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 69 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
1701.1.d.a	$1701$	$1$	1701.d	7.b	$2$	$2$	$2$	$0.849$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1701.1.d.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-q^{4}-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+q^{16}+\cdots$
1701.1.j.a	$1701$	$1$	1701.j	63.j	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.q.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}^{2}q^{13}+q^{16}+\cdots$
1701.1.j.b	$1701$	$1$	1701.j	63.j	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.q.b	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+q^{4}+q^{7}+\zeta_{6}^{2}q^{13}+q^{16}-\zeta_{6}^{2}q^{19}+\cdots$
1701.1.j.c	$1701$	$1$	1701.j	63.j	$6$	$4$	$2$	$0.849$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓		1701.1.q.c	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\beta _{3}q^{2}-q^{4}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
1701.1.k.a	$1701$	$1$	1701.k	63.k	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.m.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{6}q^{4}-q^{7}+(1+\zeta_{6})q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
1701.1.k.b	$1701$	$1$	1701.k	63.k	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.m.b	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{16}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
1701.1.l.a	$1701$	$1$	1701.l	63.l	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.d.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{6}^{2}q^{4}-q^{7}+(-1-\zeta_{6})q^{13}-\zeta_{6}q^{16}+\cdots$
1701.1.l.b	$1701$	$1$	1701.l	63.l	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.d.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}+(1+\zeta_{6})q^{13}+\cdots$
1701.1.m.a	$1701$	$1$	1701.m	7.d	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.m.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{13}+\cdots$
1701.1.m.b	$1701$	$1$	1701.m	7.d	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.m.b	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-\zeta_{6}q^{16}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
1701.1.n.a	$1701$	$1$	1701.n	63.n	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.q.b	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}-\zeta_{6}q^{13}-\zeta_{6}q^{16}+\cdots$
1701.1.n.b	$1701$	$1$	1701.n	63.n	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.q.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{6}^{2}q^{4}+q^{7}+\zeta_{6}q^{13}-\zeta_{6}q^{16}+\cdots$
1701.1.n.c	$1701$	$1$	1701.n	63.n	$6$	$4$	$2$	$0.849$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓		1701.1.q.c	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
1701.1.q.a	$1701$	$1$	1701.q	21.h	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.q.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}q^{4}-\zeta_{6}q^{7}-q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
1701.1.q.b	$1701$	$1$	1701.q	21.h	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.q.b	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{7}+q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
1701.1.q.c	$1701$	$1$	1701.q	21.h	$6$	$4$	$2$	$0.849$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓		1701.1.q.c	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}+\beta _{2}q^{7}+\cdots$
1701.1.t.a	$1701$	$1$	1701.t	63.t	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.m.b	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{4}-q^{7}+q^{16}+(1-\zeta_{6}^{2})q^{19}+\cdots$
1701.1.t.b	$1701$	$1$	1701.t	63.t	$6$	$2$	$1$	$0.849$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1701.1.m.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-q^{4}+\zeta_{6}q^{7}+(-1+\zeta_{6}^{2})q^{13}+q^{16}+\cdots$
1701.2.a.a	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.a	$1$	$2$	$-2$	$0$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots$
1701.2.a.b	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.b	$1$	$1$	$-2$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{5}-q^{7}-4q^{10}+\cdots$
1701.2.a.c	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.c	$1$	$1$	$-1$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}-q^{7}+3q^{8}+2q^{10}+\cdots$
1701.2.a.d	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.d	$1$	$1$	$-1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots$
1701.2.a.e	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.e	$1$	$0$	$-1$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots$
1701.2.a.f	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.e	$1$	$0$	$1$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots$
1701.2.a.g	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.d	$1$	$1$	$1$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots$
1701.2.a.h	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.c	$1$	$1$	$1$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots$
1701.2.a.i	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.b	$1$	$1$	$2$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-2q^{5}-q^{7}-4q^{10}+\cdots$
