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 926 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
45.2.e.b	$45$	$2$	45.e	9.c	$3$	$6$	$3$	$0.359$	6.0.954288.1	None		$2$	$0$	$-1$	$1$	$-3$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5})q^{2}+\beta _{4}q^{3}+\cdots$
57.2.e.b	$57$	$2$	57.e	19.c	$3$	$6$	$3$	$0.455$	6.0.954288.1	None		$2$	$0$	$1$	$-3$	$-2$	$-2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots$
63.2.f.a	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	$\Q(\zeta_{18})$	None		$2$	$0$	$-3$	$0$	$-3$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
63.2.f.b	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	6.0.309123.1	None		$2$	$0$	$1$	$-4$	$5$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$
74.2.c.c	$74$	$2$	74.c	37.c	$3$	$6$	$3$	$0.591$	6.0.4406832.1	None		$2$	$0$	$-3$	$0$	$-1$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{3})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\beta _{3}q^{4}+\cdots$
77.2.e.a	$77$	$2$	77.e	7.c	$3$	$6$	$3$	$0.615$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$-3$	$-6$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots$
77.2.e.b	$77$	$2$	77.e	7.c	$3$	$6$	$3$	$0.615$	6.0.1783323.2	None		$2$	$0$	$0$	$1$	$2$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{3}+\beta _{5})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$
93.2.e.b	$93$	$2$	93.e	31.c	$3$	$6$	$3$	$0.743$	6.0.591408.1	None		$2$	$0$	$0$	$-3$	$-4$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots$
95.2.e.b	$95$	$2$	95.e	19.c	$3$	$6$	$3$	$0.759$	6.0.3518667.1	None		$2$	$0$	$-1$	$-1$	$3$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots$
99.2.e.d	$99$	$2$	99.e	9.c	$3$	$6$	$3$	$0.791$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$0$	$-3$	$3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$
111.2.e.a	$111$	$2$	111.e	37.c	$3$	$6$	$3$	$0.886$	6.0.1415907.1	None		$2$	$0$	$0$	$3$	$2$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{2}+(1+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots$
119.2.e.a	$119$	$2$	119.e	7.c	$3$	$6$	$3$	$0.950$	6.0.64827.1	None		$2$	$0$	$1$	$-1$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
122.2.c.b	$122$	$2$	122.c	61.c	$3$	$6$	$3$	$0.974$	6.0.5938947.1	None		$2$	$0$	$-3$	$-2$	$2$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}-\beta _{2}q^{3}+(-1+\beta _{4})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
124.2.e.a	$124$	$2$	124.e	31.c	$3$	$6$	$3$	$0.990$	6.0.954288.1	None		$2$	$0$	$0$	$1$	$-1$	$-1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
126.2.e.c	$126$	$2$	126.e	63.h	$3$	$6$	$3$	$1.006$	6.0.309123.1	None		$2$	$0$	$-6$	$2$	$1$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-\beta _{2}-\beta _{4})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
126.2.e.d	$126$	$2$	126.e	63.h	$3$	$6$	$3$	$1.006$	6.0.309123.1	None		$2$	$0$	$6$	$-2$	$-5$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(\beta _{3}-\beta _{4}-\beta _{5})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
126.2.h.c	$126$	$2$	126.h	63.g	$3$	$6$	$3$	$1.006$	6.0.309123.1	None		$2$	$0$	$-3$	$4$	$10$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(1-\beta _{5})q^{3}+(-1-\beta _{4})q^{4}+\cdots$
126.2.h.d	$126$	$2$	126.h	63.g	$3$	$6$	$3$	$1.006$	6.0.309123.1	None		$2$	$0$	$3$	$2$	$-2$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
129.2.e.b	$129$	$2$	129.e	43.c	$3$	$6$	$3$	$1.030$	6.0.1783323.2	None		$2$	$0$	$-2$	$3$	$-3$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+\beta _{4}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
129.2.e.c	$129$	$2$	129.e	43.c	$3$	$6$	$3$	$1.030$	6.0.64827.1	None		$2$	$0$	$2$	$-3$	$1$	$5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}-\beta _{5}q^{3}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
133.2.e.b	$133$	$2$	133.e	19.c	$3$	$6$	$3$	$1.062$	6.0.309123.1	None		$2$	$0$	$-2$	$-1$	$3$	$6$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(\beta _{1}-\beta _{5})q^{3}+\cdots$
135.2.e.b	$135$	$2$	135.e	9.c	$3$	$6$	$3$	$1.078$	6.0.954288.1	None		$2$	$0$	$1$	$0$	$3$	$-5$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
143.2.e.a	$143$	$2$	143.e	13.c	$3$	$6$	$3$	$1.142$	6.0.1714608.1	None		$2$	$0$	$-3$	$0$	$6$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{2}+(-\beta _{3}+\beta _{5})q^{3}-\beta _{4}q^{4}+\cdots$
143.2.e.b	$143$	$2$	143.e	13.c	$3$	$6$	$3$	$1.142$	6.0.3518667.1	None		$2$	$0$	$1$	$-1$	$-2$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-3+\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots$
146.2.c.a	$146$	$2$	146.c	73.c	$3$	$6$	$3$	$1.166$	6.0.6040683.1	None		$2$	$0$	$3$	$0$	$2$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}-\beta _{2}q^{3}-\beta _{4}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
