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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 310 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
448.1.l.a	$448$	$1$	448.l	112.l	$4$	$2$	$1$	$0.224$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{7}-iq^{9}+(1+i)q^{11}+iq^{25}+\cdots$
448.1.r.a	$448$	$1$	448.r	28.g	$6$	$4$	$2$	$0.224$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots$
448.1.bf.a	$448$	$1$	448.bf	448.af	$16$	$8$	$1$	$0.224$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{5}q^{7}-\zeta_{16}^{3}q^{8}+\cdots$
448.2.a.a	$448$	$2$	448.a	1.a	$1$	$1$	$1$	$3.577$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots$
448.2.a.b	$448$	$2$	448.a	1.a	$1$	$1$	$1$	$3.577$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
448.2.a.c	$448$	$2$	448.a	1.a	$1$	$1$	$1$	$3.577$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{5}+q^{7}+q^{9}-8q^{15}+\cdots$
448.2.a.d	$448$	$2$	448.a	1.a	$1$	$1$	$1$	$3.577$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots$
448.2.a.e	$448$	$2$	448.a	1.a	$1$	$1$	$1$	$3.577$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots$
448.2.a.f	$448$	$2$	448.a	1.a	$1$	$1$	$1$	$3.577$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$
448.2.a.g	$448$	$2$	448.a	1.a	$1$	$1$	$1$	$3.577$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots$
448.2.a.h	$448$	$2$	448.a	1.a	$1$	$1$	$1$	$3.577$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots$
448.2.a.i	$448$	$2$	448.a	1.a	$1$	$2$	$2$	$3.577$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots$
448.2.a.j	$448$	$2$	448.a	1.a	$1$	$2$	$2$	$3.577$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots$
448.2.b.a	$448$	$2$	448.b	8.b	$2$	$2$	$2$	$3.577$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-2iq^{5}-q^{7}-q^{9}-iq^{11}+\cdots$
448.2.b.b	$448$	$2$	448.b	8.b	$2$	$2$	$2$	$3.577$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2iq^{5}+q^{7}-q^{9}-iq^{11}+\cdots$
448.2.b.c	$448$	$2$	448.b	8.b	$2$	$4$	$4$	$3.577$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}q^{3}-\zeta_{12}q^{5}-q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
448.2.b.d	$448$	$2$	448.b	8.b	$2$	$4$	$4$	$3.577$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}q^{3}+\zeta_{12}q^{5}+q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
448.2.e.a	$448$	$2$	448.e	56.e	$2$	$8$	$8$	$3.577$	8.0.629407744.1	$_{}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+(-3-\beta _{7})q^{9}+\cdots$
448.2.e.b	$448$	$2$	448.e	56.e	$2$	$8$	$8$	$3.577$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{24}^{2}q^{3}+\zeta_{24}^{6}q^{5}-\zeta_{24}^{4}q^{7}+\cdots$
448.2.f.a	$448$	$2$	448.f	28.d	$2$	$2$	$2$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-4$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots$
448.2.f.b	$448$	$2$	448.f	28.d	$2$	$2$	$2$	$3.577$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{7}-3q^{9}-2\beta q^{11}-2\beta q^{23}+\cdots$
448.2.f.c	$448$	$2$	448.f	28.d	$2$	$2$	$2$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{3}+2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots$
448.2.f.d	$448$	$2$	448.f	28.d	$2$	$8$	$8$	$3.577$	$\Q(\zeta_{16})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{4}q^{7}+\cdots$
448.2.i.a	$448$	$2$	448.i	7.c	$3$	$2$	$1$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-3$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
448.2.i.b	$448$	$2$	448.i	7.c	$3$	$2$	$1$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
448.2.i.c	$448$	$2$	448.i	7.c	$3$	$2$	$1$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
448.2.i.d	$448$	$2$	448.i	7.c	$3$	$2$	$1$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
448.2.i.e	$448$	$2$	448.i	7.c	$3$	$2$	$1$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
