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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 172 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
405.1.h.a	$405$	$1$	405.h	45.h	$6$	$2$	$1$	$0.202$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{5}-q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots$
405.1.h.b	$405$	$1$	405.h	45.h	$6$	$2$	$1$	$0.202$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{5}+q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots$
405.2.a.a	$405$	$2$	405.a	1.a	$1$	$1$	$1$	$3.234$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+2q^{10}-5q^{11}+\cdots$
405.2.a.b	$405$	$2$	405.a	1.a	$1$	$1$	$1$	$3.234$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-3q^{7}+3q^{8}-q^{10}+\cdots$
405.2.a.c	$405$	$2$	405.a	1.a	$1$	$1$	$1$	$3.234$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}+2q^{7}-3q^{11}-4q^{13}+\cdots$
405.2.a.d	$405$	$2$	405.a	1.a	$1$	$1$	$1$	$3.234$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}+2q^{7}+3q^{11}-4q^{13}+\cdots$
405.2.a.e	$405$	$2$	405.a	1.a	$1$	$1$	$1$	$3.234$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots$
405.2.a.f	$405$	$2$	405.a	1.a	$1$	$1$	$1$	$3.234$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}+2q^{10}+5q^{11}+\cdots$
405.2.a.g	$405$	$2$	405.a	1.a	$1$	$2$	$2$	$3.234$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{7}+\cdots$
405.2.a.h	$405$	$2$	405.a	1.a	$1$	$2$	$2$	$3.234$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots$
405.2.a.i	$405$	$2$	405.a	1.a	$1$	$3$	$3$	$3.234$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
405.2.a.j	$405$	$2$	405.a	1.a	$1$	$3$	$3$	$3.234$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
405.2.b.a	$405$	$2$	405.b	5.b	$2$	$4$	$4$	$3.234$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-2+\beta _{1}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
405.2.b.b	$405$	$2$	405.b	5.b	$2$	$4$	$4$	$3.234$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-2+\beta _{1}+\beta _{3})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
405.2.b.c	$405$	$2$	405.b	5.b	$2$	$4$	$4$	$3.234$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$
405.2.b.d	$405$	$2$	405.b	5.b	$2$	$4$	$4$	$3.234$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$
405.2.b.e	$405$	$2$	405.b	5.b	$2$	$4$	$4$	$3.234$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots$
405.2.e.a	$405$	$2$	405.e	9.c	$3$	$2$	$1$	$3.234$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-2$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
405.2.e.b	$405$	$2$	405.e	9.c	$3$	$2$	$1$	$3.234$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
405.2.e.c	$405$	$2$	405.e	9.c	$3$	$2$	$1$	$3.234$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}-3q^{8}+\cdots$
405.2.e.d	$405$	$2$	405.e	9.c	$3$	$2$	$1$	$3.234$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$
405.2.e.e	$405$	$2$	405.e	9.c	$3$	$2$	$1$	$3.234$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$
405.2.e.f	$405$	$2$	405.e	9.c	$3$	$2$	$1$	$3.234$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+3q^{8}+\cdots$
405.2.e.g	$405$	$2$	405.e	9.c	$3$	$2$	$1$	$3.234$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+2q^{10}+\cdots$
405.2.e.h	$405$	$2$	405.e	9.c	$3$	$2$	$1$	$3.234$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots$
405.2.e.i	$405$	$2$	405.e	9.c	$3$	$4$	$2$	$3.234$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$2$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots$
405.2.e.j	$405$	$2$	405.e	9.c	$3$	$4$	$2$	$3.234$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$-1$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
