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 66 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
1740.1.f.a	$1740$	$1$	1740.f	435.b	$2$	$1$	$1$	$0.868$	$\Q$	$D_{3}$	$\Q(\sqrt{-435}) $	None	✓	✓			1740.1.f.a	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-q^{3}-q^{5}+q^{9}-q^{11}+q^{15}+q^{23}+\cdots$
1740.1.f.b	$1740$	$1$	1740.f	435.b	$2$	$1$	$1$	$0.868$	$\Q$	$D_{3}$	$\Q(\sqrt{-435}) $	None	✓	✓			1740.1.f.a	$2$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-q^{3}+q^{5}+q^{9}+q^{11}-q^{15}-q^{23}+\cdots$
1740.1.f.c	$1740$	$1$	1740.f	435.b	$2$	$1$	$1$	$0.868$	$\Q$	$D_{3}$	$\Q(\sqrt{-435}) $	None	✓	✓			1740.1.f.a	$2$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+q^{3}-q^{5}+q^{9}+q^{11}-q^{15}+q^{23}+\cdots$
1740.1.f.d	$1740$	$1$	1740.f	435.b	$2$	$1$	$1$	$0.868$	$\Q$	$D_{3}$	$\Q(\sqrt{-435}) $	None	✓	✓			1740.1.f.a	$2$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{5}+q^{9}-q^{11}+q^{15}-q^{23}+\cdots$
1740.1.v.a	$1740$	$1$	1740.v	1740.v	$4$	$4$	$2$	$0.868$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-29}) $	None		✓			1740.1.v.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}-q^{5}-\zeta_{8}^{2}q^{6}+\cdots$
1740.1.v.b	$1740$	$1$	1740.v	1740.v	$4$	$4$	$2$	$0.868$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-29}) $	None		✓			1740.1.v.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+q^{5}+\zeta_{8}^{2}q^{6}+\cdots$
1740.1.v.c	$1740$	$1$	1740.v	1740.v	$4$	$8$	$4$	$0.868$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-29}) $	None		✓			1740.1.v.c	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{6}q^{4}+\cdots$
1740.1.v.d	$1740$	$1$	1740.v	1740.v	$4$	$8$	$4$	$0.868$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-29}) $	None		✓			1740.1.v.c	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{24}^{3}q^{2}-\zeta_{24}^{7}q^{3}+\zeta_{24}^{6}q^{4}+\cdots$
1740.1.bm.a	$1740$	$1$	1740.bm	1740.am	$4$	$4$	$2$	$0.868$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			1740.1.bm.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}-q^{5}+\zeta_{8}^{2}q^{6}+\cdots$
1740.1.bm.b	$1740$	$1$	1740.bm	1740.am	$4$	$4$	$2$	$0.868$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			1740.1.bm.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+q^{5}+\zeta_{8}^{2}q^{6}+\cdots$
1740.1.cf.a	$1740$	$1$	1740.cf	1740.bf	$28$	$24$	$2$	$0.868$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		✓			1740.1.cf.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{56}^{17}q^{2}-\zeta_{56}^{25}q^{3}-\zeta_{56}^{6}q^{4}+\cdots$
1740.1.cf.b	$1740$	$1$	1740.cf	1740.bf	$28$	$24$	$2$	$0.868$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		✓			1740.1.cf.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q+\zeta_{56}^{17}q^{2}-\zeta_{56}^{5}q^{3}-\zeta_{56}^{6}q^{4}+\cdots$
1740.2.a.a	$1740$	$2$	1740.a	1.a	$1$	$1$	$1$	$13.894$	$\Q$	$_{}$	None	None	✓	✓			1740.2.a.a	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-6q^{11}+6q^{13}+\cdots$
1740.2.a.b	$1740$	$2$	1740.a	1.a	$1$	$1$	$1$	$13.894$	$\Q$	$_{}$	None	None	✓	✓			1740.2.a.b	$1$	$0$	$0$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}+3q^{11}-2q^{13}+\cdots$
1740.2.a.c	$1740$	$2$	1740.a	1.a	$1$	$1$	$1$	$13.894$	$\Q$	$_{}$	None	None	✓	✓			1740.2.a.c	$1$	$1$	$0$	$-1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
1740.2.a.d	$1740$	$2$	1740.a	1.a	$1$	$1$	$1$	$13.894$	$\Q$	$_{}$	None	None	✓	✓			1740.2.a.d	$1$	$0$	$0$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}+3q^{13}+\cdots$
