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 831 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4002.2.a.be	$4002$	$2$	4002.a	1.a	$1$	$5$	$5$	$31.956$	5.5.2389280.1	None	✓	$1$	$1$	$-5$	$-5$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
4004.2.a.f	$4004$	$2$	4004.a	1.a	$1$	$5$	$5$	$31.972$	5.5.463341.1	None	✓	$1$	$1$	$0$	$3$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
4008.2.a.f	$4008$	$2$	4008.a	1.a	$1$	$5$	$5$	$32.004$	5.5.284897.1	None	✓	$1$	$1$	$0$	$5$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-\beta _{3}+\beta _{4})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
4014.2.a.r	$4014$	$2$	4014.a	1.a	$1$	$5$	$5$	$32.052$	5.5.356173.1	None	✓	$1$	$1$	$5$	$0$	$-5$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
4016.2.a.d	$4016$	$2$	4016.a	1.a	$1$	$5$	$5$	$32.068$	5.5.138917.1	None	✓	$1$	$0$	$0$	$-2$	$7$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{3}+(2+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
4016.2.a.e	$4016$	$2$	4016.a	1.a	$1$	$5$	$5$	$32.068$	5.5.242773.1	None	✓	$1$	$1$	$0$	$1$	$-6$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$
4020.2.a.e	$4020$	$2$	4020.a	1.a	$1$	$5$	$5$	$32.100$	5.5.1257629.1	None	✓	$1$	$1$	$0$	$-5$	$5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
4025.2.a.p	$4025$	$2$	4025.a	1.a	$1$	$5$	$5$	$32.140$	5.5.2147108.1	None	✓	$1$	$0$	$-2$	$0$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
4025.2.a.q	$4025$	$2$	4025.a	1.a	$1$	$5$	$5$	$32.140$	5.5.255877.1	None	✓	$1$	$1$	$1$	$4$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
4025.2.a.r	$4025$	$2$	4025.a	1.a	$1$	$5$	$5$	$32.140$	5.5.122821.1	None	✓	$1$	$0$	$3$	$6$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(\beta _{3}+\beta _{4})q^{4}+\cdots$
4026.2.a.u	$4026$	$2$	4026.a	1.a	$1$	$5$	$5$	$32.148$	5.5.9176805.1	None	✓	$1$	$0$	$-5$	$5$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
4026.2.a.v	$4026$	$2$	4026.a	1.a	$1$	$5$	$5$	$32.148$	5.5.11492689.1	None	✓	$1$	$0$	$5$	$-5$	$7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots$
4048.2.a.y	$4048$	$2$	4048.a	1.a	$1$	$5$	$5$	$32.323$	5.5.10722353.1	None	✓	$1$	$0$	$0$	$-1$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
4048.2.a.z	$4048$	$2$	4048.a	1.a	$1$	$5$	$5$	$32.323$	5.5.486337.1	None	✓	$1$	$0$	$0$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{4})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
4048.2.a.ba	$4048$	$2$	4048.a	1.a	$1$	$5$	$5$	$32.323$	5.5.372289.1	None	✓	$1$	$0$	$0$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+\beta _{1}q^{5}+(1+\beta _{2})q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots$
4048.2.a.bb	$4048$	$2$	4048.a	1.a	$1$	$5$	$5$	$32.323$	5.5.170701.1	None	✓	$1$	$0$	$0$	$5$	$-3$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-\beta _{1}-\beta _{4})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
4059.2.a.o	$4059$	$2$	4059.a	1.a	$1$	$5$	$5$	$32.411$	5.5.24217.1	None	✓	$1$	$0$	$2$	$0$	$8$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2}+\beta _{4})q^{4}+(2+\cdots)q^{5}+\cdots$
4059.2.a.p	$4059$	$2$	4059.a	1.a	$1$	$5$	$5$	$32.411$	5.5.36497.1	None	✓	$1$	$0$	$2$	$0$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{4})q^{4}+(1-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
4059.2.a.q	$4059$	$2$	4059.a	1.a	$1$	$5$	$5$	$32.411$	5.5.147109.1	None	✓	$1$	$1$	$3$	$0$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
4060.2.a.p	$4060$	$2$	4060.a	1.a	$1$	$5$	$5$	$32.419$	5.5.5139425.1	None	✓	$1$	$1$	$0$	$-4$	$-5$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-q^{5}-q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
4060.2.a.q	$4060$	$2$	4060.a	1.a	$1$	$5$	$5$	$32.419$	5.5.710984.1	None	✓	$1$	$0$	$0$	$3$	$5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
4068.2.a.k	$4068$	$2$	4068.a	1.a	$1$	$5$	$5$	$32.483$	5.5.27451700.1	None	✓	$1$	$0$	$0$	$0$	$6$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}-\beta _{4}q^{7}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
4070.2.a.m	$4070$	$2$	4070.a	1.a	$1$	$5$	$5$	$32.499$	5.5.2405453.1	None	✓	$1$	$0$	$-5$	$-1$	$5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
4070.2.a.n	$4070$	$2$	4070.a	1.a	$1$	$5$	$5$	$32.499$	5.5.81509.1	None	✓	$1$	$1$	$-5$	$0$	$-5$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots$
4070.2.a.o	$4070$	$2$	4070.a	1.a	$1$	$5$	$5$	$32.499$	5.5.982524.1	None	✓	$1$	$0$	$-5$	$6$	$5$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
