177$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{13}q^{3}+(-1-\beta _{3}+\beta _{5}+\beta _{8})q^{5}+\cdots$
1024.2.g.d	$1024$	$2$	1024.g	32.g	$8$	$16$	$4$	$8.177$	$\Q(\zeta_{48})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	$q+(\zeta_{48}^{11}+\zeta_{48}^{14})q^{3}+(-\zeta_{48}-\zeta_{48}^{2}+\cdots)q^{5}+\cdots$
1024.2.g.e	$1024$	$2$	1024.g	32.g	$8$	$16$	$4$	$8.177$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{2}q^{3}+(-\beta _{3}-\beta _{10})q^{5}+(\beta _{4}+\beta _{9}+\cdots)q^{7}+\cdots$
1024.2.g.f	$1024$	$2$	1024.g	32.g	$8$	$16$	$4$	$8.177$	$\Q(\zeta_{48})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{48}^{15}q^{3}+(1+\zeta_{48}^{8}+\zeta_{48}^{13}+\cdots)q^{5}+\cdots$
1024.2.g.g	$1024$	$2$	1024.g	32.g	$8$	$16$	$4$	$8.177$	$\Q(\zeta_{48})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	$q+(\zeta_{48}^{11}+\zeta_{48}^{14})q^{3}+(\zeta_{48}+\zeta_{48}^{2}+\cdots)q^{5}+\cdots$
1024.2.g.h	$1024$	$2$	1024.g	32.g	$8$	$16$	$4$	$8.177$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{13}q^{3}+(1+\beta _{3}-\beta _{5}-\beta _{8})q^{5}+\cdots$
1024.3.c.a	$1024$	$3$	1024.c	4.b	$2$	$2$	$2$	$27.902$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-7\beta q^{5}+9q^{9}-17\beta q^{13}-2^{4}q^{17}+\cdots$
1024.3.c.b	$1024$	$3$	1024.c	4.b	$2$	$2$	$2$	$27.902$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}+9q^{9}+7\beta q^{13}+2^{4}q^{17}+\cdots$
1024.3.c.c	$1024$	$3$	1024.c	4.b	$2$	$4$	$4$	$27.902$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-5\beta _{1}q^{5}-\beta _{3}q^{7}-15q^{9}+\cdots$

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