LMFDB - Newform search results

The results below are complete, since the LMFDB contains all newforms with trivial character and $Nk^2$ at most 40000

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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 (40 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				A-L signs			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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	5	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9280.2.a.a	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				4640.2.a.b	$1$	$0$	$0$	$-2$	$-1$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots$
9280.2.a.c	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				4640.2.a.a	$1$	$0$	$0$	$-2$	$1$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots$
9280.2.a.d	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				1160.2.a.a	$1$	$0$	$0$	$-2$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
9280.2.a.f	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				580.2.a.b	$1$	$0$	$0$	$0$	$-1$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-3q^{9}+4q^{11}+6q^{13}+\cdots$
9280.2.a.g	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				1160.2.a.b	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+2q^{13}-6q^{17}-8q^{19}+\cdots$
9280.2.a.j	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				4640.2.a.c	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots$
9280.2.a.n	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				580.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}+2q^{11}+2q^{13}+2q^{19}+\cdots$
9280.2.a.o	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				145.2.a.a	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots$
9280.2.a.p	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				4640.2.a.c	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}+2q^{11}-2q^{13}+\cdots$
9280.2.a.q	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				290.2.a.a	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}+2q^{11}+6q^{13}+\cdots$
9280.2.a.r	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				4640.2.a.b	$1$	$0$	$0$	$2$	$-1$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots$
9280.2.a.s	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				1160.2.a.d	$1$	$0$	$0$	$2$	$1$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-4q^{7}+q^{9}-6q^{13}+\cdots$
9280.2.a.u	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				4640.2.a.a	$1$	$0$	$0$	$2$	$1$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots$
9280.2.a.v	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	$\Q$	None	✓				1160.2.a.c	$1$	$0$	$0$	$2$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+4q^{7}+q^{9}+2q^{13}+\cdots$
9280.2.a.w	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	$\Q(\sqrt{2}) $	None	✓				145.2.a.b	$1$	$0$	$0$	$-4$	$-2$	$4$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
9280.2.a.x	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	$\Q(\sqrt{13}) $	None	✓				290.2.a.c	$1$	$0$	$0$	$-1$	$-2$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+(1+\beta )q^{7}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots$
9280.2.a.z	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	$\Q(\sqrt{13}) $	None	✓				290.2.a.b	$1$	$0$	$0$	$-1$	$2$	$5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+(3-\beta )q^{7}+\beta q^{9}+(2+\cdots)q^{11}+\cdots$
9280.2.a.ba	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	$\Q(\sqrt{2}) $	None	✓				4640.2.a.h	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}-\beta q^{7}-3q^{9}+\beta q^{11}+2q^{13}+\cdots$
9280.2.a.bg	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.229.1	None	✓				4640.2.a.j	$1$	$0$	$0$	$-3$	$3$	$7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+q^{5}+(2+2\beta _{1}-\beta _{2})q^{7}+\cdots$
9280.2.a.bj	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				145.2.a.c	$1$	$0$	$0$	$-2$	$-3$	$4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-q^{5}+(1+\beta _{1})q^{7}+\cdots$
9280.2.a.bn	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.469.1	None	✓				290.2.a.d	$1$	$0$	$0$	$-1$	$-3$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(1+\beta _{1}-2\beta _{2})q^{9}+\cdots$
9280.2.a.bq	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.229.1	None	✓				1160.2.a.g	$1$	$0$	$0$	$1$	$3$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}+(1-\beta _{1})q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots$
9280.2.a.bs	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				1160.2.a.f	$1$	$0$	$0$	$2$	$-3$	$-4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1})q^{7}+\cdots$
9280.2.a.bt	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				580.2.a.d	$1$	$0$	$0$	$2$	$-3$	$-2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots$
9280.2.a.bu	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				145.2.a.d	$1$	$0$	$0$	$2$	$3$	$-2$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots$
9280.2.a.bv	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				1160.2.a.e	$1$	$0$	$0$	$2$	$3$	$2$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots$
9280.2.a.bw	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.564.1	None	✓				580.2.a.c	$1$	$0$	$0$	$2$	$3$	$4$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(4+\cdots)q^{9}+\cdots$
9280.2.a.bx	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.229.1	None	✓				4640.2.a.j	$1$	$0$	$0$	$3$	$3$	$-7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+q^{5}+(-2-2\beta _{1}+\beta _{2})q^{7}+\cdots$
9280.2.a.by	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.621.1	None	✓				290.2.a.e	$1$	$0$	$0$	$3$	$3$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots$
9280.2.a.bz	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	4.4.11344.1	None	✓				4640.2.a.l	$1$	$0$	$0$	$-2$	$4$	$-2$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+q^{5}+\beta _{3}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
9280.2.a.cb	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	$\Q(\zeta_{24})^+$	None	✓				4640.2.a.p	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+\beta _{2}q^{7}-q^{9}+\beta _{2}q^{11}+\cdots$
9280.2.a.ce	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	$\Q(\sqrt{6}, \sqrt{10})$	None	✓				4640.2.a.n	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+q^{5}+\beta _{3}q^{7}+3q^{9}+\beta _{3}q^{11}+\cdots$
9280.2.a.cf	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	4.4.11344.1	None	✓				4640.2.a.l	$1$	$0$	$0$	$2$	$4$	$2$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+q^{5}-\beta _{3}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
9280.2.a.cj	$9280$	$2$	9280.a	1.a	$1$	$5$	$5$	$74.101$	5.5.6083172.1	None	✓				1160.2.a.i	$1$	$0$	$0$	$1$	$-5$	$-1$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(-\beta _{2}+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
9280.2.a.ck	$9280$	$2$	9280.a	1.a	$1$	$5$	$5$	$74.101$	5.5.3145252.1	None	✓		✓		1160.2.a.h	$1$	$0$	$0$	$1$	$5$	$7$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+q^{5}+(1-\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots$
9280.2.a.cl	$9280$	$2$	9280.a	1.a	$1$	$5$	$5$	$74.101$	5.5.580484.1	None	✓				1160.2.a.j	$1$	$0$	$0$	$3$	$-5$	$-7$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{3}-q^{5}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
9280.2.a.cq	$9280$	$2$	9280.a	1.a	$1$	$7$	$7$	$74.101$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				4640.2.a.w	$1$	$0$	$0$	$-1$	$-7$	$1$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots$
9280.2.a.cr	$9280$	$2$	9280.a	1.a	$1$	$7$	$7$	$74.101$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				4640.2.a.w	$1$	$0$	$0$	$1$	$-7$	$-1$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(\beta _{1}-\beta _{5})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
9280.2.a.ct	$9280$	$2$	9280.a	1.a	$1$	$10$	$10$	$74.101$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		4640.2.a.ba	$2$	$0$	$0$	$0$	$-10$	$0$	$-$	$+$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+\beta _{7}q^{7}+(3+\beta _{2})q^{9}+\cdots$
9280.2.a.cu	$9280$	$2$	9280.a	1.a	$1$	$10$	$10$	$74.101$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		4640.2.a.z	$2$	$0$	$0$	$0$	$10$	$0$	$-$	$-$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}-\beta _{9}q^{7}+(2+\beta _{2})q^{9}+\cdots$

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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.