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 1668 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
8008.2.a.i	$8008$	$2$	8008.a	1.a	$1$	$3$	$3$	$63.944$	3.3.229.1	None	✓	$1$	$1$	$0$	$2$	$6$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(2-\beta _{1})q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots$
8010.2.a.x	$8010$	$2$	8010.a	1.a	$1$	$3$	$3$	$63.960$	3.3.148.1	None	✓	$1$	$1$	$-3$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(-1-\beta _{1}-2\beta _{2})q^{7}+\cdots$
8010.2.a.y	$8010$	$2$	8010.a	1.a	$1$	$3$	$3$	$63.960$	3.3.469.1	None	✓	$1$	$0$	$-3$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-\beta _{1}q^{7}-q^{8}+q^{10}+\cdots$
8010.2.a.z	$8010$	$2$	8010.a	1.a	$1$	$3$	$3$	$63.960$	3.3.148.1	None	✓	$1$	$0$	$-3$	$0$	$3$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(-2-\beta _{2})q^{7}-q^{8}+\cdots$
8010.2.a.ba	$8010$	$2$	8010.a	1.a	$1$	$3$	$3$	$63.960$	3.3.148.1	None	✓	$1$	$1$	$3$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(-1-\beta _{1})q^{7}+q^{8}+\cdots$
8010.2.a.bb	$8010$	$2$	8010.a	1.a	$1$	$3$	$3$	$63.960$	3.3.404.1	None	✓	$1$	$0$	$3$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
8010.2.a.bc	$8010$	$2$	8010.a	1.a	$1$	$3$	$3$	$63.960$	3.3.404.1	None	✓	$1$	$0$	$3$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(1+\beta _{1})q^{7}+q^{8}+\cdots$
8015.2.a.g	$8015$	$2$	8015.a	1.a	$1$	$3$	$3$	$64.000$	3.3.148.1	None	✓	$1$	$1$	$1$	$-1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
8016.2.a.l	$8016$	$2$	8016.a	1.a	$1$	$3$	$3$	$64.008$	3.3.148.1	None	✓	$1$	$1$	$0$	$3$	$-3$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{2})q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots$
8016.2.a.m	$8016$	$2$	8016.a	1.a	$1$	$3$	$3$	$64.008$	3.3.1300.1	None	✓	$1$	$0$	$0$	$3$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
8016.2.a.n	$8016$	$2$	8016.a	1.a	$1$	$3$	$3$	$64.008$	3.3.148.1	None	✓	$1$	$0$	$0$	$3$	$6$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(2-\beta _{2})q^{5}+(2-2\beta _{1})q^{7}+q^{9}+\cdots$
8019.2.a.a	$8019$	$2$	8019.a	1.a	$1$	$3$	$3$	$64.032$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}-2\beta _{2})q^{5}+\cdots$
8019.2.a.b	$8019$	$2$	8019.a	1.a	$1$	$3$	$3$	$64.032$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots$
8023.2.a.a	$8023$	$2$	8023.a	1.a	$1$	$3$	$3$	$64.064$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$2$	$3$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2\beta _{1}-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
8024.2.a.s	$8024$	$2$	8024.a	1.a	$1$	$3$	$3$	$64.072$	3.3.229.1	None	✓	$1$	$0$	$0$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
8024.2.a.t	$8024$	$2$	8024.a	1.a	$1$	$3$	$3$	$64.072$	3.3.229.1	None	✓	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots$
8024.2.a.u	$8024$	$2$	8024.a	1.a	$1$	$3$	$3$	$64.072$	3.3.568.1	None	✓	$1$	$0$	$0$	$3$	$4$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}-2q^{9}+\cdots$
8025.2.a.t	$8025$	$2$	8025.a	1.a	$1$	$3$	$3$	$64.080$	$\Q(\zeta_{18})^+$	None	✓	$1$	$2$	$-3$	$-3$	$0$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
8025.2.a.u	$8025$	$2$	8025.a	1.a	$1$	$3$	$3$	$64.080$	3.3.169.1	None	✓	$1$	$1$	$-1$	$-3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
8025.2.a.v	$8025$	$2$	8025.a	1.a	$1$	$3$	$3$	$64.080$	3.3.169.1	None	✓	$1$	$0$	$1$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{2}+q^{3}+(2-2\beta _{1}+\cdots)q^{4}+\cdots$
8030.2.a.r	$8030$	$2$	8030.a	1.a	$1$	$3$	$3$	$64.120$	3.3.316.1	None	✓	$1$	$1$	$-3$	$-1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
8030.2.a.s	$8030$	$2$	8030.a	1.a	$1$	$3$	$3$	$64.120$	3.3.229.1	None	✓	$1$	$1$	$-3$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
8030.2.a.t	$8030$	$2$	8030.a	1.a	$1$	$3$	$3$	$64.120$	3.3.229.1	None	✓	$1$	$1$	$3$	$-2$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
8036.2.a.h	$8036$	$2$	8036.a	1.a	$1$	$3$	$3$	$64.168$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(2\beta _{1}-2\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots$
8037.2.a.e	$8037$	$2$	8037.a	1.a	$1$	$3$	$3$	$64.176$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$0$	$3$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
8037.2.a.f	$8037$	$2$	8037.a	1.a	$1$	$3$	$3$	$64.176$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots$
