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 112 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
340.1.ba.a	$340$	$1$	340.ba	340.aa	$8$	$4$	$1$	$0.170$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓			340.1.ba.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
340.1.ba.b	$340$	$1$	340.ba	340.aa	$8$	$4$	$1$	$0.170$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓			340.1.ba.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{3}q^{8}+\cdots$
340.1.bc.a	$340$	$1$	340.bc	340.ac	$16$	$8$	$1$	$0.170$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	340.1.bc.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}-\zeta_{16}^{6}q^{5}+\cdots$
340.1.bj.a	$340$	$1$	340.bj	340.aj	$16$	$8$	$1$	$0.170$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	340.1.bc.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{3}q^{5}+\cdots$
340.2.a.a	$340$	$2$	340.a	1.a	$1$	$1$	$1$	$2.715$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	340.2.a.a	$1$	$1$	$0$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-3q^{9}+2q^{11}-6q^{13}+\cdots$
340.2.a.b	$340$	$2$	340.a	1.a	$1$	$3$	$3$	$2.715$	3.3.404.1	$_{}$	None	None	✓	✓	✓	✓	340.2.a.b	$1$	$0$	$0$	$0$	$3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}-\beta _{2}q^{7}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots$
340.2.c.a	$340$	$2$	340.c	17.b	$2$	$6$	$6$	$2.715$	6.0.37161216.1	$_{}$	None	None		✓	✓	✓	340.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{4})q^{3}+\beta _{4}q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots$
340.2.e.a	$340$	$2$	340.e	5.b	$2$	$8$	$8$	$2.715$	8.0.2058981376.2	$_{}$	None	None		✓	✓	✓	340.2.e.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+\beta _{2}q^{5}+(\beta _{5}-\beta _{6}+\beta _{7})q^{7}+\cdots$
340.2.g.a	$340$	$2$	340.g	85.c	$2$	$8$	$8$	$2.715$	8.0.$\cdots$.4	$_{}$	None	None		✓	✓	✓	340.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{9}+\cdots$
340.2.i.a	$340$	$2$	340.i	340.i	$4$	$2$	$1$	$2.715$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.i.a	$4$	$0$	$2$	$0$	$2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i+1)q^{2}-2 i q^{4}+(2 i+1)q^{5}+\cdots$
340.2.i.b	$340$	$2$	340.i	340.i	$4$	$2$	$1$	$2.715$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.i.b	$4$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i+1)q^{2}-2 i q^{4}+(-i+2)q^{5}+\cdots$
340.2.i.c	$340$	$2$	340.i	340.i	$4$	$96$	$48$	$2.715$		$_{}$	None	None		✓	✓		340.2.i.c	$4$	$0$	$-4$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
340.2.l.a	$340$	$2$	340.l	20.e	$4$	$8$	$4$	$2.715$	8.0.18939904.2	$_{}$	None	None		✓			340.2.l.a	$4$	$0$	$4$	$0$	$-16$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{2}+\beta _{5}-\beta _{7})q^{2}+(-1-2\beta _{3}+\cdots)q^{3}+\cdots$
340.2.l.b	$340$	$2$	340.l	20.e	$4$	$88$	$44$	$2.715$		$_{}$	None	None		✓	✓		340.2.l.b	$4$	$0$	$-4$	$0$	$16$	$0$			$\mathrm{SU}(2)[C_{4}]$
340.2.m.a	$340$	$2$	340.m	85.j	$4$	$2$	$1$	$2.715$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			340.2.m.a	$2$	$1$	$0$	$-4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i-2)q^{3}+(i-2)q^{5}-5 i q^{9}+\cdots$
340.2.m.b	$340$	$2$	340.m	85.j	$4$	$2$	$1$	$2.715$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			340.2.m.a	$2$	$0$	$0$	$4$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i+2)q^{3}+(-2 i+1)q^{5}+\cdots$
340.2.m.c	$340$	$2$	340.m	85.j	$4$	$12$	$6$	$2.715$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		340.2.m.c	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{3}+(\beta _{3}-\beta _{9}+\beta _{10})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
340.2.o.a	$340$	$2$	340.o	17.c	$4$	$12$	$6$	$2.715$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓	✓	340.2.o.a	$2$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{6}+\beta _{7}+\beta _{10})q^{3}+\beta _{3}q^{5}+\cdots$
340.2.r.a	$340$	$2$	340.r	340.r	$4$	$2$	$1$	$2.715$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.r.a	$4$	$0$	$2$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(i-2)q^{5}+\cdots$
340.2.r.b	$340$	$2$	340.r	340.r	$4$	$2$	$1$	$2.715$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.r.a	$4$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(-i+2)q^{5}+\cdots$
340.2.r.c	$340$	$2$	340.r	340.r	$4$	$96$	$48$	$2.715$		$_{}$	None	None		✓	✓		340.2.r.c	$8$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
340.2.s.a	$340$	$2$	340.s	340.s	$4$	$2$	$1$	$2.715$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.i.b	$4$	$1$	$-2$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(2 i-1)q^{5}+\cdots$
340.2.s.b	$340$	$2$	340.s	340.s	$4$	$2$	$1$	$2.715$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.i.a	$4$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(i+2)q^{5}+\cdots$
340.2.s.c	$340$	$2$	340.s	340.s	$4$	$96$	$48$	$2.715$		$_{}$	None	None		✓	✓		340.2.i.c	$4$	$0$	$4$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