1740.2.a.e	$1740$	$2$	1740.a	1.a	$1$	$1$	$1$	$13.894$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1740.2.a.e	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}-3q^{11}-q^{13}+\cdots$
1740.2.a.f	$1740$	$2$	1740.a	1.a	$1$	$1$	$1$	$13.894$	$\Q$	$_{}$	None	None	✓	✓			1740.2.a.f	$1$	$0$	$0$	$1$	$1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-5q^{7}+q^{9}+5q^{11}-5q^{13}+\cdots$
1740.2.a.g	$1740$	$2$	1740.a	1.a	$1$	$1$	$1$	$13.894$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1740.2.a.g	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}+q^{13}+\cdots$
1740.2.a.h	$1740$	$2$	1740.a	1.a	$1$	$1$	$1$	$13.894$	$\Q$	$_{}$	None	None	✓	✓			1740.2.a.h	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
1740.2.a.i	$1740$	$2$	1740.a	1.a	$1$	$2$	$2$	$13.894$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓	✓		1740.2.a.i	$1$	$1$	$0$	$-2$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-\beta q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
1740.2.a.j	$1740$	$2$	1740.a	1.a	$1$	$2$	$2$	$13.894$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	1740.2.a.j	$1$	$0$	$0$	$-2$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
1740.2.a.k	$1740$	$2$	1740.a	1.a	$1$	$2$	$2$	$13.894$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓		1740.2.a.k	$1$	$1$	$0$	$-2$	$2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-2-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$
1740.2.a.l	$1740$	$2$	1740.a	1.a	$1$	$2$	$2$	$13.894$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓			1740.2.a.l	$1$	$0$	$0$	$2$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
1740.2.a.m	$1740$	$2$	1740.a	1.a	$1$	$2$	$2$	$13.894$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			1740.2.a.m	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
1740.2.a.n	$1740$	$2$	1740.a	1.a	$1$	$2$	$2$	$13.894$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	✓	✓		1740.2.a.n	$1$	$0$	$0$	$2$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
1740.2.b.a	$1740$	$2$	1740.b	145.d	$2$	$14$	$14$	$13.894$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			1740.2.b.a	$2$	$0$	$0$	$-14$	$2$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}-\beta _{9}q^{7}+q^{9}-\beta _{5}q^{11}+\cdots$
1740.2.b.b	$1740$	$2$	1740.b	145.d	$2$	$14$	$14$	$13.894$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			1740.2.b.a	$2$	$0$	$0$	$14$	$2$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}-\beta _{9}q^{7}+q^{9}+\beta _{5}q^{11}+\cdots$
1740.2.g.a	$1740$	$2$	1740.g	5.b	$2$	$2$	$2$	$13.894$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1740.2.g.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots$
1740.2.g.b	$1740$	$2$	1740.g	5.b	$2$	$2$	$2$	$13.894$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1740.2.g.b	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-2-i)q^{5}+2iq^{7}-q^{9}+\cdots$
1740.2.g.c	$1740$	$2$	1740.g	5.b	$2$	$12$	$12$	$13.894$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1740.2.g.c	$2$	$0$	$0$	$0$	$2$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{9}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots$
1740.2.g.d	$1740$	$2$	1740.g	5.b	$2$	$12$	$12$	$13.894$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1740.2.g.d	$2$	$0$	$0$	$0$	$2$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+\beta _{9}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