148.2.e.a	$148$	$2$	148.e	37.c	$3$	$6$	$3$	$1.182$	6.0.27870912.1	None		$2$	$0$	$0$	$-1$	$3$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{5})q^{7}+\cdots$
152.2.i.c	$152$	$2$	152.i	19.c	$3$	$6$	$3$	$1.214$	6.0.2696112.1	None		$2$	$0$	$0$	$-1$	$-1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
21.4.e.b	$21$	$4$	21.e	7.c	$3$	$6$	$3$	$1.239$	6.0.9924270768.1	None		$2$	$0$	$-1$	$9$	$-11$	$-13$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(3-3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots$
169.2.c.b	$169$	$2$	169.c	13.c	$3$	$6$	$3$	$1.349$	6.0.64827.1	None		$2$	$0$	$-2$	$2$	$8$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+\cdots$
169.2.c.c	$169$	$2$	169.c	13.c	$3$	$6$	$3$	$1.349$	6.0.64827.1	None		$2$	$0$	$2$	$2$	$-8$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{4})q^{2}+(1-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots$
171.2.f.b	$171$	$2$	171.f	19.c	$3$	$6$	$3$	$1.365$	6.0.954288.1	None		$2$	$0$	$-1$	$0$	$2$	$-2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots$
175.2.e.d	$175$	$2$	175.e	7.c	$3$	$6$	$3$	$1.397$	6.0.1783323.2	None		$2$	$0$	$-1$	$3$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots$
175.2.e.e	$175$	$2$	175.e	7.c	$3$	$6$	$3$	$1.397$	6.0.1783323.2	None		$2$	$0$	$1$	$-3$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots$
180.2.i.b	$180$	$2$	180.i	9.c	$3$	$6$	$3$	$1.437$	6.0.954288.1	None		$2$	$0$	$0$	$-1$	$3$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
182.2.e.c	$182$	$2$	182.e	91.h	$3$	$6$	$3$	$1.453$	6.0.4740147.1	None		$2$	$0$	$-6$	$1$	$0$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+\beta _{4}q^{3}+q^{4}+(\beta _{4}+\beta _{5})q^{5}+\cdots$
182.2.f.b	$182$	$2$	182.f	7.c	$3$	$6$	$3$	$1.453$	6.0.309123.1	None		$2$	$0$	$3$	$0$	$2$	$-4$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
182.2.h.c	$182$	$2$	182.h	91.g	$3$	$6$	$3$	$1.453$	6.0.4740147.1	None		$2$	$0$	$3$	$-2$	$0$	$-12$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{1})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots$
183.2.e.d	$183$	$2$	183.e	61.c	$3$	$6$	$3$	$1.461$	6.0.5938947.1	None		$2$	$0$	$-1$	$6$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+q^{3}+(-\beta _{3}-2\beta _{4}+\beta _{5})q^{4}+\cdots$
183.2.e.e	$183$	$2$	183.e	61.c	$3$	$6$	$3$	$1.461$	6.0.5938947.1	None		$2$	$0$	$2$	$-6$	$3$	$6$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4}+\beta _{5})q^{2}-q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
189.2.e.e	$189$	$2$	189.e	7.c	$3$	$6$	$3$	$1.509$	6.0.309123.1	None		$2$	$0$	$-2$	$0$	$-1$	$2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$
189.2.e.f	$189$	$2$	189.e	7.c	$3$	$6$	$3$	$1.509$	6.0.309123.1	None		$2$	$0$	$2$	$0$	$1$	$2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
189.2.f.a	$189$	$2$	189.f	9.c	$3$	$6$	$3$	$1.509$	6.0.309123.1	None		$2$	$0$	$-1$	$0$	$-5$	$3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots$
189.2.f.b	$189$	$2$	189.f	9.c	$3$	$6$	$3$	$1.509$	$\Q(\zeta_{18})$	None		$2$	$0$	$3$	$0$	$3$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$
194.2.c.b	$194$	$2$	194.c	97.c	$3$	$6$	$3$	$1.549$	6.0.591408.1	None		$2$	$0$	$3$	$2$	$-1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots$
195.2.i.d	$195$	$2$	195.i	13.c	$3$	$6$	$3$	$1.557$	6.0.1714608.1	None		$2$	$0$	$0$	$3$	$6$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{3}+\beta _{5})q^{2}+(1+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
195.2.i.e	$195$	$2$	195.i	13.c	$3$	$6$	$3$	$1.557$	6.0.591408.1	None		$2$	$0$	$0$	$3$	$-6$	$5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{2}+(1-\beta _{4})q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
198.2.e.d	$198$	$2$	198.e	9.c	$3$	$6$	$3$	$1.581$	6.0.954288.1	None		$2$	$0$	$-3$	$1$	$-1$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{3})q^{2}+\beta _{4}q^{3}+\beta _{3}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
198.2.e.e	$198$	$2$	198.e	9.c	$3$	$6$	$3$	$1.581$	6.0.954288.1	None		$2$	$0$	$3$	$-1$	$5$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(-1-\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots$
199.2.c.a	$199$	$2$	199.c	199.c	$3$	$6$	$3$	$1.589$	6.0.127961883.1	None		$2$	$0$	$0$	$-1$	$-4$	$5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}-2\beta _{4}q^{4}+(-1+\beta _{2})q^{5}+\cdots$
206.2.c.b	$206$	$2$	206.c	103.c	$3$	$6$	$3$	$1.645$	6.0.1783323.2	None		$2$	$0$	$3$	$-6$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}+(-1-\beta _{3})q^{3}-\beta _{4}q^{4}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.