8043.2.a.m	$8043$	$2$	8043.a	1.a	$1$	$3$	$3$	$64.224$	3.3.148.1	None	✓	$1$	$0$	$-1$	$3$	$-2$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
8048.2.a.m	$8048$	$2$	8048.a	1.a	$1$	$3$	$3$	$64.264$	3.3.257.1	None	✓	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots$
8050.2.a.bg	$8050$	$2$	8050.a	1.a	$1$	$3$	$3$	$64.280$	3.3.148.1	None	✓	$1$	$1$	$-3$	$-4$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots$
8050.2.a.bh	$8050$	$2$	8050.a	1.a	$1$	$3$	$3$	$64.280$	3.3.316.1	None	✓	$1$	$1$	$-3$	$-2$	$0$	$3$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots$
8050.2.a.bi	$8050$	$2$	8050.a	1.a	$1$	$3$	$3$	$64.280$	3.3.148.1	None	✓	$1$	$1$	$-3$	$2$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{6}+\cdots$
8050.2.a.bj	$8050$	$2$	8050.a	1.a	$1$	$3$	$3$	$64.280$	3.3.404.1	None	✓	$1$	$1$	$-3$	$2$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
8050.2.a.bk	$8050$	$2$	8050.a	1.a	$1$	$3$	$3$	$64.280$	3.3.564.1	None	✓	$1$	$1$	$3$	$-2$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
8050.2.a.bl	$8050$	$2$	8050.a	1.a	$1$	$3$	$3$	$64.280$	3.3.148.1	None	✓	$1$	$1$	$3$	$-2$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
8050.2.a.bm	$8050$	$2$	8050.a	1.a	$1$	$3$	$3$	$64.280$	3.3.148.1	None	✓	$1$	$1$	$3$	$-2$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{6}+\cdots$
8050.2.a.bn	$8050$	$2$	8050.a	1.a	$1$	$3$	$3$	$64.280$	3.3.316.1	None	✓	$1$	$0$	$3$	$2$	$0$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots$
8055.2.a.m	$8055$	$2$	8055.a	1.a	$1$	$3$	$3$	$64.319$	3.3.788.1	None	✓	$1$	$1$	$0$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}+\beta _{2}q^{7}+(1-\beta _{1}+\beta _{2})q^{11}+\cdots$
8058.2.a.j	$8058$	$2$	8058.a	1.a	$1$	$3$	$3$	$64.343$	3.3.257.1	None	✓	$1$	$1$	$-3$	$3$	$2$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
8058.2.a.k	$8058$	$2$	8058.a	1.a	$1$	$3$	$3$	$64.343$	3.3.257.1	None	✓	$1$	$1$	$3$	$-3$	$0$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+(2+\cdots)q^{7}+\cdots$
8064.2.a.bs	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.148.1	None	✓	$1$	$1$	$0$	$0$	$-2$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}-q^{7}+(-1+\beta _{1})q^{11}+\cdots$
8064.2.a.bt	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.148.1	None	✓	$1$	$1$	$0$	$0$	$-2$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}-q^{7}+(-1+\beta _{1})q^{11}+\cdots$
8064.2.a.bu	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.316.1	None	✓	$1$	$0$	$0$	$0$	$-2$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}-q^{7}+(-\beta _{1}+\beta _{2})q^{11}+\cdots$
8064.2.a.bv	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.564.1	None	✓	$1$	$0$	$0$	$0$	$-2$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}-q^{7}+(2+\beta _{1}-\beta _{2})q^{11}+\cdots$
8064.2.a.bw	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.564.1	None	✓	$1$	$1$	$0$	$0$	$-2$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}-q^{7}+(2+\beta _{1}-\beta _{2})q^{11}+\cdots$
8064.2.a.bx	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.564.1	None	✓	$1$	$1$	$0$	$0$	$-2$	$3$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+q^{7}+(-2-\beta _{1}+\beta _{2})q^{11}+\cdots$
8064.2.a.by	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.564.1	None	✓	$1$	$1$	$0$	$0$	$-2$	$3$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+q^{7}+(-2-\beta _{1}+\beta _{2})q^{11}+\cdots$
8064.2.a.bz	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.148.1	None	✓	$1$	$1$	$0$	$0$	$-2$	$3$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+q^{7}+(1-\beta _{1})q^{11}+\cdots$
8064.2.a.ca	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.148.1	None	✓	$1$	$0$	$0$	$0$	$-2$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+q^{7}+(1-\beta _{1})q^{11}+\cdots$
8064.2.a.cb	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.316.1	None	✓	$1$	$0$	$0$	$0$	$-2$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+q^{7}+(\beta _{1}-\beta _{2})q^{11}+\cdots$
8064.2.a.cc	$8064$	$2$	8064.a	1.a	$1$	$3$	$3$	$64.391$	3.3.564.1	None	✓	$1$	$1$	$0$	$0$	$2$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{5}-q^{7}+(-2-\beta _{1}+\beta _{2})q^{11}+\cdots$

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Elliptic 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.