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 277 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
560.1.p.a	$560$	$1$	560.p	35.c	$2$	$1$	$1$	$0.279$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓				140.1.h.a	$2$	$0$	$0$	$-1$	$-1$	$1$		$1$		$q-q^{3}-q^{5}+q^{7}+q^{11}+q^{13}+q^{15}+\cdots$
560.1.p.b	$560$	$1$	560.p	35.c	$2$	$1$	$1$	$0.279$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓				140.1.h.a	$2$	$0$	$0$	$1$	$1$	$-1$		$1$		$q+q^{3}+q^{5}-q^{7}+q^{11}-q^{13}+q^{15}+\cdots$
560.1.bt.a	$560$	$1$	560.bt	140.p	$6$	$4$	$2$	$0.279$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	560.1.bt.a	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots$
560.2.a.a	$560$	$2$	560.a	1.a	$1$	$1$	$1$	$4.472$	$\Q$	$_{}$	None	None	✓				140.2.a.b	$1$	$1$	$0$	$-3$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots$
560.2.a.b	$560$	$2$	560.a	1.a	$1$	$1$	$1$	$4.472$	$\Q$	$_{}$	None	None	✓		✓	✓	35.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+5q^{13}+\cdots$
560.2.a.c	$560$	$2$	560.a	1.a	$1$	$1$	$1$	$4.472$	$\Q$	$_{}$	None	None	✓		✓	✓	140.2.a.a	$1$	$1$	$0$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots$
560.2.a.d	$560$	$2$	560.a	1.a	$1$	$1$	$1$	$4.472$	$\Q$	$_{}$	None	None	✓				70.2.a.a	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-3q^{9}-4q^{11}-6q^{13}+\cdots$
560.2.a.e	$560$	$2$	560.a	1.a	$1$	$1$	$1$	$4.472$	$\Q$	$_{}$	None	None	✓				280.2.a.b	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}+5q^{11}+q^{13}+\cdots$
560.2.a.f	$560$	$2$	560.a	1.a	$1$	$1$	$1$	$4.472$	$\Q$	$_{}$	None	None	✓				280.2.a.a	$1$	$0$	$0$	$3$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots$
560.2.a.g	$560$	$2$	560.a	1.a	$1$	$2$	$2$	$4.472$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		280.2.a.d	$1$	$0$	$0$	$-1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}-q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots$
560.2.a.h	$560$	$2$	560.a	1.a	$1$	$2$	$2$	$4.472$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓		✓		280.2.a.c	$1$	$0$	$0$	$1$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+q^{7}+(5+\beta )q^{9}+(-4+\cdots)q^{11}+\cdots$
560.2.a.i	$560$	$2$	560.a	1.a	$1$	$2$	$2$	$4.472$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓	✓	35.2.a.b	$1$	$0$	$0$	$1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots$
560.2.e.a	$560$	$2$	560.e	140.c	$2$	$4$	$4$	$4.472$	$\Q(\sqrt{5}, \sqrt{-7})$	$_{}$	$\Q(\sqrt{-35}) $	None		✓			560.2.e.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}-4q^{9}+\beta _{3}q^{11}+\cdots$
560.2.e.b	$560$	$2$	560.e	140.c	$2$	$4$	$4$	$4.472$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			560.2.e.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}-2\beta _{2})q^{7}+q^{9}+\cdots$
560.2.e.c	$560$	$2$	560.e	140.c	$2$	$8$	$8$	$4.472$	8.0.121550625.1	$_{}$	$\Q(\sqrt{-35}) $	None		✓			560.2.e.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{6}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(-3+\cdots)q^{9}+\cdots$
560.2.e.d	$560$	$2$	560.e	140.c	$2$	$8$	$8$	$4.472$	8.0.$\cdots$.5	$_{}$	None	None		✓			560.2.e.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+2\beta _{3}q^{11}+\cdots$
560.2.g.a	$560$	$2$	560.g	5.b	$2$	$2$	$2$	$4.472$	$\Q(\sqrt{-1}) $	$_{}$	None	None					140.2.e.a	$2$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+(-2-i)q^{5}-iq^{7}-6q^{9}+\cdots$
560.2.g.b	$560$	$2$	560.g	5.b	$2$	$2$	$2$	$4.472$	$\Q(\sqrt{-1}) $	$_{}$	None	None					35.2.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-2-i)q^{5}+iq^{7}+2q^{9}+\cdots$
560.2.g.c	$560$	$2$	560.g	5.b	$2$	$2$	$2$	$4.472$	$\Q(\sqrt{-1}) $	$_{}$	None	None					140.2.e.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+2i)q^{5}-iq^{7}+3q^{9}-4iq^{13}+\cdots$
560.2.g.d	$560$	$2$	560.g	5.b	$2$	$2$	$2$	$4.472$	$\Q(\sqrt{-1}) $	$_{}$	None	None					280.2.g.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}+q^{11}+\cdots$
560.2.g.e	$560$	$2$	560.g	5.b	$2$	$4$	$4$	$4.472$	$\Q(i, \sqrt{6})$	$_{}$	None	None					70.2.c.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots$
560.2.g.f	$560$	$2$	560.g	5.b	$2$	$6$	$6$	$4.472$	6.0.5161984.1	$_{}$	None	None			✓		280.2.g.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+(\beta _{2}+\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots$
560.2.k.a	$560$	$2$	560.k	28.d	$2$	$8$	$8$	$4.472$	8.0.303595776.1	$_{}$	None	None		✓			560.2.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots$
560.2.k.b	$560$	$2$	560.k	28.d	$2$	$8$	$8$	$4.472$	8.0.$\cdots$.7	$_{}$	None	None		✓			560.2.k.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}+\beta _{3}q^{5}+(\beta _{4}-\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots$
