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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 390 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
576.1.b.a	$576$	$1$	576.b	8.d	$2$	$2$	$2$	$0.287$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{2}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-iq^{7}+q^{25}+iq^{31}-3q^{49}-q^{73}+\cdots$
576.1.e.a	$576$	$1$	576.e	3.b	$2$	$2$	$2$	$0.287$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}-\beta q^{17}-q^{25}+\beta q^{29}+2q^{37}+\cdots$
576.1.g.a	$576$	$1$	576.g	4.b	$2$	$1$	$1$	$0.287$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+2q^{13}-q^{25}-2q^{37}+q^{49}-2q^{61}+\cdots$
576.1.n.a	$576$	$1$	576.n	72.j	$6$	$4$	$2$	$0.287$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{9}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{11}+\cdots$
576.1.o.a	$576$	$1$	576.o	36.f	$6$	$4$	$2$	$0.287$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-q^{9}+\cdots$
576.2.a.a	$576$	$2$	576.a	1.a	$1$	$1$	$1$	$4.599$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-4q^{5}+6q^{13}+8q^{17}+11q^{25}+\cdots$
576.2.a.b	$576$	$2$	576.a	1.a	$1$	$1$	$1$	$4.599$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots$
576.2.a.c	$576$	$2$	576.a	1.a	$1$	$1$	$1$	$4.599$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{5}-6q^{13}-2q^{17}-q^{25}-10q^{29}+\cdots$
576.2.a.d	$576$	$2$	576.a	1.a	$1$	$1$	$1$	$4.599$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots$
576.2.a.e	$576$	$2$	576.a	1.a	$1$	$1$	$1$	$4.599$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$N(\mathrm{U}(1))$	$q-4q^{7}-2q^{13}-8q^{19}-5q^{25}-4q^{31}+\cdots$
576.2.a.f	$576$	$2$	576.a	1.a	$1$	$1$	$1$	$4.599$	$\Q$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{7}-2q^{13}+8q^{19}-5q^{25}+4q^{31}+\cdots$
576.2.a.g	$576$	$2$	576.a	1.a	$1$	$1$	$1$	$4.599$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots$
576.2.a.h	$576$	$2$	576.a	1.a	$1$	$1$	$1$	$4.599$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots$
576.2.a.i	$576$	$2$	576.a	1.a	$1$	$1$	$1$	$4.599$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{5}+6q^{13}-8q^{17}+11q^{25}+\cdots$
576.2.c.a	$576$	$2$	576.c	12.b	$2$	$2$	$2$	$4.599$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}-4q^{13}+\beta q^{17}-13q^{25}+\cdots$
576.2.c.b	$576$	$2$	576.c	12.b	$2$	$2$	$2$	$4.599$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}+4q^{13}+5\beta q^{17}+3q^{25}+\cdots$
576.2.c.c	$576$	$2$	576.c	12.b	$2$	$4$	$4$	$4.599$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{11}-4q^{13}+\cdots$
576.2.d.a	$576$	$2$	576.d	8.b	$2$	$2$	$2$	$4.599$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+3iq^{11}+6q^{17}+iq^{19}+5q^{25}+\cdots$
576.2.d.b	$576$	$2$	576.d	8.b	$2$	$4$	$4$	$4.599$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-6q^{17}-\zeta_{12}^{3}q^{19}+\cdots$
576.2.d.c	$576$	$2$	576.d	8.b	$2$	$4$	$4$	$4.599$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{13}-\zeta_{12}^{3}q^{19}+\cdots$
576.2.f.a	$576$	$2$	576.f	24.f	$2$	$8$	$8$	$4.599$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{24}^{2}q^{5}-\zeta_{24}q^{7}-\zeta_{24}^{6}q^{11}+\cdots$
576.2.i.a	$576$	$2$	576.i	9.c	$3$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
576.2.i.b	$576$	$2$	576.i	9.c	$3$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$
576.2.i.c	$576$	$2$	576.i	9.c	$3$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots$
576.2.i.d	$576$	$2$	576.i	9.c	$3$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$
576.2.i.e	$576$	$2$	576.i	9.c	$3$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
576.2.i.f	$576$	$2$	576.i	9.c	$3$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