405.2.e.k	$405$	$2$	405.e	9.c	$3$	$4$	$2$	$3.234$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$1$	$0$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
405.2.e.l	$405$	$2$	405.e	9.c	$3$	$4$	$2$	$3.234$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$-2$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
405.2.f.a	$405$	$2$	405.f	15.e	$4$	$16$	$8$	$3.234$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}+(\beta _{6}-\beta _{14})q^{4}-\beta _{4}q^{5}+\beta _{10}q^{7}+\cdots$
405.2.f.b	$405$	$2$	405.f	15.e	$4$	$24$	$12$	$3.234$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
405.2.j.a	$405$	$2$	405.j	45.j	$6$	$4$	$2$	$3.234$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$1$	$-3$	$0$	$-6$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots$
405.2.j.b	$405$	$2$	405.j	45.j	$6$	$4$	$2$	$3.234$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$-3$	$0$	$-3$	$12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots$
405.2.j.c	$405$	$2$	405.j	45.j	$6$	$4$	$2$	$3.234$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\beta _{3}q^{8}+\cdots$
405.2.j.d	$405$	$2$	405.j	45.j	$6$	$4$	$2$	$3.234$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$3$	$0$	$3$	$12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
405.2.j.e	$405$	$2$	405.j	45.j	$6$	$4$	$2$	$3.234$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$3$	$0$	$6$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
405.2.j.f	$405$	$2$	405.j	45.j	$6$	$8$	$4$	$3.234$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{24}^{6}q^{2}-\zeta_{24}^{4}q^{5}-\zeta_{24}q^{7}+(2\zeta_{24}^{5}+\cdots)q^{8}+\cdots$
405.2.j.g	$405$	$2$	405.j	45.j	$6$	$8$	$4$	$3.234$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{24}^{5}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{3})q^{5}+\zeta_{24}^{6}q^{7}+\cdots$
405.2.j.h	$405$	$2$	405.j	45.j	$6$	$8$	$4$	$3.234$	8.0.12960000.1	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{4}$	$\mathrm{U}(1)[D_{6}]$	$q-\beta _{1}q^{2}+(2-\beta _{3}+2\beta _{5}+\beta _{6})q^{4}+\cdots$
405.2.k.a	$405$	$2$	405.k	27.e	$9$	$30$	$5$	$3.234$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
405.2.k.b	$405$	$2$	405.k	27.e	$9$	$42$	$7$	$3.234$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
405.2.m.a	$405$	$2$	405.m	45.l	$12$	$8$	$2$	$3.234$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
405.2.m.b	$405$	$2$	405.m	45.l	$12$	$16$	$4$	$3.234$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$-8$		$3^{4}$	$\mathrm{SU}(2)[C_{12}]$	$q+(\beta _{9}-\beta _{10})q^{2}+(-2\beta _{1}-\beta _{13}-\beta _{14}+\cdots)q^{4}+\cdots$
405.2.m.c	$405$	$2$	405.m	45.l	$12$	$16$	$4$	$3.234$	16.0.$\cdots$.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$4$		$3^{4}$	$\mathrm{SU}(2)[C_{12}]$	$q-\beta _{10}q^{2}+(-\beta _{9}-\beta _{15})q^{4}+(-\beta _{7}+\cdots)q^{5}+\cdots$
405.2.m.d	$405$	$2$	405.m	45.l	$12$	$24$	$6$	$3.234$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{12}]$
405.2.m.e	$405$	$2$	405.m	45.l	$12$	$24$	$6$	$3.234$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{12}]$
405.2.p.a	$405$	$2$	405.p	135.p	$18$	$96$	$16$	$3.234$		$_{}$	None	None		$4$	$0$	$0$	$0$	$9$	$0$			$\mathrm{SU}(2)[C_{18}]$
405.2.q.a	$405$	$2$	405.q	81.g	$27$	$306$	$17$	$3.234$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{27}]$
405.2.q.b	$405$	$2$	405.q	81.g	$27$	$342$	$19$	$3.234$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{27}]$
405.2.r.a	$405$	$2$	405.r	135.q	$36$	$192$	$16$	$3.234$		$_{}$	None	None		$4$	$0$	$12$	$0$	$12$	$-12$			$\mathrm{SU}(2)[C_{36}]$

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