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 108 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
1332.1.b.a	$1332$	$1$	1332.b	148.b	$2$	$1$	$1$	$0.665$	$\Q$	$D_{2}$	$\Q(\sqrt{-111}) $, $\Q(\sqrt{-37}) $	$\Q(\sqrt{3}) $	✓	✓			1332.1.b.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{23}+q^{25}+\cdots$
1332.1.b.b	$1332$	$1$	1332.b	148.b	$2$	$1$	$1$	$0.665$	$\Q$	$D_{2}$	$\Q(\sqrt{-111}) $, $\Q(\sqrt{-37}) $	$\Q(\sqrt{3}) $	✓	✓			1332.1.b.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{23}+q^{25}+\cdots$
1332.1.b.c	$1332$	$1$	1332.b	148.b	$2$	$2$	$2$	$0.665$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{111}) $		✓			1332.1.b.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}-2 i q^{5}+i q^{8}-2 q^{10}+\cdots$
1332.1.b.d	$1332$	$1$	1332.b	148.b	$2$	$4$	$4$	$0.665$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-111}) $	None		✓	✓		1332.1.b.d	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
1332.1.m.a	$1332$	$1$	1332.m	444.j	$4$	$4$	$2$	$0.665$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1332.1.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}+(1-\zeta_{8}^{2}+\cdots)q^{13}+\cdots$
1332.1.o.a	$1332$	$1$	1332.o	37.d	$4$	$2$	$1$	$0.665$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None			✓	✓	148.1.f.a	$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{7}-i q^{11}+(-i+1)q^{17}+(-i+1)q^{19}+\cdots$
1332.1.y.a	$1332$	$1$	1332.y	148.i	$6$	$2$	$1$	$0.665$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None			✓	✓	148.1.i.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-q^{8}-q^{10}+\cdots$
1332.1.bj.a	$1332$	$1$	1332.bj	148.j	$6$	$4$	$2$	$0.665$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1332.1.bj.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
1332.1.cd.a	$1332$	$1$	1332.cd	444.x	$12$	$8$	$2$	$0.665$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1332.1.cd.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}^{3}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots$
1332.1.cy.a	$1332$	$1$	1332.cy	148.o	$18$	$12$	$2$	$0.665$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1332.1.cy.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{13}q^{2}-\zeta_{36}^{8}q^{4}+(-\zeta_{36}^{7}+\cdots)q^{5}+\cdots$
1332.1.cz.a	$1332$	$1$	1332.cz	148.p	$18$	$6$	$1$	$0.665$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None			✓	✓	148.1.p.a	$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}^{6}+\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
1332.1.dm.a	$1332$	$1$	1332.dm	444.ai	$36$	$24$	$2$	$0.665$	$\Q(\zeta_{72})$	$D_{36}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1332.1.dm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{72}^{35}q^{2}-\zeta_{72}^{34}q^{4}+(-\zeta_{72}^{3}+\cdots)q^{5}+\cdots$
1332.1.dn.a	$1332$	$1$	1332.dn	37.i	$36$	$12$	$1$	$0.665$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1332.1.dn.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{36}^{5}-\zeta_{36}^{15})q^{7}+(\zeta_{36}^{8}-\zeta_{36}^{9}+\cdots)q^{13}+\cdots$
1332.2.a.a	$1332$	$2$	1332.a	1.a	$1$	$1$	$1$	$10.636$	$\Q$	$_{}$	None	None	✓	✓			1332.2.a.a	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{11}-6q^{13}+6q^{17}-4q^{19}+\cdots$
1332.2.a.b	$1332$	$2$	1332.a	1.a	$1$	$1$	$1$	$10.636$	$\Q$	$_{}$	None	None	✓				444.2.a.a	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{11}-2q^{13}+6q^{19}-8q^{23}+\cdots$
1332.2.a.c	$1332$	$2$	1332.a	1.a	$1$	$1$	$1$	$10.636$	$\Q$	$_{}$	None	None	✓				444.2.a.b	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+4q^{11}-6q^{13}-6q^{17}+\cdots$
1332.2.a.d	$1332$	$2$	1332.a	1.a	$1$	$1$	$1$	$10.636$	$\Q$	$_{}$	None	None	✓	✓			1332.2.a.a	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{11}-6q^{13}-6q^{17}-4q^{19}+\cdots$
1332.2.a.e	$1332$	$2$	1332.a	1.a	$1$	$1$	$1$	$10.636$	$\Q$	$_{}$	None	None	✓				148.2.a.a	$1$	$0$	$0$	$0$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-3q^{7}-5q^{11}+6q^{17}+2q^{19}+\cdots$
1332.2.a.f	$1332$	$2$	1332.a	1.a	$1$	$2$	$2$	$10.636$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		148.2.a.b	$1$	$1$	$0$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+(1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots$
1332.2.a.g	$1332$	$2$	1332.a	1.a	$1$	$2$	$2$	$10.636$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓				444.2.a.d	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+2q^{7}+(2+2\beta )q^{13}-\beta q^{17}+\cdots$
