LMFDB - Newform search results

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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 (1-50 of 84 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
890.2.a.a	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	$\Q$	None	✓	✓			890.2.a.a	$1$	$1$	$-1$	$-2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots$
890.2.a.b	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	$\Q$	None	✓	✓			890.2.a.b	$1$	$1$	$-1$	$-2$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots$
890.2.a.c	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	$\Q$	None	✓	✓			890.2.a.c	$1$	$1$	$-1$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}-3q^{9}+\cdots$
890.2.a.d	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	$\Q$	None	✓	✓			890.2.a.d	$1$	$1$	$-1$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
890.2.a.e	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	$\Q$	None	✓	✓			890.2.a.e	$1$	$0$	$-1$	$2$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots$
890.2.a.f	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	$\Q$	None	✓	✓			890.2.a.f	$1$	$1$	$1$	$-3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{8}+\cdots$
890.2.a.g	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	$\Q$	None	✓	✓	✓	✓	890.2.a.g	$1$	$1$	$1$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
890.2.a.h	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	$\Q$	None	✓	✓			890.2.a.h	$1$	$0$	$1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots$
890.2.a.i	$890$	$2$	890.a	1.a	$1$	$2$	$2$	$7.107$	$\Q(\sqrt{33}) $	None	✓	✓	✓		890.2.a.i	$1$	$1$	$-2$	$-1$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-2q^{7}+\cdots$
890.2.a.j	$890$	$2$	890.a	1.a	$1$	$2$	$2$	$7.107$	$\Q(\sqrt{3}) $	None	✓	✓	✓		890.2.a.j	$1$	$1$	$2$	$0$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(-3-\beta )q^{7}+q^{8}+\cdots$
890.2.a.k	$890$	$2$	890.a	1.a	$1$	$3$	$3$	$7.107$	3.3.404.1	None	✓	✓	✓		890.2.a.k	$1$	$0$	$-3$	$1$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
890.2.a.l	$890$	$2$	890.a	1.a	$1$	$5$	$5$	$7.107$	5.5.1186628.1	None	✓	✓	✓	✓	890.2.a.l	$1$	$0$	$5$	$1$	$-5$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{4}q^{3}+q^{4}-q^{5}+\beta _{4}q^{6}+\cdots$
890.2.a.m	$890$	$2$	890.a	1.a	$1$	$5$	$5$	$7.107$	5.5.7736352.1	None	✓	✓	✓		890.2.a.m	$1$	$0$	$5$	$1$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
890.2.a.n	$890$	$2$	890.a	1.a	$1$	$6$	$6$	$7.107$	6.6.387230992.1	None	✓	✓	✓	✓	890.2.a.n	$1$	$0$	$-6$	$3$	$6$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
890.2.b.a	$890$	$2$	890.b	5.b	$2$	$16$	$16$	$7.107$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			890.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{10}q^{2}+(\beta _{1}-\beta _{10})q^{3}-q^{4}+(\beta _{11}+\cdots)q^{5}+\cdots$
890.2.b.b	$890$	$2$	890.b	5.b	$2$	$28$	$28$	$7.107$		None		✓	✓		890.2.b.b	$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
