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 166 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
260.1.g.a	$260$	$1$	260.g	260.g	$2$	$1$	$1$	$0.130$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	✓			260.1.g.a	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{9}-q^{10}+\cdots$
260.1.g.b	$260$	$1$	260.g	260.g	$2$	$1$	$1$	$0.130$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	✓			260.1.g.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{9}-q^{10}+\cdots$
260.1.l.a	$260$	$1$	260.l	260.l	$4$	$2$	$1$	$0.130$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	260.1.l.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-i q^{2}-q^{4}+q^{5}+i q^{8}-i q^{9}+\cdots$
260.1.s.a	$260$	$1$	260.s	260.s	$4$	$2$	$1$	$0.130$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	260.1.l.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+i q^{5}-q^{8}+i q^{9}+\cdots$
260.1.w.a	$260$	$1$	260.w	260.w	$6$	$2$	$1$	$0.130$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			260.1.w.a	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots$
260.1.w.b	$260$	$1$	260.w	260.w	$6$	$2$	$1$	$0.130$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			260.1.w.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots$
260.1.be.a	$260$	$1$	260.be	260.ae	$12$	$4$	$1$	$0.130$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	260.1.be.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots$
260.1.bl.a	$260$	$1$	260.bl	260.al	$12$	$4$	$1$	$0.130$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	260.1.be.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
260.2.a.a	$260$	$2$	260.a	1.a	$1$	$1$	$1$	$2.076$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	260.2.a.a	$1$	$0$	$0$	$2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
260.2.a.b	$260$	$2$	260.a	1.a	$1$	$3$	$3$	$2.076$	3.3.564.1	$_{}$	None	None	✓	✓	✓	✓	260.2.a.b	$1$	$0$	$0$	$2$	$3$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots$
260.2.c.a	$260$	$2$	260.c	5.b	$2$	$6$	$6$	$2.076$	6.0.350464.1	$_{}$	None	None		✓	✓	✓	260.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+(-\beta _{1}-\beta _{4})q^{5}+(\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$
260.2.d.a	$260$	$2$	260.d	65.d	$2$	$8$	$8$	$2.076$	8.0.$\cdots$.3	$_{}$	None	None		✓	✓	✓	260.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}-\beta _{3}q^{5}+(\beta _{4}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots$
260.2.f.a	$260$	$2$	260.f	13.b	$2$	$6$	$6$	$2.076$	6.0.9144576.1	$_{}$	None	None		✓	✓	✓	260.2.f.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots$
260.2.i.a	$260$	$2$	260.i	13.c	$3$	$2$	$1$	$2.076$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			260.2.i.a	$2$	$0$	$0$	$-1$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
260.2.i.b	$260$	$2$	260.i	13.c	$3$	$2$	$1$	$2.076$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			260.2.i.b	$2$	$0$	$0$	$-1$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
260.2.i.c	$260$	$2$	260.i	13.c	$3$	$2$	$1$	$2.076$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			260.2.i.c	$2$	$0$	$0$	$1$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-q^{5}-5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
260.2.i.d	$260$	$2$	260.i	13.c	$3$	$2$	$1$	$2.076$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			260.2.i.d	$2$	$0$	$0$	$3$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}+q^{5}-3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$
260.2.j.a	$260$	$2$	260.j	52.f	$4$	$56$	$28$	$2.076$		$_{}$	None	None		✓	✓	✓	260.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
260.2.m.a	$260$	$2$	260.m	65.k	$4$	$2$	$1$	$2.076$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			260.2.m.a	$2$	$1$	$0$	$-4$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i-2)q^{3}+(2 i-1)q^{5}-4 i q^{7}+\cdots$
260.2.m.b	$260$	$2$	260.m	65.k	$4$	$4$	$2$	$2.076$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			260.2.m.b	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
260.2.m.c	$260$	$2$	260.m	65.k	$4$	$8$	$4$	$2.076$	8.0.$\cdots$.2	$_{}$	None	None		✓	✓		260.2.m.c	$2$	$0$	$0$	$2$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{3}+(\beta _{3}-\beta _{6})q^{5}+(\beta _{4}+\beta _{5})q^{7}+\cdots$
260.2.o.a	$260$	$2$	260.o	20.e	$4$	$72$	$36$	$2.076$		$_{}$	None	None		✓	✓	✓	260.2.o.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
260.2.p.a	$260$	$2$	260.p	260.p	$4$	$2$	$1$	$2.076$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.p.a	$4$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i-1)q^{2}-2 i q^{4}+(i+2)q^{5}+\cdots$
260.2.p.b	$260$	$2$	260.p	260.p	$4$	$2$	$1$	$2.076$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.p.a	$4$	$0$	$2$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i+1)q^{2}-2 i q^{4}+(-i-2)q^{5}+\cdots$
260.2.p.c	$260$	$2$	260.p	260.p	$4$	$8$	$4$	$2.076$	8.0.3317760000.5	$_{}$	None	None		✓			260.2.p.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots$
