LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 281 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
630.2.a.a	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓		✓	✓	210.2.a.e	$1$	$0$	$-1$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
630.2.a.b	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓		✓	✓	210.2.a.c	$1$	$1$	$-1$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
630.2.a.c	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓	✓	✓	✓	630.2.a.c	$1$	$0$	$-1$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
630.2.a.d	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓		✓	✓	70.2.a.a	$1$	$1$	$-1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
630.2.a.e	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓	✓	✓	✓	630.2.a.e	$1$	$0$	$-1$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
630.2.a.f	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓		✓	✓	210.2.a.d	$1$	$0$	$-1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
630.2.a.g	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓	✓	✓	✓	630.2.a.e	$1$	$0$	$1$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
630.2.a.h	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓		✓	✓	210.2.a.b	$1$	$0$	$1$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
630.2.a.i	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓		✓	✓	210.2.a.a	$1$	$0$	$1$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
630.2.a.j	$630$	$2$	630.a	1.a	$1$	$1$	$1$	$5.031$	$\Q$	None	✓	✓	✓	✓	630.2.a.c	$1$	$0$	$1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
630.2.b.a	$630$	$2$	630.b	21.c	$2$	$8$	$8$	$5.031$	8.0.7442857984.4	None		✓			630.2.b.a	$2$	$0$	$0$	$0$	$-8$	$-4$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-q^{4}-q^{5}+\beta _{6}q^{7}-\beta _{3}q^{8}+\cdots$
630.2.b.b	$630$	$2$	630.b	21.c	$2$	$8$	$8$	$5.031$	8.0.7442857984.4	None		✓			630.2.b.a	$2$	$0$	$0$	$0$	$8$	$-4$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-q^{4}+q^{5}+\beta _{6}q^{7}+\beta _{3}q^{8}+\cdots$
630.2.d.a	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		✓			630.2.d.a	$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$
630.2.d.b	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	$\Q(\sqrt{-2}, \sqrt{5})$	None		✓			630.2.d.b	$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$
630.2.d.c	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	$\Q(\sqrt{-2}, \sqrt{5})$	None		✓			630.2.d.b	$4$	$0$	$4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
630.2.d.d	$630$	$2$	630.d	105.g	$2$	$4$	$4$	$5.031$	$\Q(\sqrt{-2}, \sqrt{-5})$	None		✓			630.2.d.a	$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$
630.2.g.a	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	$\Q(\sqrt{-1}) $	None		✓			630.2.g.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(-i-2)q^{5}+i q^{7}+\cdots$
630.2.g.b	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	$\Q(\sqrt{-1}) $	None		✓			630.2.g.b	$2$	$1$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(2 i-1)q^{5}-i q^{7}+\cdots$
630.2.g.c	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	$\Q(\sqrt{-1}) $	None					210.2.g.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(-2 i-1)q^{5}+i q^{7}+\cdots$
630.2.g.d	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	$\Q(\sqrt{-1}) $	None					210.2.g.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(2 i+1)q^{5}-i q^{7}+\cdots$
630.2.g.e	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	$\Q(\sqrt{-1}) $	None		✓			630.2.g.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(2 i+1)q^{5}+i q^{7}+\cdots$
630.2.g.f	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	$\Q(\sqrt{-1}) $	None		✓			630.2.g.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(-i+2)q^{5}-i q^{7}+\cdots$
630.2.g.g	$630$	$2$	630.g	5.b	$2$	$4$	$4$	$5.031$	$\Q(i, \sqrt{6})$	None			✓		70.2.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots$
630.2.i.a	$630$	$2$	630.i	63.h	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None		✓			630.2.i.a	$2$	$1$	$-2$	$-3$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
630.2.i.b	$630$	$2$	630.i	63.h	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None		✓			630.2.i.b	$2$	$1$	$-2$	$-3$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots$
630.2.i.c	$630$	$2$	630.i	63.h	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None		✓			630.2.i.c	$2$	$0$	$2$	$3$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
