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 195 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
420.1.o.a	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $		✓			420.1.o.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-i q^{2}-i q^{3}-q^{4}-q^{5}-q^{6}+\cdots$
420.1.o.b	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $		✓			420.1.o.a	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+i q^{2}-i q^{3}-q^{4}+q^{5}+q^{6}+\cdots$
420.1.be.a	$420$	$1$	420.be	420.ae	$6$	$4$	$2$	$0.210$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			420.1.be.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{5}+\cdots$
420.1.be.b	$420$	$1$	420.be	420.ae	$6$	$4$	$2$	$0.210$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			420.1.be.a	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
420.2.a.a	$420$	$2$	420.a	1.a	$1$	$1$	$1$	$3.354$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	420.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$
420.2.a.b	$420$	$2$	420.a	1.a	$1$	$1$	$1$	$3.354$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	420.2.a.b	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots$
420.2.a.c	$420$	$2$	420.a	1.a	$1$	$1$	$1$	$3.354$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	420.2.a.c	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$
420.2.a.d	$420$	$2$	420.a	1.a	$1$	$1$	$1$	$3.354$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	420.2.a.d	$1$	$0$	$0$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$
420.2.c.a	$420$	$2$	420.c	28.d	$2$	$16$	$16$	$3.354$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			420.2.c.a	$2$	$0$	$2$	$-16$	$0$	$-4$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots$
420.2.c.b	$420$	$2$	420.c	28.d	$2$	$16$	$16$	$3.354$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			420.2.c.a	$2$	$0$	$2$	$16$	$0$	$4$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots$
420.2.d.a	$420$	$2$	420.d	21.c	$2$	$2$	$2$	$3.354$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			420.2.d.a	$2$	$0$	$0$	$-3$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{3}-q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
420.2.d.b	$420$	$2$	420.d	21.c	$2$	$2$	$2$	$3.354$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			420.2.d.a	$2$	$0$	$0$	$3$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{6})q^{3}+q^{5}+(3-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
420.2.d.c	$420$	$2$	420.d	21.c	$2$	$4$	$4$	$3.354$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			420.2.d.c	$2$	$0$	$0$	$-2$	$4$	$-6$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
420.2.d.d	$420$	$2$	420.d	21.c	$2$	$4$	$4$	$3.354$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			420.2.d.c	$2$	$0$	$0$	$2$	$-4$	$-6$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
420.2.f.a	$420$	$2$	420.f	105.g	$2$	$8$	$8$	$3.354$	$\Q(\sqrt{-3}, \sqrt{-5}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-35}) $	None		✓			420.2.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}-\beta _{6})q^{7}+\cdots$
420.2.f.b	$420$	$2$	420.f	105.g	$2$	$8$	$8$	$3.354$	$\Q(i, \sqrt{2}, \sqrt{5})$	$_{}$	None	None		✓			420.2.f.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}-\beta _{2}q^{5}+(\beta _{5}+\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots$
420.2.i.a	$420$	$2$	420.i	140.c	$2$	$48$	$48$	$3.354$		$_{}$	None	None		✓	✓	✓	420.2.i.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
420.2.k.a	$420$	$2$	420.k	5.b	$2$	$2$	$2$	$3.354$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			420.2.k.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-i-2)q^{5}+i q^{7}-q^{9}+\cdots$
420.2.k.b	$420$	$2$	420.k	5.b	$2$	$2$	$2$	$3.354$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			420.2.k.b	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-i+2)q^{5}+i q^{7}-q^{9}+\cdots$
420.2.l.a	$420$	$2$	420.l	60.h	$2$	$4$	$4$	$3.354$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			420.2.l.a	$4$	$0$	$0$	$-4$	$0$	$4$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{2}+(\beta_{2}-1)q^{3}-2 q^{4}+\beta_{3} q^{5}+\cdots$
420.2.l.b	$420$	$2$	420.l	60.h	$2$	$4$	$4$	$3.354$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			420.2.l.a	$4$	$0$	$0$	$4$	$0$	$-4$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{2}+(-\beta_{2}+1)q^{3}-2 q^{4}+\cdots$
420.2.l.c	$420$	$2$	420.l	60.h	$2$	$8$	$8$	$3.354$	8.0.386672896.3	$_{}$	None	None		✓			420.2.l.c	$2$	$0$	$0$	$-2$	$-8$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{2}q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+\cdots$
420.2.l.d	$420$	$2$	420.l	60.h	$2$	$8$	$8$	$3.354$	8.0.386672896.3	$_{}$	None	None		✓			420.2.l.c	$2$	$0$	$0$	$-2$	$8$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{6}q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+\cdots$
420.2.l.e	$420$	$2$	420.l	60.h	$2$	$8$	$8$	$3.354$	8.0.386672896.3	$_{}$	None	None		✓			420.2.l.c	$2$	$0$	$0$	$2$	$-8$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{6}q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+\cdots$
420.2.l.f	$420$	$2$	420.l	60.h	$2$	$8$	$8$	$3.354$	8.0.386672896.3	$_{}$	None	None		✓			420.2.l.c	$2$	$0$	$0$	$2$	$8$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{2}q^{3}+(1-\beta _{4}-\beta _{6})q^{4}+\cdots$
