LMFDB - Newform search results

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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 454 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
63.2.g.b	$63$	$2$	63.g	63.g	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	None		$2$	$0$	$2$	$2$	$-8$	$-1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
63.2.h.b	$63$	$2$	63.h	63.h	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	None		$2$	$0$	$-4$	$-1$	$4$	$-4$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$
67.2.c.a	$67$	$2$	67.c	67.c	$3$	$10$	$5$	$0.535$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$2$	$-8$	$-6$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
91.2.e.c	$91$	$2$	91.e	7.c	$3$	$10$	$5$	$0.727$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-4$	$0$	$-2$	$1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots$
111.2.e.b	$111$	$2$	111.e	37.c	$3$	$10$	$5$	$0.886$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$-5$	$2$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-1+\beta _{6})q^{3}+(-2+2\beta _{6}+\cdots)q^{4}+\cdots$
117.2.e.b	$117$	$2$	117.e	9.c	$3$	$10$	$5$	$0.934$	10.0.$\cdots$.1	None		$2$	$0$	$-2$	$1$	$-1$	$2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{9}q^{2}+(\beta _{1}-\beta _{5}+\beta _{9})q^{3}+(\beta _{1}-\beta _{6}+\cdots)q^{4}+\cdots$
133.2.e.c	$133$	$2$	133.e	19.c	$3$	$10$	$5$	$1.062$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$1$	$3$	$-1$	$-10$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{6}+\beta _{7})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots$
146.2.c.b	$146$	$2$	146.c	73.c	$3$	$10$	$5$	$1.166$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-5$	$2$	$-2$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}-\beta _{2}q^{3}+(-1-\beta _{4})q^{4}-\beta _{8}q^{5}+\cdots$
182.2.e.d	$182$	$2$	182.e	91.h	$3$	$10$	$5$	$1.453$	10.0.$\cdots$.1	None		$2$	$0$	$10$	$-1$	$-2$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{5}q^{6}+\cdots$
182.2.h.d	$182$	$2$	182.h	91.g	$3$	$10$	$5$	$1.453$	10.0.$\cdots$.1	None		$2$	$0$	$-5$	$2$	$-2$	$0$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-\beta _{4}+\beta _{5})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
189.2.g.b	$189$	$2$	189.g	63.g	$3$	$10$	$5$	$1.509$	10.0.$\cdots$.1	None		$2$	$0$	$-2$	$0$	$8$	$-1$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots$
189.2.h.b	$189$	$2$	189.h	63.h	$3$	$10$	$5$	$1.509$	10.0.$\cdots$.1	None		$2$	$0$	$4$	$0$	$-4$	$-4$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{5})q^{2}+(1+\beta _{3})q^{4}+(\beta _{6}-\beta _{9})q^{5}+\cdots$
201.2.e.b	$201$	$2$	201.e	67.c	$3$	$10$	$5$	$1.605$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-2$	$-10$	$2$	$-1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
201.2.e.c	$201$	$2$	201.e	67.c	$3$	$10$	$5$	$1.605$	10.0.$\cdots$.1	None		$2$	$0$	$0$	$10$	$6$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{9}q^{2}+q^{3}+(\beta _{1}-2\beta _{4}-2\beta _{5})q^{4}+\cdots$
215.2.e.c	$215$	$2$	215.e	43.c	$3$	$10$	$5$	$1.717$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-4$	$1$	$-5$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{7})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
218.2.c.b	$218$	$2$	218.c	109.c	$3$	$10$	$5$	$1.741$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-10$	$-2$	$1$	$4$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{8}q^{5}+\cdots$
218.2.c.c	$218$	$2$	218.c	109.c	$3$	$10$	$5$	$1.741$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$10$	$1$	$-8$	$-1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-\beta _{8}q^{3}+q^{4}+(-2-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