4070.2.a.p	$4070$	$2$	4070.a	1.a	$1$	$5$	$5$	$32.499$	5.5.236549.1	None	✓	$1$	$1$	$5$	$-6$	$5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
4074.2.a.y	$4074$	$2$	4074.a	1.a	$1$	$5$	$5$	$32.531$	5.5.643312.1	None	✓	$1$	$1$	$-5$	$5$	$-4$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}-q^{6}+\cdots$
4075.2.a.c	$4075$	$2$	4075.a	1.a	$1$	$5$	$5$	$32.539$	5.5.24217.1	None	✓	$1$	$1$	$2$	$0$	$0$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}-\beta _{3}q^{3}-\beta _{4}q^{4}+\cdots$
4075.2.a.d	$4075$	$2$	4075.a	1.a	$1$	$5$	$5$	$32.539$	5.5.65657.1	None	✓	$1$	$0$	$5$	$5$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\cdots$
4086.2.a.j	$4086$	$2$	4086.a	1.a	$1$	$5$	$5$	$32.627$	5.5.307829.1	None	✓	$1$	$1$	$5$	$0$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
4092.2.a.m	$4092$	$2$	4092.a	1.a	$1$	$5$	$5$	$32.675$	5.5.1172057.1	None	✓	$1$	$1$	$0$	$-5$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1}+\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
4095.2.a.bj	$4095$	$2$	4095.a	1.a	$1$	$5$	$5$	$32.699$	5.5.255877.1	None	✓	$1$	$0$	$0$	$0$	$-5$	$-5$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(2+\beta _{1})q^{4}-q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots$
4104.2.a.o	$4104$	$2$	4104.a	1.a	$1$	$5$	$5$	$32.771$	5.5.4873296.1	None	✓	$1$	$1$	$0$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{4})q^{5}-\beta _{2}q^{7}+(-\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots$
4104.2.a.p	$4104$	$2$	4104.a	1.a	$1$	$5$	$5$	$32.771$	5.5.7986588.1	None	✓	$1$	$0$	$0$	$0$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
4104.2.a.q	$4104$	$2$	4104.a	1.a	$1$	$5$	$5$	$32.771$	5.5.7986588.1	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
4104.2.a.r	$4104$	$2$	4104.a	1.a	$1$	$5$	$5$	$32.771$	5.5.4873296.1	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{4})q^{5}-\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$
4107.2.a.j	$4107$	$2$	4107.a	1.a	$1$	$5$	$5$	$32.795$	5.5.6083576.1	None	✓	$1$	$0$	$0$	$5$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
4107.2.a.k	$4107$	$2$	4107.a	1.a	$1$	$5$	$5$	$32.795$	5.5.6083576.1	None	✓	$1$	$0$	$0$	$5$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
4110.2.a.bb	$4110$	$2$	4110.a	1.a	$1$	$5$	$5$	$32.819$	5.5.1900864.1	None	✓	$1$	$0$	$5$	$-5$	$-5$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
4112.2.a.o	$4112$	$2$	4112.a	1.a	$1$	$5$	$5$	$32.834$	5.5.179024.1	None	✓	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
4112.2.a.p	$4112$	$2$	4112.a	1.a	$1$	$5$	$5$	$32.834$	5.5.288385.1	None	✓	$1$	$1$	$0$	$3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{3}+\beta _{2}q^{5}+(-\beta _{3}+\beta _{4})q^{7}+\cdots$
4114.2.a.be	$4114$	$2$	4114.a	1.a	$1$	$5$	$5$	$32.850$	5.5.7679496.1	None	✓	$1$	$0$	$-5$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
4114.2.a.bf	$4114$	$2$	4114.a	1.a	$1$	$5$	$5$	$32.850$	5.5.7679496.1	None	✓	$1$	$0$	$5$	$1$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
4119.2.a.c	$4119$	$2$	4119.a	1.a	$1$	$5$	$5$	$32.890$	5.5.81509.1	None	✓	$1$	$1$	$-2$	$5$	$-11$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+q^{3}+(-\beta _{3}-\beta _{4})q^{4}+(-2+\cdots)q^{5}+\cdots$
4120.2.a.j	$4120$	$2$	4120.a	1.a	$1$	$5$	$5$	$32.898$	5.5.122821.1	None	✓	$1$	$1$	$0$	$-1$	$-5$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}-q^{5}+(\beta _{1}+\beta _{2}+\beta _{4})q^{7}+\cdots$
4122.2.a.o	$4122$	$2$	4122.a	1.a	$1$	$5$	$5$	$32.914$	5.5.495317.1	None	✓	$1$	$0$	$-5$	$0$	$-2$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots$
4122.2.a.p	$4122$	$2$	4122.a	1.a	$1$	$5$	$5$	$32.914$	5.5.1772453.1	None	✓	$1$	$1$	$5$	$0$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{4}q^{5}+(-1+\beta _{2}+\beta _{4})q^{7}+\cdots$
4128.2.a.u	$4128$	$2$	4128.a	1.a	$1$	$5$	$5$	$32.962$	5.5.246832.1	None	✓	$1$	$1$	$0$	$-5$	$-4$	$2$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{3})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots$
4128.2.a.v	$4128$	$2$	4128.a	1.a	$1$	$5$	$5$	$32.962$	5.5.331312.1	None	✓	$1$	$1$	$0$	$-5$	$4$	$-4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{2})q^{5}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
4128.2.a.w	$4128$	$2$	4128.a	1.a	$1$	$5$	$5$	$32.962$	5.5.1564636.1	None	✓	$1$	$0$	$0$	$-5$	$4$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{3})q^{5}+\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots$

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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.