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 193 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
275.1.c.a	$275$	$1$	275.c	11.b	$2$	$1$	$1$	$0.137$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓		✓	✓	55.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-q^{9}-q^{11}+q^{16}-2q^{31}+\cdots$
275.1.s.a	$275$	$1$	275.s	275.s	$10$	$4$	$1$	$0.137$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	275.1.s.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+(\zeta_{10}-\zeta_{10}^{3})q^{3}-\zeta_{10}^{2}q^{4}-q^{5}+\cdots$
275.1.v.a	$275$	$1$	275.v	275.v	$10$	$4$	$1$	$0.137$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	275.1.v.a	$4$	$0$	$0$	$-2$	$4$	$0$		$1$		$q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+q^{5}+\cdots$
275.2.a.a	$275$	$2$	275.a	1.a	$1$	$1$	$1$	$2.196$	$\Q$	$_{}$	None	None	✓				55.2.a.a	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}-q^{11}-2q^{13}+\cdots$
275.2.a.b	$275$	$2$	275.a	1.a	$1$	$1$	$1$	$2.196$	$\Q$	$_{}$	None	None	✓				11.2.a.a	$1$	$0$	$2$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+2q^{7}+\cdots$
275.2.a.c	$275$	$2$	275.a	1.a	$1$	$2$	$2$	$2.196$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				55.2.a.b	$1$	$0$	$-2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-2\beta q^{3}+(1-2\beta )q^{4}+\cdots$
275.2.a.d	$275$	$2$	275.a	1.a	$1$	$2$	$2$	$2.196$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	275.2.a.d	$1$	$1$	$-1$	$-3$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
275.2.a.e	$275$	$2$	275.a	1.a	$1$	$2$	$2$	$2.196$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓	✓		275.2.a.e	$1$	$1$	$-1$	$-1$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-3q^{6}+\cdots$
275.2.a.f	$275$	$2$	275.a	1.a	$1$	$2$	$2$	$2.196$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			275.2.a.e	$1$	$0$	$1$	$1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}-3q^{6}+\cdots$
275.2.a.g	$275$	$2$	275.a	1.a	$1$	$2$	$2$	$2.196$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			275.2.a.d	$1$	$0$	$1$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{6}+\cdots$
275.2.a.h	$275$	$2$	275.a	1.a	$1$	$4$	$4$	$2.196$	$\Q(\sqrt{3}, \sqrt{11})$	$_{}$	None	None	✓		✓		55.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(2+\beta _{3})q^{4}+\cdots$
275.2.b.a	$275$	$2$	275.b	5.b	$2$	$2$	$2$	$2.196$	$\Q(\sqrt{-1}) $	$_{}$	None	None					11.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-i q^{3}-2 q^{4}+2 q^{6}+2 i q^{7}+\cdots$
275.2.b.b	$275$	$2$	275.b	5.b	$2$	$2$	$2$	$2.196$	$\Q(\sqrt{-1}) $	$_{}$	None	None					55.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+3 i q^{8}+3 q^{9}-q^{11}+\cdots$
275.2.b.c	$275$	$2$	275.b	5.b	$2$	$4$	$4$	$2.196$	$\Q(i, \sqrt{13})$	$_{}$	None	None		✓			275.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{3})q^{4}+\cdots$
275.2.b.d	$275$	$2$	275.b	5.b	$2$	$4$	$4$	$2.196$	$\Q(\zeta_{8})$	$_{}$	None	None					55.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}+(-\beta_{3}-1)q^{4}+\cdots$
275.2.b.e	$275$	$2$	275.b	5.b	$2$	$4$	$4$	$2.196$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			275.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