448.2.i.f	$448$	$2$	448.i	7.c	$3$	$2$	$1$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
448.2.i.g	$448$	$2$	448.i	7.c	$3$	$4$	$2$	$3.577$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+(2\beta _{1}-\beta _{2}+2\beta _{3})q^{5}+\cdots$
448.2.i.h	$448$	$2$	448.i	7.c	$3$	$4$	$2$	$3.577$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+3\beta _{2}q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$
448.2.i.i	$448$	$2$	448.i	7.c	$3$	$4$	$2$	$3.577$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1-\zeta_{12}^{2})q^{5}+\cdots$
448.2.i.j	$448$	$2$	448.i	7.c	$3$	$4$	$2$	$3.577$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+\cdots$
448.2.j.a	$448$	$2$	448.j	112.j	$4$	$4$	$2$	$3.577$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{2}q^{7}+3\beta _{1}q^{9}+(-2+2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
448.2.j.b	$448$	$2$	448.j	112.j	$4$	$4$	$2$	$3.577$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2})q^{7}-3\beta _{1}q^{9}+\cdots$
448.2.j.c	$448$	$2$	448.j	112.j	$4$	$4$	$2$	$3.577$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots$
448.2.j.d	$448$	$2$	448.j	112.j	$4$	$16$	$8$	$3.577$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{3}+\beta _{5}q^{5}+(-1+\beta _{13})q^{7}+\cdots$
448.2.m.a	$448$	$2$	448.m	16.e	$4$	$2$	$1$	$3.577$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2+2i)q^{5}+iq^{7}+3iq^{9}+(-1+\cdots)q^{11}+\cdots$
448.2.m.b	$448$	$2$	448.m	16.e	$4$	$2$	$1$	$3.577$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2-2i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots$
448.2.m.c	$448$	$2$	448.m	16.e	$4$	$8$	$4$	$3.577$	8.0.214798336.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{3}+\beta _{1}q^{5}+\beta _{5}q^{7}+(-\beta _{5}-\beta _{7})q^{9}+\cdots$
448.2.m.d	$448$	$2$	448.m	16.e	$4$	$12$	$6$	$3.577$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-4$	$4$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5})q^{5}-\beta _{3}q^{7}+\cdots$
448.2.p.a	$448$	$2$	448.p	28.f	$6$	$2$	$1$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-1$	$-3$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots$
448.2.p.b	$448$	$2$	448.p	28.f	$6$	$2$	$1$	$3.577$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
448.2.p.c	$448$	$2$	448.p	28.f	$6$	$4$	$2$	$3.577$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots$
448.2.p.d	$448$	$2$	448.p	28.f	$6$	$4$	$2$	$3.577$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1+\zeta_{12}^{2})q^{5}+\cdots$
448.2.p.e	$448$	$2$	448.p	28.f	$6$	$16$	$8$	$3.577$	16.0.$\cdots$.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{20}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{14}q^{3}+\beta _{13}q^{5}+\beta _{9}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots$
448.2.q.a	$448$	$2$	448.q	56.m	$6$	$8$	$4$	$3.577$	8.0.12960000.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}+\beta _{7})q^{3}+\beta _{6}q^{5}+(2\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots$
448.2.q.b	$448$	$2$	448.q	56.m	$6$	$12$	$6$	$3.577$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-6$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{3}+(\beta _{6}-\beta _{7})q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots$
448.2.q.c	$448$	$2$	448.q	56.m	$6$	$12$	$6$	$3.577$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$6$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{3}+(-\beta _{6}+\beta _{7})q^{5}+(-\beta _{4}+\beta _{10}+\cdots)q^{7}+\cdots$
448.2.t.a	$448$	$2$	448.t	56.p	$6$	$8$	$4$	$3.577$	8.0.49787136.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{3}+\beta _{6}q^{5}+(\beta _{5}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots$

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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.