1740.2.l.a	$1740$	$2$	1740.l	29.b	$2$	$2$	$2$	$13.894$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1740.2.l.a	$2$	$0$	$0$	$0$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+q^{5}+q^{7}-q^{9}-3iq^{11}+\cdots$
1740.2.l.b	$1740$	$2$	1740.l	29.b	$2$	$2$	$2$	$13.894$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1740.2.l.b	$2$	$0$	$0$	$0$	$2$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+q^{5}+4q^{7}-q^{9}-3iq^{11}+\cdots$
1740.2.l.c	$1740$	$2$	1740.l	29.b	$2$	$6$	$6$	$13.894$	6.0.399424.1	$_{}$	None	None		✓			1740.2.l.c	$2$	$0$	$0$	$0$	$6$	$-6$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+q^{5}+(-1-\beta _{1})q^{7}-q^{9}+\cdots$
1740.2.l.d	$1740$	$2$	1740.l	29.b	$2$	$10$	$10$	$13.894$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓	✓		1740.2.l.d	$2$	$0$	$0$	$0$	$-10$	$-4$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}-q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots$
1740.2.bb.a	$1740$	$2$	1740.bb	145.e	$4$	$2$	$1$	$13.894$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1740.2.bb.a	$2$	$0$	$0$	$-2$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{3}+(2-i)q^{5}+(2+2i)q^{7}+q^{9}+\cdots$
1740.2.bb.b	$1740$	$2$	1740.bb	145.e	$4$	$28$	$14$	$13.894$		$_{}$	None	None		✓			1740.2.bb.b	$2$	$0$	$0$	$-28$	$-4$	$-4$			$\mathrm{SU}(2)[C_{4}]$
1740.2.bb.c	$1740$	$2$	1740.bb	145.e	$4$	$30$	$15$	$13.894$		$_{}$	None	None		✓	✓		1740.2.bb.c	$2$	$0$	$0$	$30$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1740.2.bc.a	$1740$	$2$	1740.bc	145.j	$4$	$2$	$1$	$13.894$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1740.2.bb.a	$2$	$1$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-iq^{3}+(-2-i)q^{5}+(2-2i)q^{7}+\cdots$
1740.2.bc.b	$1740$	$2$	1740.bc	145.j	$4$	$28$	$14$	$13.894$		$_{}$	None	None		✓			1740.2.bb.b	$2$	$0$	$0$	$0$	$4$	$-4$			$\mathrm{SU}(2)[C_{4}]$
1740.2.bc.c	$1740$	$2$	1740.bc	145.j	$4$	$30$	$15$	$13.894$		$_{}$	None	None		✓	✓		1740.2.bb.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1740.2.bk.a	$1740$	$2$	1740.bk	87.f	$4$	$4$	$2$	$13.894$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1740.2.bk.a	$2$	$1$	$0$	$-4$	$-4$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{8}+\zeta_{8}^{2})q^{3}-q^{5}+(-2+\cdots)q^{7}+\cdots$
1740.2.bk.b	$1740$	$2$	1740.bk	87.f	$4$	$4$	$2$	$13.894$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1740.2.bk.a	$2$	$0$	$0$	$4$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\zeta_{8}-\zeta_{8}^{2})q^{3}+q^{5}+(-2-\zeta_{8}+\cdots)q^{7}+\cdots$
1740.2.bk.c	$1740$	$2$	1740.bk	87.f	$4$	$36$	$18$	$13.894$		$_{}$	None	None		✓			1740.2.bk.c	$2$	$0$	$0$	$-6$	$36$	$8$			$\mathrm{SU}(2)[C_{4}]$
1740.2.bk.d	$1740$	$2$	1740.bk	87.f	$4$	$36$	$18$	$13.894$		$_{}$	None	None		✓			1740.2.bk.c	$2$	$0$	$0$	$6$	$-36$	$8$			$\mathrm{SU}(2)[C_{4}]$
1740.3.m.a	$1740$	$3$	1740.m	3.b	$2$	$4$	$4$	$47.412$	$\Q(\sqrt{-5}, \sqrt{-29})$	$_{}$	None	None		✓			1740.3.m.a	$2$	$0$	$0$	$-8$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{2})q^{3}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots$
1740.3.m.b	$1740$	$3$	1740.m	3.b	$2$	$72$	$72$	$47.412$		$_{}$	None	None		✓	✓		1740.3.m.b	$2$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{2}]$
1740.3.p.a	$1740$	$3$	1740.p	87.d	$2$	$80$	$80$	$47.412$		$_{}$	None	None		✓	✓	✓	1740.3.p.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1740.3.bl.a	$1740$	$3$	1740.bl	29.c	$4$	$80$	$40$	$47.412$		$_{}$	None	None		✓	✓	✓	1740.3.bl.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.