890.2.c.a	$890$	$2$	890.c	89.b	$2$	$2$	$2$	$7.107$	$\Q(\sqrt{-2}) $	None		✓			890.2.c.a	$2$	$0$	$-2$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+q^{5}+\beta q^{7}-q^{8}+3q^{9}+\cdots$
890.2.c.b	$890$	$2$	890.c	89.b	$2$	$2$	$2$	$7.107$	$\Q(\sqrt{-2}) $	None		✓			890.2.c.b	$2$	$0$	$2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+3q^{9}+\cdots$
890.2.c.c	$890$	$2$	890.c	89.b	$2$	$6$	$6$	$7.107$	6.0.977437696.2	None		✓			890.2.c.c	$2$	$0$	$-6$	$0$	$6$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
890.2.c.d	$890$	$2$	890.c	89.b	$2$	$6$	$6$	$7.107$	6.0.1681072128.1	None		✓			890.2.c.d	$2$	$0$	$6$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
890.2.c.e	$890$	$2$	890.c	89.b	$2$	$6$	$6$	$7.107$	6.0.50922496.1	None		✓			890.2.c.e	$2$	$0$	$6$	$0$	$6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{5}q^{3}+q^{4}+q^{5}+\beta _{5}q^{6}+\cdots$
890.2.c.f	$890$	$2$	890.c	89.b	$2$	$8$	$8$	$7.107$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓		890.2.c.f	$2$	$0$	$-8$	$0$	$-8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
890.2.d.a	$890$	$2$	890.d	445.c	$2$	$2$	$2$	$7.107$	$\Q(\sqrt{-1}) $	None		✓			890.2.d.a	$2$	$0$	$0$	$-2$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{3}-q^{4}+(i-2)q^{5}-i q^{6}+\cdots$
890.2.d.b	$890$	$2$	890.d	445.c	$2$	$2$	$2$	$7.107$	$\Q(\sqrt{-1}) $	None		✓			890.2.d.a	$2$	$1$	$0$	$2$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{3}-q^{4}+(i-2)q^{5}+i q^{6}+\cdots$
890.2.d.c	$890$	$2$	890.d	445.c	$2$	$4$	$4$	$7.107$	$\Q(i, \sqrt{10})$	None		✓			890.2.d.c	$4$	$0$	$0$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}-q^{4}+(1-2\beta _{1})q^{5}+\cdots$
890.2.d.d	$890$	$2$	890.d	445.c	$2$	$36$	$36$	$7.107$		None		✓	✓		890.2.d.d	$4$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{2}]$
890.2.f.a	$890$	$2$	890.f	89.c	$4$	$2$	$1$	$7.107$	$\Q(\sqrt{-1}) $	None		✓			890.2.f.a	$2$	$1$	$-2$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(-i-1)q^{3}+q^{4}-i q^{5}+\cdots$
890.2.f.b	$890$	$2$	890.f	89.c	$4$	$2$	$1$	$7.107$	$\Q(\sqrt{-1}) $	None		✓			890.2.f.b	$2$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+q^{4}-i q^{5}+(-2 i-2)q^{7}+\cdots$
890.2.f.c	$890$	$2$	890.f	89.c	$4$	$2$	$1$	$7.107$	$\Q(\sqrt{-1}) $	None		✓			890.2.f.c	$2$	$0$	$-2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+q^{4}-i q^{5}+(2 i+2)q^{7}+\cdots$
890.2.f.d	$890$	$2$	890.f	89.c	$4$	$2$	$1$	$7.107$	$\Q(\sqrt{-1}) $	None		✓			890.2.f.d	$2$	$1$	$2$	$-4$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(-2 i-2)q^{3}+q^{4}+i q^{5}+\cdots$
890.2.f.e	$890$	$2$	890.f	89.c	$4$	$2$	$1$	$7.107$	$\Q(\sqrt{-1}) $	None		✓			890.2.f.e	$2$	$1$	$2$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(-2 i-2)q^{3}+q^{4}-i q^{5}+\cdots$
890.2.f.f	$890$	$2$	890.f	89.c	$4$	$6$	$3$	$7.107$	6.0.6594624.1	None		✓			890.2.f.f	$2$	$0$	$-6$	$0$	$0$	$2$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+q^{4}-\beta _{2}q^{5}+\beta _{5}q^{7}-q^{8}+\cdots$
