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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 119 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4608.2.a.a	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}+(-2-\beta )q^{7}+2q^{11}+\cdots$
4608.2.a.b	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}-\beta q^{7}+(-2+2\beta )q^{11}+\cdots$
4608.2.a.c	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2\beta q^{7}+3\beta q^{11}+6q^{13}+\cdots$
4608.2.a.d	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}+\beta q^{7}+(2-2\beta )q^{11}+\cdots$
4608.2.a.e	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}+(2+\beta )q^{7}-2q^{11}+\cdots$
4608.2.a.f	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}-4q^{7}-\beta q^{11}+2\beta q^{13}+\cdots$
4608.2.a.g	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-3\beta q^{7}-6q^{11}-4\beta q^{13}+\cdots$
4608.2.a.h	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-\beta q^{7}-2q^{11}-2q^{17}+4q^{19}+\cdots$
4608.2.a.i	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(-2+3\beta )q^{11}+4\beta q^{17}+(6-\beta )q^{19}+\cdots$
4608.2.a.j	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+\beta q^{7}+2q^{11}-2q^{17}-4q^{19}+\cdots$
4608.2.a.k	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-2}) $	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(2-3\beta )q^{11}+4\beta q^{17}+(-6+\beta )q^{19}+\cdots$
4608.2.a.l	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+3\beta q^{7}+6q^{11}-4\beta q^{13}+\cdots$
4608.2.a.m	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}+4q^{7}+\beta q^{11}+2\beta q^{13}+\cdots$
4608.2.a.n	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(-2+\beta )q^{7}-2q^{11}+\cdots$
4608.2.a.o	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}-\beta q^{7}+(-2-2\beta )q^{11}+\cdots$
4608.2.a.p	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2\beta q^{7}-3\beta q^{11}-6q^{13}+\cdots$
4608.2.a.q	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+\beta q^{7}+(2+2\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
4608.2.a.r	$4608$	$2$	4608.a	1.a	$1$	$2$	$2$	$36.795$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(2-\beta )q^{7}+2q^{11}+2\beta q^{13}+\cdots$
4608.2.a.s	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	$\Q(\zeta_{24})^+$	$\Q(\sqrt{-6}) $	✓	$4$	$1$	$0$	$0$	$-8$	$0$	$+$	$2^{2}$	$N(\mathrm{U}(1))$	$q+(-2-\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}-\beta _{3}q^{11}+\cdots$
4608.2.a.t	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	4.4.4352.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-\beta _{3}q^{7}+(-2-\beta _{2})q^{11}+\cdots$
4608.2.a.u	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	$\Q(\zeta_{24})^+$	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-\beta _{1}q^{7}-2q^{11}-\beta _{2}q^{13}+\cdots$
4608.2.a.v	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	$\Q(\zeta_{24})^+$	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-2\beta _{2}q^{13}+\cdots$
4608.2.a.w	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	$\Q(\zeta_{24})^+$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{11}+\beta _{2}q^{13}+\cdots$
4608.2.a.x	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{3}q^{11}-\beta _{3}q^{13}+\cdots$
4608.2.a.y	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}-\beta _{3}q^{13}+\cdots$
4608.2.a.z	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	$\Q(\zeta_{24})^+$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}+2\beta _{2}q^{13}+\cdots$
4608.2.a.ba	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	4.4.4352.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+\beta _{3}q^{7}+(2+\beta _{2})q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
4608.2.a.bb	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	$\Q(\zeta_{24})^+$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{11}-\beta _{2}q^{13}+\cdots$
4608.2.a.bc	$4608$	$2$	4608.a	1.a	$1$	$4$	$4$	$36.795$	$\Q(\zeta_{24})^+$	$\Q(\sqrt{-6}) $	✓	$4$	$0$	$0$	$0$	$8$	$0$	$-$	$2^{2}$	$N(\mathrm{U}(1))$	$q+(2+\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\beta _{3}q^{11}+\cdots$
4608.2.c.a	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3\beta q^{7}-4q^{11}-6q^{13}+3\beta q^{17}+\cdots$
4608.2.c.b	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3\beta q^{7}-4q^{11}+6q^{13}+3\beta q^{17}+\cdots$
4608.2.c.c	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+\beta q^{7}-2q^{13}-\beta q^{17}-2\beta q^{19}+\cdots$
4608.2.c.d	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}-\beta q^{7}-2q^{13}-\beta q^{17}+2\beta q^{19}+\cdots$
4608.2.c.e	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}-\beta q^{7}+2q^{13}+\beta q^{17}-2\beta q^{19}+\cdots$
4608.2.c.f	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+\beta q^{7}+2q^{13}+\beta q^{17}+2\beta q^{19}+\cdots$
4608.2.c.g	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3\beta q^{7}+4q^{11}-6q^{13}-3\beta q^{17}+\cdots$
4608.2.c.h	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3\beta q^{7}+4q^{11}+6q^{13}-3\beta q^{17}+\cdots$
4608.2.c.i	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots$
4608.2.c.j	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots$
4608.2.c.k	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}+3\zeta_{8}^{2}q^{17}+\cdots$
4608.2.c.l	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{5}-3\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}-2\zeta_{8}^{3}q^{13}+\cdots$
4608.2.c.m	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}-2\zeta_{8}^{3}q^{13}+\cdots$
4608.2.c.n	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+3\zeta_{8}^{2}q^{17}+\cdots$
4608.2.c.o	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+\cdots$
4608.2.c.p	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+\cdots$
4608.2.c.q	$4608$	$2$	4608.c	12.b	$2$	$8$	$8$	$36.795$	$\Q(\zeta_{16})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{16}^{2}q^{5}+(-\zeta_{16}-\zeta_{16}^{3})q^{7}-\zeta_{16}^{5}q^{11}+\cdots$
4608.2.c.r	$4608$	$2$	4608.c	12.b	$2$	$8$	$8$	$36.795$	$\Q(\zeta_{16})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{16}^{2}q^{5}+(-\zeta_{16}-\zeta_{16}^{3})q^{7}-\zeta_{16}^{5}q^{11}+\cdots$
4608.2.d.a	$4608$	$2$	4608.d	8.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}-4q^{7}+\beta q^{11}-2\beta q^{13}+\cdots$
4608.2.d.b	$4608$	$2$	4608.d	8.b	$2$	$2$	$2$	$36.795$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+4q^{7}-\beta q^{11}-2\beta q^{13}+\cdots$
4608.2.d.c	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-2-\zeta_{8}^{3})q^{7}+\zeta_{8}q^{11}+\cdots$

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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.