560.2.q.a	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	$\Q(\sqrt{-3}) $	$_{}$	None	None					140.2.i.b	$2$	$1$	$0$	$-3$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$
560.2.q.b	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	$\Q(\sqrt{-3}) $	$_{}$	None	None					70.2.e.d	$2$	$0$	$0$	$-2$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
560.2.q.c	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	$\Q(\sqrt{-3}) $	$_{}$	None	None					280.2.q.c	$2$	$0$	$0$	$-2$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
560.2.q.d	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	$\Q(\sqrt{-3}) $	$_{}$	None	None					70.2.e.b	$2$	$0$	$0$	$-2$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
560.2.q.e	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	$\Q(\sqrt{-3}) $	$_{}$	None	None					280.2.q.b	$2$	$0$	$0$	$-1$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$
560.2.q.f	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	$\Q(\sqrt{-3}) $	$_{}$	None	None					140.2.i.a	$2$	$0$	$0$	$1$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$
560.2.q.g	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	$\Q(\sqrt{-3}) $	$_{}$	None	None					70.2.e.c	$2$	$0$	$0$	$1$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$
560.2.q.h	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	$\Q(\sqrt{-3}) $	$_{}$	None	None					280.2.q.a	$2$	$0$	$0$	$1$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots$
560.2.q.i	$560$	$2$	560.q	7.c	$3$	$2$	$1$	$4.472$	$\Q(\sqrt{-3}) $	$_{}$	None	None					70.2.e.a	$2$	$0$	$0$	$3$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$
560.2.q.j	$560$	$2$	560.q	7.c	$3$	$4$	$2$	$4.472$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					280.2.q.d	$2$	$0$	$0$	$-2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
560.2.q.k	$560$	$2$	560.q	7.c	$3$	$4$	$2$	$4.472$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None					35.2.e.a	$2$	$0$	$0$	$2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
560.2.q.l	$560$	$2$	560.q	7.c	$3$	$6$	$3$	$4.472$	6.0.11337408.1	$_{}$	None	None			✓		280.2.q.e	$2$	$0$	$0$	$0$	$-3$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
560.2.r.a	$560$	$2$	560.r	560.r	$4$	$184$	$92$	$4.472$		$_{}$	None	None		✓	✓	✓	560.2.r.a	$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
560.2.t.a	$560$	$2$	560.t	80.j	$4$	$144$	$72$	$4.472$		$_{}$	None	None		✓	✓	✓	560.2.t.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
560.2.x.a	$560$	$2$	560.x	20.e	$4$	$12$	$6$	$4.472$	12.0.$\cdots$.1	$_{}$	None	None		✓			560.2.x.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{4}-\beta _{8})q^{3}+(-\beta _{6}+\beta _{9})q^{5}+\cdots$
560.2.x.b	$560$	$2$	560.x	20.e	$4$	$24$	$12$	$4.472$		$_{}$	None	None		✓	✓		560.2.x.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
560.2.bb.a	$560$	$2$	560.bb	80.q	$4$	$2$	$1$	$4.472$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			560.2.bb.a	$2$	$1$	$-2$	$-2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+(-1-i)q^{3}+2iq^{4}+\cdots$
560.2.bb.b	$560$	$2$	560.bb	80.q	$4$	$2$	$1$	$4.472$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			560.2.bb.a	$2$	$0$	$2$	$2$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{2}+(1+i)q^{3}+2iq^{4}+(2+\cdots)q^{5}+\cdots$
560.2.bb.c	$560$	$2$	560.bb	80.q	$4$	$70$	$35$	$4.472$		$_{}$	None	None		✓			560.2.bb.c	$2$	$0$	$-2$	$-2$	$-4$	$-70$			$\mathrm{SU}(2)[C_{4}]$
560.2.bb.d	$560$	$2$	560.bb	80.q	$4$	$70$	$35$	$4.472$		$_{}$	None	None		✓			560.2.bb.c	$2$	$0$	$2$	$2$	$2$	$70$			$\mathrm{SU}(2)[C_{4}]$
560.2.bc.a	$560$	$2$	560.bc	112.j	$4$	$128$	$64$	$4.472$		$_{}$	None	None		✓	✓	✓	560.2.bc.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
560.2.bd.a	$560$	$2$	560.bd	16.e	$4$	$44$	$22$	$4.472$		$_{}$	None	None		✓			560.2.bd.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
560.2.bd.b	$560$	$2$	560.bd	16.e	$4$	$52$	$26$	$4.472$		$_{}$	None	None		✓	✓		560.2.bd.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
560.2.be.a	$560$	$2$	560.be	560.ae	$4$	$184$	$92$	$4.472$		$_{}$	None	None		✓	✓	✓	560.2.be.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
560.2.bj.a	$560$	$2$	560.bj	35.f	$4$	$4$	$2$	$4.472$	$\Q(i, \sqrt{10})$	$_{}$	None	None					35.2.f.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots$
560.2.bj.b	$560$	$2$	560.bj	35.f	$4$	$8$	$4$	$4.472$	8.0.$\cdots$.3	$_{}$	None	None					140.2.m.a	$4$	$0$	$0$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(\beta _{2}-\beta _{6})q^{5}+(-\beta _{4}+\beta _{6}+\cdots)q^{7}+\cdots$

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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.