890.2.f.g	$890$	$2$	890.f	89.c	$4$	$8$	$4$	$7.107$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			890.2.f.g	$2$	$0$	$-8$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{2}q^{6}+\cdots$
890.2.f.h	$890$	$2$	890.f	89.c	$4$	$8$	$4$	$7.107$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			890.2.f.h	$2$	$0$	$-8$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{4}q^{6}+\cdots$
890.2.f.i	$890$	$2$	890.f	89.c	$4$	$12$	$6$	$7.107$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			890.2.f.i	$2$	$0$	$12$	$2$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+\beta _{4}q^{3}+q^{4}-\beta _{5}q^{5}+\beta _{4}q^{6}+\cdots$
890.2.f.j	$890$	$2$	890.f	89.c	$4$	$16$	$8$	$7.107$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		890.2.f.j	$2$	$0$	$16$	$4$	$0$	$-2$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{7}q^{5}+\beta _{1}q^{6}+\cdots$
890.2.i.a	$890$	$2$	890.i	445.e	$4$	$2$	$1$	$7.107$	$\Q(\sqrt{-1}) $	None		✓			890.2.i.a	$2$	$1$	$0$	$-4$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}+(2 i-2)q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots$
890.2.i.b	$890$	$2$	890.i	445.e	$4$	$2$	$1$	$7.107$	$\Q(\sqrt{-1}) $	None		✓			890.2.i.a	$2$	$0$	$0$	$4$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{2}+(-2 i+2)q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots$
890.2.i.c	$890$	$2$	890.i	445.e	$4$	$44$	$22$	$7.107$		None		✓			890.2.i.c	$2$	$0$	$0$	$-2$	$-8$	$4$			$\mathrm{SU}(2)[C_{4}]$
890.2.i.d	$890$	$2$	890.i	445.e	$4$	$44$	$22$	$7.107$		None		✓			890.2.i.c	$2$	$0$	$0$	$2$	$8$	$-4$			$\mathrm{SU}(2)[C_{4}]$
890.2.k.a	$890$	$2$	890.k	445.l	$8$	$88$	$22$	$7.107$		None		✓			890.2.k.a	$2$	$0$	$0$	$-4$	$0$	$-4$			$\mathrm{SU}(2)[C_{8}]$
890.2.k.b	$890$	$2$	890.k	445.l	$8$	$92$	$23$	$7.107$		None		✓	✓		890.2.k.b	$2$	$0$	$0$	$-4$	$4$	$4$			$\mathrm{SU}(2)[C_{8}]$
890.2.n.a	$890$	$2$	890.n	445.m	$8$	$88$	$22$	$7.107$		None		✓			890.2.k.a	$2$	$0$	$0$	$8$	$0$	$-4$			$\mathrm{SU}(2)[C_{8}]$
890.2.n.b	$890$	$2$	890.n	445.m	$8$	$92$	$23$	$7.107$		None		✓	✓		890.2.k.b	$2$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{8}]$
890.2.o.a	$890$	$2$	890.o	89.e	$11$	$60$	$6$	$7.107$		None		✓			890.2.o.a	$2$	$0$	$-6$	$4$	$-6$	$6$			$\mathrm{SU}(2)[C_{11}]$
890.2.o.b	$890$	$2$	890.o	89.e	$11$	$80$	$8$	$7.107$		None		✓			890.2.o.b	$2$	$0$	$-8$	$2$	$8$	$-2$			$\mathrm{SU}(2)[C_{11}]$
890.2.o.c	$890$	$2$	890.o	89.e	$11$	$80$	$8$	$7.107$		None		✓			890.2.o.c	$2$	$0$	$8$	$-2$	$-8$	$-4$			$\mathrm{SU}(2)[C_{11}]$
890.2.o.d	$890$	$2$	890.o	89.e	$11$	$80$	$8$	$7.107$		None		✓			890.2.o.d	$2$	$0$	$8$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{11}]$
890.2.p.a	$890$	$2$	890.p	445.q	$22$	$440$	$44$	$7.107$		None		✓	✓	✓	890.2.p.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{22}]$
890.2.q.a	$890$	$2$	890.q	89.f	$22$	$60$	$6$	$7.107$		None		✓			890.2.q.a	$2$	$0$	$-6$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{22}]$

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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.