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 74 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
1218.2.a.a	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓	✓	✓	1218.2.a.a	$1$	$0$	$-1$	$-1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots$
1218.2.a.b	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓	✓	✓	1218.2.a.b	$1$	$0$	$-1$	$-1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots$
1218.2.a.c	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓	✓	✓	1218.2.a.c	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
1218.2.a.d	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓			1218.2.a.d	$1$	$0$	$1$	$-1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
1218.2.a.e	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓	✓	✓	1218.2.a.e	$1$	$1$	$1$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
1218.2.a.f	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓			1218.2.a.f	$1$	$0$	$1$	$-1$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots$
1218.2.a.g	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓			1218.2.a.g	$1$	$0$	$1$	$1$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots$
1218.2.a.h	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓			1218.2.a.h	$1$	$0$	$1$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
1218.2.a.i	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓			1218.2.a.i	$1$	$0$	$1$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
1218.2.a.j	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓			1218.2.a.j	$1$	$0$	$1$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
1218.2.a.k	$1218$	$2$	1218.a	1.a	$1$	$1$	$1$	$9.726$	$\Q$	None	✓	✓			1218.2.a.k	$1$	$0$	$1$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
1218.2.a.l	$1218$	$2$	1218.a	1.a	$1$	$2$	$2$	$9.726$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	1218.2.a.l	$1$	$1$	$-2$	$-2$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
1218.2.a.m	$1218$	$2$	1218.a	1.a	$1$	$2$	$2$	$9.726$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	1218.2.a.m	$1$	$1$	$2$	$-2$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots$
1218.2.a.n	$1218$	$2$	1218.a	1.a	$1$	$2$	$2$	$9.726$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	1218.2.a.n	$1$	$0$	$2$	$-2$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
1218.2.a.o	$1218$	$2$	1218.a	1.a	$1$	$3$	$3$	$9.726$	3.3.568.1	None	✓	✓	✓	✓	1218.2.a.o	$1$	$1$	$-3$	$-3$	$0$	$3$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+q^{7}+\cdots$
1218.2.a.p	$1218$	$2$	1218.a	1.a	$1$	$3$	$3$	$9.726$	3.3.229.1	None	✓	✓	✓	✓	1218.2.a.p	$1$	$0$	$-3$	$3$	$0$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}-q^{6}+\cdots$
1218.2.a.q	$1218$	$2$	1218.a	1.a	$1$	$3$	$3$	$9.726$	3.3.1304.1	None	✓	✓	✓	✓	1218.2.a.q	$1$	$0$	$-3$	$3$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta _{2})q^{5}-q^{6}+\cdots$
1218.2.a.r	$1218$	$2$	1218.a	1.a	$1$	$3$	$3$	$9.726$	3.3.2920.1	None	✓	✓	✓		1218.2.a.r	$1$	$0$	$3$	$3$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots$
1218.2.f.a	$1218$	$2$	1218.f	21.c	$2$	$4$	$4$	$9.726$	$\Q(i, \sqrt{6})$	None		✓			1218.2.f.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{6}+(-1+\cdots)q^{7}+\cdots$
1218.2.f.b	$1218$	$2$	1218.f	21.c	$2$	$4$	$4$	$9.726$	$\Q(\zeta_{12})$	None		✓			1218.2.f.b	$4$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}^{3}q^{2}+(1-2\zeta_{12}^{2})q^{3}-q^{4}+\cdots$
1218.2.f.c	$1218$	$2$	1218.f	21.c	$2$	$4$	$4$	$9.726$	$\Q(\zeta_{12})$	None		✓			1218.2.f.c	$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}-\beta_{3} q^{3}-q^{4}-2\beta_{3} q^{5}+\cdots$
1218.2.f.d	$1218$	$2$	1218.f	21.c	$2$	$8$	$8$	$9.726$	8.0.342102016.5	None		✓			1218.2.f.d	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{7}q^{3}-q^{4}+(-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
1218.2.f.e	$1218$	$2$	1218.f	21.c	$2$	$8$	$8$	$9.726$	8.0.342102016.5	None		✓			1218.2.f.e	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-\beta _{2}-\beta _{4})q^{3}-q^{4}+2\beta _{2}q^{5}+\cdots$
1218.2.f.f	$1218$	$2$	1218.f	21.c	$2$	$12$	$12$	$9.726$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			1218.2.f.f	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{8}q^{3}-q^{4}+(-\beta _{1}+\beta _{9}+\cdots)q^{5}+\cdots$
1218.2.f.g	$1218$	$2$	1218.f	21.c	$2$	$16$	$16$	$9.726$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			1218.2.f.g	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{10}q^{5}-\beta _{1}q^{6}+\cdots$
1218.2.f.h	$1218$	$2$	1218.f	21.c	$2$	$16$	$16$	$9.726$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			1218.2.f.h	$4$	$0$	$0$	$0$	$0$	$14$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{15}q^{3}-q^{4}+\beta _{8}q^{5}-\beta _{9}q^{6}+\cdots$