219.2.e.b	$219$	$2$	219.e	73.c	$3$	$10$	$5$	$1.749$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$1$	$-10$	$-2$	$14$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-q^{3}+(-1-\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
231.2.i.f	$231$	$2$	231.i	7.c	$3$	$10$	$5$	$1.845$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-2$	$5$	$4$	$-1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots$
238.2.e.f	$238$	$2$	238.e	7.c	$3$	$10$	$5$	$1.900$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-5$	$0$	$1$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{2}-\beta _{1}q^{3}+\beta _{4}q^{4}+\beta _{9}q^{5}+\cdots$
254.2.c.d	$254$	$2$	254.c	127.c	$3$	$10$	$5$	$2.028$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-10$	$-1$	$-2$	$-6$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{2}+\beta _{5})q^{5}+\cdots$
35.4.e.c	$35$	$4$	35.e	7.c	$3$	$10$	$5$	$2.065$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-1$	$8$	$25$	$-62$	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{3}-\beta _{5}+2\beta _{6}+\cdots)q^{3}+\cdots$
266.2.e.e	$266$	$2$	266.e	7.c	$3$	$10$	$5$	$2.124$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-5$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{5})q^{2}-\beta _{2}q^{3}+\beta _{5}q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
266.2.g.b	$266$	$2$	266.g	133.h	$3$	$10$	$5$	$2.124$	10.0.$\cdots$.1	None		$2$	$0$	$10$	$3$	$6$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(\beta _{3}-\beta _{6}+\beta _{8})q^{3}+q^{4}+(1+\cdots)q^{5}+\cdots$
266.2.h.b	$266$	$2$	266.h	133.g	$3$	$10$	$5$	$2.124$	10.0.$\cdots$.1	None		$2$	$0$	$-5$	$-6$	$-3$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{6})q^{2}+(-\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots$
273.2.i.e	$273$	$2$	273.i	7.c	$3$	$10$	$5$	$2.180$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$0$	$5$	$3$	$4$	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{8})q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$
277.2.c.b	$277$	$2$	277.c	277.c	$3$	$10$	$5$	$2.212$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-4$	$5$	$4$	$6$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{6})q^{2}-\beta _{5}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$
285.2.i.f	$285$	$2$	285.i	19.c	$3$	$10$	$5$	$2.276$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$1$	$5$	$-5$	$4$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{4}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
287.2.e.c	$287$	$2$	287.e	7.c	$3$	$10$	$5$	$2.292$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$2$	$2$	$-2$	$8$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{7}q^{2}+\beta _{8}q^{3}+(\beta _{1}-\beta _{2}-\beta _{6})q^{4}+\cdots$
296.2.i.c	$296$	$2$	296.i	37.c	$3$	$10$	$5$	$2.364$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$0$	$-1$	$3$	$3$	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{9}q^{3}+(\beta _{2}+\beta _{6}+\beta _{9})q^{5}+(1-\beta _{7}+\cdots)q^{7}+\cdots$
299.2.e.c	$299$	$2$	299.e	13.c	$3$	$10$	$5$	$2.388$	10.0.$\cdots$.1	None		$2$	$0$	$1$	$3$	$-14$	$-7$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{4}-\beta _{5}+\beta _{8})q^{3}-\beta _{9}q^{4}+\cdots$
314.2.c.b	$314$	$2$	314.c	157.c	$3$	$10$	$5$	$2.507$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-10$	$4$	$-1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(\beta _{1}-\beta _{3}-\beta _{7})q^{3}+q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
325.2.e.c	$325$	$2$	325.e	13.c	$3$	$10$	$5$	$2.595$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$-3$	$0$	$2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{8})q^{3}+\cdots$
325.2.e.d	$325$	$2$	325.e	13.c	$3$	$10$	$5$	$2.595$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$3$	$0$	$-2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6}-\beta _{8})q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots$