260.2.p.d	$260$	$2$	260.p	260.p	$4$	$64$	$32$	$2.076$		$_{}$	None	None		✓	✓		260.2.p.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
260.2.r.a	$260$	$2$	260.r	65.f	$4$	$2$	$1$	$2.076$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			260.2.m.a	$2$	$0$	$0$	$-4$	$4$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i-2)q^{3}+(-i+2)q^{5}+4 q^{7}+\cdots$
260.2.r.b	$260$	$2$	260.r	65.f	$4$	$4$	$2$	$2.076$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			260.2.m.b	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{9}+\cdots$
260.2.r.c	$260$	$2$	260.r	65.f	$4$	$8$	$4$	$2.076$	8.0.$\cdots$.2	$_{}$	None	None		✓	✓		260.2.m.c	$2$	$0$	$0$	$2$	$-2$	$-8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{7})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
260.2.u.a	$260$	$2$	260.u	260.u	$4$	$2$	$1$	$2.076$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.u.a	$4$	$1$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i-1)q^{2}-2 i q^{4}+(i-2)q^{5}+\cdots$
260.2.u.b	$260$	$2$	260.u	260.u	$4$	$2$	$1$	$2.076$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.u.a	$4$	$0$	$2$	$0$	$2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i+1)q^{2}-2 i q^{4}+(-2 i+1)q^{5}+\cdots$
260.2.u.c	$260$	$2$	260.u	260.u	$4$	$72$	$36$	$2.076$		$_{}$	None	None		✓	✓		260.2.u.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
260.2.x.a	$260$	$2$	260.x	13.e	$6$	$8$	$4$	$2.076$	8.0.22581504.2	$_{}$	None	None		✓	✓	✓	260.2.x.a	$2$	$0$	$0$	$-2$	$0$	$6$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{2}-\beta _{4}-2\beta _{6}-\beta _{7})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots$
260.2.z.a	$260$	$2$	260.z	65.l	$6$	$16$	$8$	$2.076$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	260.2.z.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{3}+\beta _{14}q^{5}-\beta _{8}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
260.2.ba.a	$260$	$2$	260.ba	65.n	$6$	$12$	$6$	$2.076$	12.0.$\cdots$.1	$_{}$	None	None		✓	✓	✓	260.2.ba.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}-\beta _{10})q^{3}+(-\beta _{7}-\beta _{11})q^{5}+\cdots$
260.2.bc.a	$260$	$2$	260.bc	260.ac	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.bc.a	$4$	$0$	$-2$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots$
260.2.bc.b	$260$	$2$	260.bc	260.ac	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.bc.a	$4$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots$
260.2.bc.c	$260$	$2$	260.bc	260.ac	$12$	$144$	$36$	$2.076$		$_{}$	None	None		✓	✓		260.2.bc.c	$8$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{12}]$
260.2.bf.a	$260$	$2$	260.bf	65.t	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			260.2.bf.a	$2$	$0$	$0$	$-2$	$8$	$4$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(2+\zeta_{12}^{3})q^{5}+\cdots$
260.2.bf.b	$260$	$2$	260.bf	65.t	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			260.2.bf.b	$2$	$0$	$0$	$4$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1-\zeta_{12})q^{3}+(-1+2\zeta_{12}^{3})q^{5}+\cdots$
260.2.bf.c	$260$	$2$	260.bf	65.t	$12$	$20$	$5$	$2.076$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		260.2.bf.c	$2$	$0$	$0$	$-2$	$-6$	$-6$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
260.2.bg.a	$260$	$2$	260.bg	260.ag	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.bg.a	$4$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+\cdots)q^{4}+\cdots$
260.2.bg.b	$260$	$2$	260.bg	260.ag	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.bg.a	$4$	$0$	$2$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{4}+\cdots$
260.2.bg.c	$260$	$2$	260.bg	260.ag	$12$	$144$	$36$	$2.076$		$_{}$	None	None		✓	✓		260.2.bg.c	$8$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
260.2.bj.a	$260$	$2$	260.bj	260.aj	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.bj.a	$4$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots$
260.2.bj.b	$260$	$2$	260.bj	260.aj	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			260.2.bj.a	$4$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots$
260.2.bj.c	$260$	$2$	260.bj	260.aj	$12$	$144$	$36$	$2.076$		$_{}$	None	None		✓	✓		260.2.bj.c	$8$	$0$	$-6$	$0$	$-24$	$0$			$\mathrm{SU}(2)[C_{12}]$
260.2.bk.a	$260$	$2$	260.bk	65.o	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			260.2.bf.b	$2$	$1$	$0$	$-2$	$-8$	$-12$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-2+\zeta_{12}^{3})q^{5}+\cdots$
260.2.bk.b	$260$	$2$	260.bk	65.o	$12$	$4$	$1$	$2.076$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			260.2.bf.a	$2$	$0$	$0$	$4$	$-4$	$6$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1+\zeta_{12})q^{3}+(-1-2\zeta_{12}^{3})q^{5}+\cdots$
260.2.bk.c	$260$	$2$	260.bk	65.o	$12$	$20$	$5$	$2.076$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		260.2.bf.c	$2$	$0$	$0$	$-2$	$12$	$6$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+2\beta _{7}+\cdots)q^{3}+\cdots$

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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.