1218.2.g.a	$1218$	$2$	1218.g	29.b	$2$	$2$	$2$	$9.726$	$\Q(\sqrt{-1}) $	None		✓			1218.2.g.a	$2$	$0$	$0$	$0$	$-8$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}-q^{4}-4 q^{5}+q^{6}+\cdots$
1218.2.g.b	$1218$	$2$	1218.g	29.b	$2$	$2$	$2$	$9.726$	$\Q(\sqrt{-1}) $	None		✓			1218.2.g.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-i q^{3}-q^{4}-q^{6}-q^{7}+\cdots$
1218.2.g.c	$1218$	$2$	1218.g	29.b	$2$	$2$	$2$	$9.726$	$\Q(\sqrt{-1}) $	None		✓			1218.2.g.c	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-i q^{3}-q^{4}-q^{6}-q^{7}+\cdots$
1218.2.g.d	$1218$	$2$	1218.g	29.b	$2$	$2$	$2$	$9.726$	$\Q(\sqrt{-1}) $	None		✓			1218.2.g.d	$2$	$0$	$0$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-i q^{3}-q^{4}+2 q^{5}+q^{6}+\cdots$
1218.2.g.e	$1218$	$2$	1218.g	29.b	$2$	$2$	$2$	$9.726$	$\Q(\sqrt{-1}) $	None		✓			1218.2.g.e	$2$	$0$	$0$	$0$	$8$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}+4 q^{5}-q^{6}+\cdots$
1218.2.g.f	$1218$	$2$	1218.g	29.b	$2$	$4$	$4$	$9.726$	$\Q(i, \sqrt{7})$	None		✓			1218.2.g.f	$2$	$0$	$0$	$0$	$-4$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
1218.2.g.g	$1218$	$2$	1218.g	29.b	$2$	$4$	$4$	$9.726$	$\Q(i, \sqrt{57})$	None		✓			1218.2.g.g	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}-q^{6}+q^{7}+\cdots$
1218.2.g.h	$1218$	$2$	1218.g	29.b	$2$	$4$	$4$	$9.726$	$\Q(i, \sqrt{5})$	None		✓			1218.2.g.h	$2$	$0$	$0$	$0$	$4$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{5}+\cdots$
1218.2.g.i	$1218$	$2$	1218.g	29.b	$2$	$6$	$6$	$9.726$	6.0.399424.1	None		✓	✓		1218.2.g.i	$2$	$0$	$0$	$0$	$-4$	$-6$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
1218.2.h.a	$1218$	$2$	1218.h	609.h	$2$	$40$	$40$	$9.726$		None		✓			1218.2.h.a	$4$	$0$	$-40$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{2}]$
1218.2.h.b	$1218$	$2$	1218.h	609.h	$2$	$40$	$40$	$9.726$		None		✓			1218.2.h.a	$4$	$0$	$40$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{2}]$
1218.2.i.a	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.64827.1	None		✓			1218.2.i.a	$2$	$0$	$-3$	$-3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{5})q^{2}-\beta _{5}q^{3}-\beta _{5}q^{4}+\beta _{1}q^{5}+\cdots$
1218.2.i.b	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.1783323.2	None		✓			1218.2.i.b	$2$	$0$	$-3$	$3$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots$
1218.2.i.c	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.64827.1	None		✓			1218.2.i.c	$2$	$0$	$3$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{5}q^{2}+(-1+\beta _{5})q^{3}+(-1+\beta _{5})q^{4}+\cdots$
1218.2.i.d	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.1783323.2	None		✓			1218.2.i.d	$2$	$0$	$3$	$-3$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}-\beta _{4}q^{3}-\beta _{4}q^{4}+\beta _{1}q^{5}+\cdots$
1218.2.i.e	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.18825075.4	None		✓			1218.2.i.e	$2$	$0$	$3$	$-3$	$5$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{3})q^{2}+\beta _{3}q^{3}+\beta _{3}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$
1218.2.i.f	$1218$	$2$	1218.i	7.c	$3$	$6$	$3$	$9.726$	6.0.1783323.2	None		✓			1218.2.i.f	$2$	$0$	$3$	$3$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}+\beta _{4}q^{3}-\beta _{4}q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots$
1218.2.i.g	$1218$	$2$	1218.i	7.c	$3$	$12$	$6$	$9.726$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			1218.2.i.g	$2$	$0$	$-6$	$-6$	$-3$	$0$		$3^{6}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{8}q^{2}+(-1+\beta _{8})q^{3}+(-1+\beta _{8}+\cdots)q^{4}+\cdots$
1218.2.i.h	$1218$	$2$	1218.i	7.c	$3$	$12$	$6$	$9.726$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			1218.2.i.h	$2$	$0$	$-6$	$6$	$3$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots$
1218.2.i.i	$1218$	$2$	1218.i	7.c	$3$	$12$	$6$	$9.726$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			1218.2.i.i	$2$	$0$	$6$	$6$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{2}+(1-\beta _{6})q^{3}+(-1+\beta _{6})q^{4}+\cdots$
1218.2.m.a	$1218$	$2$	1218.m	203.g	$4$	$40$	$20$	$9.726$		None		✓			1218.2.m.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1218.2.m.b	$1218$	$2$	1218.m	203.g	$4$	$40$	$20$	$9.726$		None		✓			1218.2.m.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1218.2.p.a	$1218$	$2$	1218.p	203.j	$6$	$36$	$18$	$9.726$		None		✓			1218.2.p.a	$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
1218.2.p.b	$1218$	$2$	1218.p	203.j	$6$	$44$	$22$	$9.726$		None		✓	✓		1218.2.p.b	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{6}]$

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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.