1701.2.a.j	$1701$	$2$	1701.a	1.a	$1$	$1$	$1$	$13.583$	$\Q$	$_{}$	None	None	✓	✓			1701.2.a.a	$1$	$0$	$2$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+4q^{5}-q^{7}+8q^{10}+\cdots$
1701.2.a.k	$1701$	$2$	1701.a	1.a	$1$	$2$	$2$	$13.583$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			1701.2.a.k	$2$	$1$	$0$	$0$	$0$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{4}+\beta q^{5}+q^{7}-\beta q^{11}-q^{13}+\cdots$
1701.2.a.l	$1701$	$2$	1701.a	1.a	$1$	$2$	$2$	$13.583$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			1701.2.a.l	$2$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}+q^{7}-\beta q^{8}-3q^{10}+\cdots$
1701.2.a.m	$1701$	$2$	1701.a	1.a	$1$	$2$	$2$	$13.583$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			1701.2.a.m	$2$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+q^{7}-\beta q^{8}-3\beta q^{11}+\cdots$
1701.2.a.n	$1701$	$2$	1701.a	1.a	$1$	$3$	$3$	$13.583$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓			1701.2.a.n	$1$	$0$	$0$	$0$	$-3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{2})q^{5}-q^{7}+\cdots$
1701.2.a.o	$1701$	$2$	1701.a	1.a	$1$	$3$	$3$	$13.583$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓			1701.2.a.n	$1$	$1$	$0$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{2})q^{5}-q^{7}+\cdots$
1701.2.a.p	$1701$	$2$	1701.a	1.a	$1$	$4$	$4$	$13.583$	4.4.27648.1	$_{}$	None	None	✓	✓			1701.2.a.p	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
1701.2.a.q	$1701$	$2$	1701.a	1.a	$1$	$4$	$4$	$13.583$	4.4.27648.1	$_{}$	None	None	✓	✓			1701.2.a.q	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+q^{7}+\cdots$
1701.2.a.r	$1701$	$2$	1701.a	1.a	$1$	$4$	$4$	$13.583$	$\Q(\sqrt{6}, \sqrt{10})$	$_{}$	None	None	✓	✓			1701.2.a.r	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(2-\beta _{2})q^{4}+\beta _{1}q^{5}-q^{7}+\cdots$
1701.2.a.s	$1701$	$2$	1701.a	1.a	$1$	$4$	$4$	$13.583$	4.4.29952.1	$_{}$	None	None	✓	✓			1701.2.a.s	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}-q^{7}+\cdots$
1701.2.a.t	$1701$	$2$	1701.a	1.a	$1$	$4$	$4$	$13.583$	4.4.13068.1	$_{}$	None	None	✓	✓			1701.2.a.t	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}+q^{7}+\cdots$
1701.2.a.u	$1701$	$2$	1701.a	1.a	$1$	$6$	$6$	$13.583$	6.6.7328637.1	$_{}$	None	None	✓	✓	✓		1701.2.a.u	$1$	$1$	$-3$	$0$	$-3$	$-6$	$+$	$3$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{2}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots$
1701.2.a.v	$1701$	$2$	1701.a	1.a	$1$	$6$	$6$	$13.583$	6.6.7328637.1	$_{}$	None	None	✓	✓	✓		1701.2.a.u	$1$	$0$	$3$	$0$	$3$	$-6$	$-$	$3$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{2}+(2+\beta _{3}-\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots$
1701.2.a.w	$1701$	$2$	1701.a	1.a	$1$	$9$	$9$	$13.583$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓		1701.2.a.w	$1$	$1$	$-3$	$0$	$-12$	$9$	$+$	$3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(1-\beta _{1}-\beta _{8})q^{4}+(-1+\beta _{8})q^{5}+\cdots$
1701.2.a.x	$1701$	$2$	1701.a	1.a	$1$	$9$	$9$	$13.583$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓		1701.2.a.w	$1$	$0$	$3$	$0$	$12$	$9$	$-$	$3^{2}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(1-\beta _{1}-\beta _{8})q^{4}+(1-\beta _{8})q^{5}+\cdots$
1701.2.c.a	$1701$	$2$	1701.c	21.c	$2$	$2$	$2$	$13.583$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1701.2.c.a	$2$	$0$	$0$	$0$	$-6$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}-q^{4}-3 q^{5}+(-\beta+2)q^{7}+\cdots$
1701.2.c.b	$1701$	$2$	1701.c	21.c	$2$	$2$	$2$	$13.583$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1701.2.c.a	$2$	$0$	$0$	$0$	$6$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}-q^{4}+3 q^{5}+(\beta+2)q^{7}+\cdots$
1701.2.c.c	$1701$	$2$	1701.c	21.c	$2$	$2$	$2$	$13.583$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			1701.2.c.c	$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}+(-3+\zeta_{6})q^{7}+(4-8\zeta_{6})q^{13}+\cdots$
1701.2.c.d	$1701$	$2$	1701.c	21.c	$2$	$2$	$2$	$13.583$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			1701.2.c.d	$4$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2 q^{4}+(-\beta+2)q^{7}-\beta q^{13}+4 q^{16}+\cdots$
1701.2.c.e	$1701$	$2$	1701.c	21.c	$2$	$12$	$12$	$13.583$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1701.2.c.e	$4$	$0$	$0$	$0$	$0$	$-12$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-2-\beta _{5}+\beta _{6})q^{4}+\beta _{1}q^{5}+\cdots$
1701.2.c.f	$1701$	$2$	1701.c	21.c	$2$	$12$	$12$	$13.583$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1701.2.c.f	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+(-1+\beta _{3})q^{4}+\beta _{2}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
1701.2.c.g	$1701$	$2$	1701.c	21.c	$2$	$16$	$16$	$13.583$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1701.2.c.g	$4$	$0$	$0$	$0$	$0$	$2$		$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-1+\beta _{1})q^{4}-\beta _{10}q^{5}+\cdots$
1701.2.c.h	$1701$	$2$	1701.c	21.c	$2$	$48$	$48$	$13.583$		$_{}$	None	None		✓	✓		1701.2.c.h	$4$	$0$	$0$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{2}]$

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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.