Newform search results

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 281 matches)

 

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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
630.2.a.a	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.b	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.c	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.d	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.e	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.f	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.g	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
630.2.a.h	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
630.2.a.i	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
630.2.a.j	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
630.2.b.a	$630$	$2$	630.b	21.c	$2$	$8$	$8$	$5.031$	8.0.7442857984.4	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-4\)		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-q^{4}-q^{5}+\beta _{6}q^{7}-\beta _{3}q^{8}+\cdots\)
630.2.b.b	$630$	$2$	630.b	21.c	$2$	$8$	$8$	$5.031$	8.0.7442857984.4	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(-4\)		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-q^{4}+q^{5}+\beta _{6}q^{7}+\beta _{3}q^{8}+\cdots\)
630.2.d.a	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.d.b	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.c	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.d	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.g.a	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-2-i)q^{5}+iq^{7}+\cdots\)
630.2.g.b	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-1+2i)q^{5}-iq^{7}+\cdots\)
630.2.g.c	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots\)
630.2.g.d	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(1+2i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.e	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots\)
630.2.g.f	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(2-i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.g	$630$	$2$	630.g	5.b	$2$	$4$	$4$	$5.031$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
630.2.i.a	$630$	$2$	630.i	63.h	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-2\)	\(-3\)	\(-1\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.b	$630$	$2$	630.i	63.h	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-2\)	\(-3\)	\(1\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.c	$630$	$2$	630.i	63.h	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(3\)	\(-1\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.d	$630$	$2$	630.i	63.h	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(3\)	\(1\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.e	$630$	$2$	630.i	63.h	$3$	$4$	$2$	$5.031$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(4\)	\(-6\)	\(2\)	\(-2\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-2-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
630.2.i.f	$630$	$2$	630.i	63.h	$3$	$12$	$6$	$5.031$	12.0.\(\cdots\).1	None		$2$	$0$	\(-12\)	\(2\)	\(-6\)	\(4\)		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(\beta _{4}-\beta _{7})q^{3}+q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots\)
630.2.i.g	$630$	$2$	630.i	63.h	$3$	$12$	$6$	$5.031$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(12\)	\(0\)	\(-6\)	\(4\)		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}-\beta _{8}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
630.2.i.h	$630$	$2$	630.i	63.h	$3$	$12$	$6$	$5.031$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(12\)	\(2\)	\(6\)	\(8\)		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-\beta _{2}+\beta _{6})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
630.2.i.i	$630$	$2$	630.i	63.h	$3$	$16$	$8$	$5.031$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-16\)	\(2\)	\(8\)	\(4\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+(-\beta _{1}+\beta _{7})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
630.2.j.a	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.b	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-3\)	\(1\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.c	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-3\)	\(1\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.d	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.e	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(3\)	\(1\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.f	$630$	$2$	630.j	9.c	$3$	$4$	$2$	$5.031$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
630.2.j.g	$630$	$2$	630.j	9.c	$3$	$4$	$2$	$5.031$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(2\)	\(1\)	\(2\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots\)
630.2.j.h	$630$	$2$	630.j	9.c	$3$	$4$	$2$	$5.031$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(2\)	\(2\)	\(-2\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
630.2.j.i	$630$	$2$	630.j	9.c	$3$	$6$	$3$	$5.031$	6.0.954288.1	None		$2$	$0$	\(-3\)	\(-1\)	\(-3\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
630.2.j.j	$630$	$2$	630.j	9.c	$3$	$6$	$3$	$5.031$	6.0.954288.1	None		$2$	$0$	\(-3\)	\(-1\)	\(3\)	\(-3\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
630.2.j.k	$630$	$2$	630.j	9.c	$3$	$6$	$3$	$5.031$	6.0.954288.1	None		$2$	$0$	\(-3\)	\(1\)	\(-3\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+\beta _{3}q^{4}+\beta _{3}q^{5}+\cdots\)
630.2.j.l	$630$	$2$	630.j	9.c	$3$	$8$	$4$	$5.031$	8.0.856615824.2	None		$2$	$0$	\(-4\)	\(-3\)	\(4\)	\(4\)		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots\)
630.2.k.a	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
630.2.k.b	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
630.2.k.c	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
630.2.k.d	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(1\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
630.2.k.e	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
630.2.k.f	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)