275.2.e.a	$275$	$2$	275.e	55.e	$4$	$4$	$2$	$2.196$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None					55.2.e.b	$4$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{4}]$	$q+(\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{4}+(-1+3\beta _{1}+\cdots)q^{9}+\cdots$
275.2.e.b	$275$	$2$	275.e	55.e	$4$	$4$	$2$	$2.196$	$\Q(i, \sqrt{10})$	$_{}$	None	None					55.2.e.a	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+3\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
275.2.e.c	$275$	$2$	275.e	55.e	$4$	$8$	$4$	$2.196$	8.0.1499238400.2	$_{}$	$\Q(\sqrt{-55}) $	None		✓			275.2.e.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{2}q^{2}+(-2\beta _{4}-\beta _{6})q^{4}+\beta _{5}q^{7}+\cdots$
275.2.e.d	$275$	$2$	275.e	55.e	$4$	$16$	$8$	$2.196$	16.0.$\cdots$.2	$_{}$	None	None		✓	✓		275.2.e.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{9}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{4}-\beta _{7}+\cdots)q^{4}+\cdots$
275.2.g.a	$275$	$2$	275.g	275.g	$5$	$112$	$28$	$2.196$		$_{}$	None	None		✓	✓	✓	275.2.g.a	$2$	$0$	$-1$	$1$	$0$	$-4$			$\mathrm{SU}(2)[C_{5}]$
275.2.h.a	$275$	$2$	275.h	11.c	$5$	$8$	$2$	$2.196$	8.0.13140625.1	$_{}$	None	None					55.2.g.b	$2$	$0$	$2$	$5$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
275.2.h.b	$275$	$2$	275.h	11.c	$5$	$8$	$2$	$2.196$	8.0.159390625.1	$_{}$	None	None					55.2.g.a	$2$	$0$	$4$	$-1$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$
275.2.h.c	$275$	$2$	275.h	11.c	$5$	$16$	$4$	$2.196$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			275.2.h.c	$2$	$0$	$0$	$-2$	$0$	$4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{14}q^{3}+(-1+\cdots)q^{4}+\cdots$
275.2.h.d	$275$	$2$	275.h	11.c	$5$	$16$	$4$	$2.196$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					55.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}+\beta _{12}+\beta _{13})q^{2}+(-\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots$
275.2.h.e	$275$	$2$	275.h	11.c	$5$	$16$	$4$	$2.196$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			275.2.h.c	$2$	$0$	$0$	$2$	$0$	$-4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}-\beta _{5}+\beta _{9})q^{2}+\beta _{14}q^{3}+(-1+\cdots)q^{4}+\cdots$
275.2.i.a	$275$	$2$	275.i	25.d	$5$	$44$	$11$	$2.196$		$_{}$	None	None		✓			275.2.i.a	$2$	$0$	$-1$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{5}]$
275.2.i.b	$275$	$2$	275.i	25.d	$5$	$60$	$15$	$2.196$		$_{}$	None	None		✓	✓		275.2.i.b	$2$	$0$	$-1$	$-2$	$6$	$0$			$\mathrm{SU}(2)[C_{5}]$
275.2.j.a	$275$	$2$	275.j	275.j	$5$	$112$	$28$	$2.196$		$_{}$	None	None		✓	✓	✓	275.2.g.a	$2$	$0$	$-1$	$-4$	$-5$	$-4$			$\mathrm{SU}(2)[C_{5}]$
275.2.k.a	$275$	$2$	275.k	275.k	$5$	$4$	$1$	$2.196$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			275.2.k.a	$2$	$1$	$-2$	$-6$	$-5$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}+\zeta_{10}^{3})q^{2}+(-2-\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
275.2.k.b	$275$	$2$	275.k	275.k	$5$	$4$	$1$	$2.196$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			275.2.k.b	$2$	$1$	$-2$	$-6$	$-5$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}+\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
275.2.k.c	$275$	$2$	275.k	275.k	$5$	$4$	$1$	$2.196$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			275.2.k.c	$2$	$0$	$1$	$0$	$5$	$-10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{3}q^{2}+(1+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{3}+\cdots$