630.2.i.d	$630$	$2$	630.i	63.h	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None		✓			630.2.i.d	$2$	$0$	$2$	$3$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots$
630.2.i.e	$630$	$2$	630.i	63.h	$3$	$4$	$2$	$5.031$	$\Q(\sqrt{2}, \sqrt{-3})$	None		✓			630.2.i.e	$2$	$0$	$4$	$-6$	$2$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-2-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
630.2.i.f	$630$	$2$	630.i	63.h	$3$	$12$	$6$	$5.031$	12.0.$\cdots$.1	None		✓			630.2.i.f	$2$	$0$	$-12$	$2$	$-6$	$4$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(\beta _{4}-\beta _{7})q^{3}+q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots$
630.2.i.g	$630$	$2$	630.i	63.h	$3$	$12$	$6$	$5.031$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			630.2.i.g	$2$	$0$	$12$	$0$	$-6$	$4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-\beta _{8}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots$
630.2.i.h	$630$	$2$	630.i	63.h	$3$	$12$	$6$	$5.031$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			630.2.i.h	$2$	$0$	$12$	$2$	$6$	$8$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-\beta _{2}+\beta _{6})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
630.2.i.i	$630$	$2$	630.i	63.h	$3$	$16$	$8$	$5.031$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		630.2.i.i	$2$	$0$	$-16$	$2$	$8$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-\beta _{1}+\beta _{7})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots$
630.2.j.a	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None		✓			630.2.j.a	$2$	$1$	$-1$	$0$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.b	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None		✓			630.2.j.b	$2$	$0$	$1$	$-3$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.c	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None		✓			630.2.j.c	$2$	$0$	$1$	$-3$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.d	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None		✓			630.2.j.d	$2$	$0$	$1$	$0$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.e	$630$	$2$	630.j	9.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None		✓			630.2.j.e	$2$	$0$	$1$	$3$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
630.2.j.f	$630$	$2$	630.j	9.c	$3$	$4$	$2$	$5.031$	$\Q(\zeta_{12})$	None		✓			630.2.j.f	$2$	$0$	$2$	$0$	$-2$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta_1 q^{2}+\beta_{2} q^{3}+(\beta_1-1)q^{4}+\cdots$
630.2.j.g	$630$	$2$	630.j	9.c	$3$	$4$	$2$	$5.031$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		✓			630.2.j.g	$2$	$0$	$2$	$1$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots$
630.2.j.h	$630$	$2$	630.j	9.c	$3$	$4$	$2$	$5.031$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			630.2.j.h	$2$	$0$	$2$	$2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
630.2.j.i	$630$	$2$	630.j	9.c	$3$	$6$	$3$	$5.031$	6.0.954288.1	None		✓			630.2.j.i	$2$	$0$	$-3$	$-1$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
630.2.j.j	$630$	$2$	630.j	9.c	$3$	$6$	$3$	$5.031$	6.0.954288.1	None		✓			630.2.j.j	$2$	$0$	$-3$	$-1$	$3$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
630.2.j.k	$630$	$2$	630.j	9.c	$3$	$6$	$3$	$5.031$	6.0.954288.1	None		✓			630.2.j.k	$2$	$0$	$-3$	$1$	$-3$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+\beta _{3}q^{4}+\beta _{3}q^{5}+\cdots$
630.2.j.l	$630$	$2$	630.j	9.c	$3$	$8$	$4$	$5.031$	8.0.856615824.2	None		✓	✓		630.2.j.l	$2$	$0$	$-4$	$-3$	$4$	$4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots$
630.2.k.a	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None					210.2.i.c	$2$	$0$	$-1$	$0$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
630.2.k.b	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None					70.2.e.c	$2$	$1$	$-1$	$0$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
630.2.k.c	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None					210.2.i.d	$2$	$0$	$-1$	$0$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
630.2.k.d	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None					70.2.e.d	$2$	$0$	$-1$	$0$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
630.2.k.e	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None					70.2.e.b	$2$	$0$	$1$	$0$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$
630.2.k.f	$630$	$2$	630.k	7.c	$3$	$2$	$1$	$5.031$	$\Q(\sqrt{-3}) $	None					70.2.e.a	$2$	$0$	$1$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$

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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.