333.2.f.c	$333$	$2$	333.f	37.c	$3$	$10$	$5$	$2.659$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$0$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{2}-2\beta _{6}+\beta _{8})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots$
342.2.f.f	$342$	$2$	342.f	171.h	$3$	$10$	$5$	$2.731$	10.0.$\cdots$.1	None		$2$	$0$	$10$	$2$	$-2$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(\beta _{1}+\beta _{8})q^{3}+q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
342.2.h.f	$342$	$2$	342.h	171.g	$3$	$10$	$5$	$2.731$	10.0.$\cdots$.1	None		$2$	$0$	$-5$	$-4$	$4$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}-\beta _{3}q^{3}+(-1-\beta _{4})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots$
344.2.i.d	$344$	$2$	344.i	43.c	$3$	$10$	$5$	$2.747$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$-5$	$2$	$4$	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{7})q^{3}+(\beta _{1}-\beta _{6})q^{5}+\cdots$
351.2.e.b	$351$	$2$	351.e	9.c	$3$	$10$	$5$	$2.803$	10.0.$\cdots$.1	None		$2$	$0$	$2$	$0$	$1$	$2$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{9})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots$
351.2.g.d	$351$	$2$	351.g	13.c	$3$	$10$	$5$	$2.803$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$0$	$-2$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{6}+\beta _{8})q^{4}+\beta _{3}q^{5}+\cdots$
351.2.g.e	$351$	$2$	351.g	13.c	$3$	$10$	$5$	$2.803$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$0$	$2$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{6}+\beta _{8})q^{4}-\beta _{3}q^{5}+\cdots$
357.2.i.f	$357$	$2$	357.i	7.c	$3$	$10$	$5$	$2.851$	10.0.$\cdots$.1	None		$2$	$0$	$2$	$5$	$-1$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}-\beta _{8})q^{2}+\beta _{4}q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$
406.2.e.a	$406$	$2$	406.e	7.c	$3$	$10$	$5$	$3.242$	10.0.$\cdots$.1	None		$2$	$0$	$-5$	$-3$	$-7$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4})q^{2}+(-\beta _{3}-\beta _{4})q^{3}-\beta _{4}q^{4}+\cdots$
406.2.e.b	$406$	$2$	406.e	7.c	$3$	$10$	$5$	$3.242$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-5$	$3$	$7$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{6})q^{2}+(-\beta _{1}-\beta _{6})q^{3}+\beta _{6}q^{4}+\cdots$
406.2.e.c	$406$	$2$	406.e	7.c	$3$	$10$	$5$	$3.242$	10.0.$\cdots$.1	None		$2$	$0$	$5$	$-3$	$-5$	$1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots$
406.2.e.d	$406$	$2$	406.e	7.c	$3$	$10$	$5$	$3.242$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$5$	$3$	$1$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{2}+(1-\beta _{5}+\beta _{6})q^{3}+(-1-\beta _{6}+\cdots)q^{4}+\cdots$
414.2.e.b	$414$	$2$	414.e	9.c	$3$	$10$	$5$	$3.306$	10.0.$\cdots$.1	None		$2$	$0$	$-5$	$1$	$-5$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}-\beta _{7}q^{3}+(-1+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
414.2.e.c	$414$	$2$	414.e	9.c	$3$	$10$	$5$	$3.306$	10.0.$\cdots$.1	None		$2$	$0$	$-5$	$1$	$5$	$5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{2}+(1+\beta _{5}-\beta _{6}-\beta _{9})q^{3}+\cdots$
414.2.e.d	$414$	$2$	414.e	9.c	$3$	$10$	$5$	$3.306$	10.0.$\cdots$.1	None		$2$	$0$	$5$	$-3$	$-1$	$5$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{7})q^{2}+\beta _{1}q^{3}+\beta _{7}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
57.4.e.a	$57$	$4$	57.e	19.c	$3$	$10$	$5$	$3.363$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-1$	$15$	$-4$	$30$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}-3\beta _{5}q^{3}+(-4-4\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$

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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.