275.2.k.d	$275$	$2$	275.k	275.k	$5$	$100$	$25$	$2.196$		$_{}$	None	None		✓	✓		275.2.k.d	$2$	$0$	$2$	$8$	$0$	$5$			$\mathrm{SU}(2)[C_{5}]$
275.2.l.a	$275$	$2$	275.l	275.l	$5$	$4$	$1$	$2.196$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			275.2.k.c	$2$	$1$	$-4$	$-5$	$-5$	$-10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-q^{2}+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots$
275.2.l.b	$275$	$2$	275.l	275.l	$5$	$4$	$1$	$2.196$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			275.2.k.b	$2$	$1$	$-2$	$-1$	$-5$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(1-2\zeta_{10}+\cdots)q^{3}+\cdots$
275.2.l.c	$275$	$2$	275.l	275.l	$5$	$4$	$1$	$2.196$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			275.2.k.a	$2$	$0$	$-2$	$4$	$5$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(2-\zeta_{10}+\cdots)q^{3}+\cdots$
275.2.l.d	$275$	$2$	275.l	275.l	$5$	$100$	$25$	$2.196$		$_{}$	None	None		✓	✓		275.2.k.d	$2$	$0$	$2$	$-2$	$5$	$5$			$\mathrm{SU}(2)[C_{5}]$
275.2.n.a	$275$	$2$	275.n	275.n	$10$	$112$	$28$	$2.196$		$_{}$	None	None		✓	✓	✓	275.2.n.a	$2$	$0$	$0$	$-10$	$-2$	$15$			$\mathrm{SU}(2)[C_{10}]$
275.2.t.a	$275$	$2$	275.t	275.t	$10$	$112$	$28$	$2.196$		$_{}$	None	None		✓	✓	✓	275.2.n.a	$2$	$0$	$-5$	$0$	$-7$	$-15$			$\mathrm{SU}(2)[C_{10}]$
275.2.y.a	$275$	$2$	275.y	25.e	$10$	$40$	$10$	$2.196$		$_{}$	None	None		✓			275.2.y.a	$2$	$0$	$0$	$0$	$5$	$0$			$\mathrm{SU}(2)[C_{10}]$
275.2.y.b	$275$	$2$	275.y	25.e	$10$	$56$	$14$	$2.196$		$_{}$	None	None		✓	✓		275.2.y.b	$2$	$0$	$0$	$0$	$-7$	$0$			$\mathrm{SU}(2)[C_{10}]$
275.2.z.a	$275$	$2$	275.z	55.j	$10$	$16$	$4$	$2.196$	16.0.$\cdots$.1	$_{}$	None	None					55.2.g.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{11}-\beta _{13}+\beta _{15})q^{3}+\cdots$
275.2.z.b	$275$	$2$	275.z	55.j	$10$	$16$	$4$	$2.196$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					55.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{6}+\beta _{12}-\beta _{15})q^{2}+(\beta _{14}-\beta _{15})q^{3}+\cdots$
275.2.z.c	$275$	$2$	275.z	55.j	$10$	$32$	$8$	$2.196$		$_{}$	None	None		✓	✓		275.2.h.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
275.2.ba.a	$275$	$2$	275.ba	275.aa	$10$	$112$	$28$	$2.196$		$_{}$	None	None		✓	✓	✓	275.2.ba.a	$2$	$0$	$-5$	$-5$	$-2$	$10$			$\mathrm{SU}(2)[C_{10}]$
275.2.bb.a	$275$	$2$	275.bb	275.ab	$10$	$112$	$28$	$2.196$		$_{}$	None	None		✓	✓	✓	275.2.ba.a	$2$	$0$	$-5$	$0$	$-7$	$-10$			$\mathrm{SU}(2)[C_{10}]$
275.2.bf.a	$275$	$2$	275.bf	275.af	$20$	$224$	$28$	$2.196$		$_{}$	None	None		✓	✓	✓	275.2.bf.a	$2$	$0$	$-10$	$-14$	$-2$	$-10$			$\mathrm{SU}(2)[C_{20}]$
275.2.bg.a	$275$	$2$	275.bg	275.ag	$20$	$224$	$28$	$2.196$		$_{}$	None	None		✓	✓	✓	275.2.bg.a	$2$	$0$	$-10$	$-4$	$-12$	$-30$			$\mathrm{SU}(2)[C_{20}]$
275.2.bl.a	$275$	$2$	275.bl	275.al	$20$	$224$	$28$	$2.196$		$_{}$	None	None		✓	✓	✓	275.2.bf.a	$2$	$0$	$-10$	$-4$	$-12$	$0$			$\mathrm{SU}(2)[C_{20}]$
275.2.bm.a	$275$	$2$	275.bm	55.l	$20$	$32$	$4$	$2.196$		$_{}$	None	None		✓			275.2.bm.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$

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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.