576.2.i.g	$576$	$2$	576.i	9.c	$3$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
576.2.i.h	$576$	$2$	576.i	9.c	$3$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$
576.2.i.i	$576$	$2$	576.i	9.c	$3$	$4$	$2$	$4.599$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
576.2.i.j	$576$	$2$	576.i	9.c	$3$	$4$	$2$	$4.599$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$
576.2.i.k	$576$	$2$	576.i	9.c	$3$	$4$	$2$	$4.599$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{12}^{3}q^{3}+(-1+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots$
576.2.i.l	$576$	$2$	576.i	9.c	$3$	$4$	$2$	$4.599$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$
576.2.i.m	$576$	$2$	576.i	9.c	$3$	$4$	$2$	$4.599$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
576.2.i.n	$576$	$2$	576.i	9.c	$3$	$8$	$4$	$4.599$	8.0.170772624.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}-\beta _{7})q^{5}+\cdots$
576.2.k.a	$576$	$2$	576.k	16.e	$4$	$2$	$1$	$4.599$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{5}+2iq^{7}+(1+i)q^{11}+(-1+\cdots)q^{13}+\cdots$
576.2.k.b	$576$	$2$	576.k	16.e	$4$	$8$	$4$	$4.599$	8.0.18939904.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{4}+\beta _{6})q^{5}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots$
576.2.k.c	$576$	$2$	576.k	16.e	$4$	$8$	$4$	$4.599$	8.0.629407744.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
576.2.l.a	$576$	$2$	576.l	48.k	$4$	$16$	$8$	$4.599$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{5}-\beta _{9}q^{7}+(\beta _{2}+\beta _{14})q^{11}+\cdots$
576.2.p.a	$576$	$2$	576.p	72.l	$6$	$16$	$8$	$4.599$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-6$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{12}q^{3}+(\beta _{3}-\beta _{4}-\beta _{7})q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots$
576.2.p.b	$576$	$2$	576.p	72.l	$6$	$16$	$8$	$4.599$	16.0.$\cdots$.3	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{3}+(\beta _{3}+\beta _{6})q^{5}+(-\beta _{14}-\beta _{15})q^{7}+\cdots$
576.2.p.c	$576$	$2$	576.p	72.l	$6$	$16$	$8$	$4.599$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$6$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{12}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{7})q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots$
576.2.r.a	$576$	$2$	576.r	72.n	$6$	$4$	$2$	$4.599$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$1$	$0$	$0$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
576.2.r.b	$576$	$2$	576.r	72.n	$6$	$4$	$2$	$4.599$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
576.2.r.c	$576$	$2$	576.r	72.n	$6$	$8$	$4$	$4.599$	$\Q(\zeta_{24})$	$_{}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{6}]$	$q+(-\zeta_{24}^{4}+\zeta_{24}^{6})q^{3}+(-1+\zeta_{24}+\cdots)q^{9}+\cdots$
576.2.r.d	$576$	$2$	576.r	72.n	$6$	$8$	$4$	$4.599$	8.0.12960000.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots$
576.2.r.e	$576$	$2$	576.r	72.n	$6$	$12$	$6$	$4.599$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-18$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{4}+\beta _{5})q^{3}+(-2-\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
576.2.r.f	$576$	$2$	576.r	72.n	$6$	$12$	$6$	$4.599$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$18$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{4}+\beta _{5})q^{3}+(2+\beta _{6})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
576.2.s.a	$576$	$2$	576.s	36.h	$6$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$6$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots$
576.2.s.b	$576$	$2$	576.s	36.h	$6$	$2$	$1$	$4.599$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-3$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$

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