420.2.l.g	$420$	$2$	420.l	60.h	$2$	$16$	$16$	$3.354$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			420.2.l.g	$4$	$0$	$0$	$0$	$0$	$-16$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{4}q^{3}+\beta _{11}q^{4}+\beta _{5}q^{5}+\cdots$
420.2.l.h	$420$	$2$	420.l	60.h	$2$	$16$	$16$	$3.354$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			420.2.l.g	$4$	$0$	$0$	$0$	$0$	$16$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{6}q^{3}+\beta _{11}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
420.2.n.a	$420$	$2$	420.n	12.b	$2$	$24$	$24$	$3.354$		$_{}$	None	None		✓			420.2.n.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
420.2.n.b	$420$	$2$	420.n	12.b	$2$	$24$	$24$	$3.354$		$_{}$	None	None		✓			420.2.n.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
420.2.q.a	$420$	$2$	420.q	7.c	$3$	$2$	$1$	$3.354$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			420.2.q.a	$2$	$0$	$0$	$1$	$-1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$
420.2.q.b	$420$	$2$	420.q	7.c	$3$	$2$	$1$	$3.354$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			420.2.q.b	$2$	$0$	$0$	$1$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$
420.2.q.c	$420$	$2$	420.q	7.c	$3$	$4$	$2$	$3.354$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		✓			420.2.q.c	$2$	$0$	$0$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+\beta _{1}q^{7}+(-1+\cdots)q^{9}+\cdots$
420.2.q.d	$420$	$2$	420.q	7.c	$3$	$4$	$2$	$3.354$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			420.2.q.d	$2$	$0$	$0$	$-2$	$2$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1})q^{3}-\beta _{1}q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$
420.2.s.a	$420$	$2$	420.s	15.e	$4$	$24$	$12$	$3.354$		$_{}$	None	None		✓	✓	✓	420.2.s.a	$4$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
420.2.t.a	$420$	$2$	420.t	20.e	$4$	$4$	$2$	$3.354$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			420.2.t.a	$4$	$0$	$4$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+2\zeta_{8}^{2}q^{4}+\cdots$
420.2.t.b	$420$	$2$	420.t	20.e	$4$	$4$	$2$	$3.354$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			420.2.t.b	$4$	$0$	$4$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+2\zeta_{8}^{2}q^{4}+\cdots$
420.2.t.c	$420$	$2$	420.t	20.e	$4$	$32$	$16$	$3.354$		$_{}$	None	None		✓			420.2.t.c	$4$	$0$	$-4$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
420.2.t.d	$420$	$2$	420.t	20.e	$4$	$32$	$16$	$3.354$		$_{}$	None	None		✓			420.2.t.d	$4$	$0$	$-4$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{4}]$
420.2.w.a	$420$	$2$	420.w	420.w	$4$	$8$	$4$	$3.354$	$\Q(i, \sqrt{6}, \sqrt{14})$	$_{}$	$\Q(\sqrt{-21}) $	None		✓			420.2.w.a	$8$	$0$	$-8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$
420.2.w.b	$420$	$2$	420.w	420.w	$4$	$8$	$4$	$3.354$	$\Q(i, \sqrt{6}, \sqrt{14})$	$_{}$	$\Q(\sqrt{-21}) $	None		✓			420.2.w.a	$8$	$0$	$8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
420.2.w.c	$420$	$2$	420.w	420.w	$4$	$160$	$80$	$3.354$		$_{}$	None	None		✓	✓		420.2.w.c	$16$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
420.2.x.a	$420$	$2$	420.x	35.f	$4$	$16$	$8$	$3.354$	16.0.$\cdots$.1	$_{}$	None	None		✓	✓	✓	420.2.x.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots$
420.2.ba.a	$420$	$2$	420.ba	420.aa	$6$	$8$	$4$	$3.354$	$\Q(\sqrt{-2}, \sqrt{-3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			420.2.ba.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{5}q^{2}+(\beta _{5}+\beta _{7})q^{3}+2\beta _{3}q^{4}-\beta _{6}q^{5}+\cdots$
420.2.ba.b	$420$	$2$	420.ba	420.aa	$6$	$8$	$4$	$3.354$	$\Q(\sqrt{-2}, \sqrt{-3}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			420.2.ba.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-\beta _{4}-\beta _{5})q^{2}+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+\cdots$
420.2.ba.c	$420$	$2$	420.ba	420.aa	$6$	$160$	$80$	$3.354$		$_{}$	None	None		✓	✓		420.2.ba.c	$16$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
420.2.bb.a	$420$	$2$	420.bb	35.j	$6$	$16$	$8$	$3.354$	16.0.$\cdots$.1	$_{}$	None	None		✓	✓	✓	420.2.bb.a	$4$	$0$	$0$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{6}q^{3}+(\beta _{1}+\beta _{14})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
420.2.bf.a	$420$	$2$	420.bf	84.n	$6$	$128$	$64$	$3.354$		$_{}$	None	None		✓	✓	✓	420.2.bf.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
420.2.bh.a	$420$	$2$	420.bh	21.g	$6$	$10$	$5$	$3.354$	10.0.$\cdots$.1	$_{}$	None	None		✓			420.2.bh.a	$2$	$0$	$0$	$-1$	$-5$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{3}+(-1-\beta _{7})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots$
420.2.bh.b	$420$	$2$	420.bh	21.g	$6$	$10$	$5$	$3.354$	10.0.$\cdots$.1	$_{}$	None	None		✓			420.2.bh.a	$2$	$0$	$0$	$1$	$5$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{3}+(1+\beta _{7})q^{5}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
420.2.bi.a	$420$	$2$	420.bi	28.f	$6$	$4$	$2$	$3.354$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			420.2.bi.a	$2$	$0$	$-4$	$2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{3}+\cdots$

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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.