340.2.u.a	$340$	$2$	340.u	17.d	$8$	$24$	$6$	$2.715$		$_{}$	None	None		✓	✓	✓	340.2.u.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
340.2.w.a	$340$	$2$	340.w	340.w	$8$	$4$	$1$	$2.715$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.w.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+(-1+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
340.2.w.b	$340$	$2$	340.w	340.w	$8$	$4$	$1$	$2.715$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.w.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$
340.2.w.c	$340$	$2$	340.w	340.w	$8$	$8$	$2$	$2.715$	8.0.205520896.4	$_{}$	None	None		✓			340.2.w.c	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{8}]$	$q+(-\beta _{1}+\beta _{3})q^{2}+\beta _{7}q^{3}+2q^{4}+(-1+\cdots)q^{5}+\cdots$
340.2.w.d	$340$	$2$	340.w	340.w	$8$	$184$	$46$	$2.715$		$_{}$	None	None		✓	✓		340.2.w.d	$4$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
340.2.z.a	$340$	$2$	340.z	340.z	$8$	$4$	$1$	$2.715$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.w.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-2q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$
340.2.z.b	$340$	$2$	340.z	340.z	$8$	$4$	$1$	$2.715$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.w.b	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(1+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
340.2.z.c	$340$	$2$	340.z	340.z	$8$	$8$	$2$	$2.715$	8.0.205520896.4	$_{}$	None	None		✓			340.2.w.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{8}]$	$q+(\beta _{1}+\beta _{3})q^{2}+\beta _{5}q^{3}-2q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
340.2.z.d	$340$	$2$	340.z	340.z	$8$	$184$	$46$	$2.715$		$_{}$	None	None		✓	✓		340.2.w.d	$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{8}]$
340.2.bb.a	$340$	$2$	340.bb	85.m	$8$	$40$	$10$	$2.715$		$_{}$	None	None		✓	✓	✓	340.2.bb.a	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{8}]$
340.2.bd.a	$340$	$2$	340.bd	85.o	$16$	$72$	$9$	$2.715$		$_{}$	None	None		✓	✓	✓	340.2.bd.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
340.2.bf.a	$340$	$2$	340.bf	68.i	$16$	$288$	$36$	$2.715$		$_{}$	None	None		✓	✓	✓	340.2.bf.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
340.2.bg.a	$340$	$2$	340.bg	340.ag	$16$	$8$	$1$	$2.715$	$\Q(\zeta_{16})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.bg.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{16}]$	$q+(-\zeta_{16}-\zeta_{16}^{5})q^{2}+2\zeta_{16}^{6}q^{4}+\cdots$
340.2.bg.b	$340$	$2$	340.bg	340.ag	$16$	$8$	$1$	$2.715$	$\Q(\zeta_{16})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.2.bg.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{16}]$	$q+(\zeta_{16}+\zeta_{16}^{5})q^{2}+2\zeta_{16}^{6}q^{4}+(-\zeta_{16}^{2}+\cdots)q^{5}+\cdots$
340.2.bg.c	$340$	$2$	340.bg	340.ag	$16$	$384$	$48$	$2.715$		$_{}$	None	None		✓	✓		340.2.bg.c	$8$	$0$	$0$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{16}]$
340.2.bi.a	$340$	$2$	340.bi	85.r	$16$	$72$	$9$	$2.715$		$_{}$	None	None		✓	✓	✓	340.2.bd.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
340.3.b.a	$340$	$3$	340.b	4.b	$2$	$64$	$64$	$9.264$		$_{}$	None	None		✓	✓	✓	340.3.b.a	$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
340.3.d.a	$340$	$3$	340.d	340.d	$2$	$1$	$1$	$9.264$	$\Q$	$_{}$	$\Q(\sqrt{-85}) $	None	✓	✓			340.3.d.a	$2$	$0$	$-2$	$0$	$-5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}-5q^{5}-8q^{8}+9q^{9}+\cdots$
340.3.d.b	$340$	$3$	340.d	340.d	$2$	$1$	$1$	$9.264$	$\Q$	$_{}$	$\Q(\sqrt{-85}) $	None	✓	✓			340.3.d.a	$2$	$0$	$-2$	$0$	$5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+5q^{5}-8q^{8}+9q^{9}+\cdots$
340.3.d.c	$340$	$3$	340.d	340.d	$2$	$1$	$1$	$9.264$	$\Q$	$_{}$	$\Q(\sqrt{-85}) $	None	✓	✓			340.3.d.a	$2$	$0$	$2$	$0$	$-5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}-5q^{5}+8q^{8}+9q^{9}+\cdots$
340.3.d.d	$340$	$3$	340.d	340.d	$2$	$1$	$1$	$9.264$	$\Q$	$_{}$	$\Q(\sqrt{-85}) $	None	✓	✓			340.3.d.a	$2$	$0$	$2$	$0$	$5$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+5q^{5}+8q^{8}+9q^{9}+\cdots$
340.3.d.e	$340$	$3$	340.d	340.d	$2$	$2$	$2$	$9.264$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.3.d.e	$4$	$0$	$0$	$0$	$-6$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-4 q^{4}+(-2\beta-3)q^{5}-4\beta q^{8}+\cdots$
340.3.d.f	$340$	$3$	340.d	340.d	$2$	$2$	$2$	$9.264$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			340.3.d.e	$4$	$0$	$0$	$0$	$6$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-4 q^{4}+(2\beta+3)q^{5}-4\beta q^{8}+\cdots$
340.3.d.g	$340$	$3$	340.d	340.d	$2$	$96$	$96$	$9.264$		$_{}$	None	None		✓	✓		340.3.d.g	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
340.3.f.a	$340$	$3$	340.f	20.d	$2$	$96$	$96$	$9.264$		$_{}$	None	None		✓	✓	✓	340.3.f.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
340.3.h.a	$340$	$3$	340.h	68.d	$2$	$72$	$72$	$9.264$		$_{}$	None	None		✓	✓	✓	340.3.h.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.