1332.2.a.h	$1332$	$2$	1332.a	1.a	$1$	$2$	$2$	$10.636$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				444.2.a.c	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+2\beta q^{7}+4q^{11}-2\beta q^{13}+\cdots$
1332.2.a.i	$1332$	$2$	1332.a	1.a	$1$	$4$	$4$	$10.636$	4.4.7168.1	$_{}$	None	None	✓	✓	✓	✓	1332.2.a.i	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(2+\beta _{3})q^{7}+\beta _{2}q^{11}+2q^{13}+\cdots$
1332.2.c.a	$1332$	$2$	1332.c	12.b	$2$	$36$	$36$	$10.636$		$_{}$	None	None		✓			1332.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1332.2.c.b	$1332$	$2$	1332.c	12.b	$2$	$36$	$36$	$10.636$		$_{}$	None	None		✓			1332.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1332.2.e.a	$1332$	$2$	1332.e	37.b	$2$	$2$	$2$	$10.636$	$\Q(\sqrt{-3}) $	$_{}$	None	None					148.2.d.a	$2$	$0$	$0$	$0$	$0$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}+q^{7}-3 q^{11}-\beta q^{13}+\beta q^{17}+\cdots$
1332.2.e.b	$1332$	$2$	1332.e	37.b	$2$	$2$	$2$	$10.636$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			1332.2.e.b	$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+4 q^{7}-2\beta q^{13}+\beta q^{19}+5 q^{25}+\cdots$
1332.2.e.c	$1332$	$2$	1332.e	37.b	$2$	$4$	$4$	$10.636$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			1332.2.e.c	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{3}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}-2q^{7}+\beta _{3}q^{11}-\beta _{2}q^{17}+\cdots$
1332.2.e.d	$1332$	$2$	1332.e	37.b	$2$	$4$	$4$	$10.636$	4.0.32448.1	$_{}$	None	None					444.2.e.b	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}-2\beta _{1}q^{13}+\cdots$
1332.2.e.e	$1332$	$2$	1332.e	37.b	$2$	$4$	$4$	$10.636$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None					444.2.e.a	$2$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+(1-\beta _{3})q^{7}+(2-2\beta _{3})q^{11}+\cdots$
1332.2.g.a	$1332$	$2$	1332.g	444.g	$2$	$4$	$4$	$10.636$	$\Q(\sqrt{-2}, \sqrt{37})$	$_{}$	$\Q(\sqrt{-37}) $	None		✓			1332.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+4q^{16}+\cdots$
1332.2.g.b	$1332$	$2$	1332.g	444.g	$2$	$4$	$4$	$10.636$	$\Q(\sqrt{-2}, \sqrt{37})$	$_{}$	$\Q(\sqrt{-37}) $	None		✓			1332.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+4q^{16}+\cdots$
1332.2.g.c	$1332$	$2$	1332.g	444.g	$2$	$4$	$4$	$10.636$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			1332.2.g.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta_{2} q^{2}+2 q^{4}+\beta_{2} q^{5}-2\beta_{2} q^{8}+\cdots$
1332.2.g.d	$1332$	$2$	1332.g	444.g	$2$	$64$	$64$	$10.636$		$_{}$	None	None		✓	✓		1332.2.g.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1332.2.i.a	$1332$	$2$	1332.i	9.c	$3$	$2$	$1$	$10.636$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1332.2.i.a	$2$	$0$	$0$	$0$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
1332.2.i.b	$1332$	$2$	1332.i	9.c	$3$	$2$	$1$	$10.636$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1332.2.i.b	$2$	$0$	$0$	$0$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
1332.2.i.c	$1332$	$2$	1332.i	9.c	$3$	$34$	$17$	$10.636$		$_{}$	None	None		✓			1332.2.i.c	$2$	$0$	$0$	$1$	$-7$	$-1$			$\mathrm{SU}(2)[C_{3}]$
1332.2.i.d	$1332$	$2$	1332.i	9.c	$3$	$34$	$17$	$10.636$		$_{}$	None	None		✓			1332.2.i.d	$2$	$0$	$0$	$1$	$7$	$-1$			$\mathrm{SU}(2)[C_{3}]$
1332.2.j.a	$1332$	$2$	1332.j	37.c	$3$	$2$	$1$	$10.636$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			1332.2.j.a	$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q-5\zeta_{6}q^{7}+7\zeta_{6}q^{13}-8\zeta_{6}q^{19}+(5+\cdots)q^{25}+\cdots$
1332.2.j.b	$1332$	$2$	1332.j	37.c	$3$	$2$	$1$	$10.636$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			1332.2.j.b	$4$	$0$	$0$	$0$	$0$	$1$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+\zeta_{6}q^{7}-5\zeta_{6}q^{13}-8\zeta_{6}q^{19}+(5+\cdots)q^{25}+\cdots$
1332.2.j.c	$1332$	$2$	1332.j	37.c	$3$	$2$	$1$	$10.636$	$\Q(\sqrt{-3}) $	$_{}$	None	None					444.2.i.a	$2$	$0$	$0$	$0$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+3\zeta_{6}q^{7}-2q^{11}+3\zeta_{6}q^{13}+\cdots$
1332.2.j.d	$1332$	$2$	1332.j	37.c	$3$	$4$	$2$	$10.636$	$\Q(\sqrt{-3}, \sqrt{37})$	$_{}$	None	None					444.2.i.b	$2$	$0$	$0$	$0$	$-1$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{5}-3\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots$
1332.2.j.e	$1332$	$2$	1332.j	37.c	$3$	$6$	$3$	$10.636$	6.0.27870912.1	$_{}$	None	None					148.2.e.a	$2$	$0$	$0$	$0$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4})q^{5}+(\beta _{1}+\beta _{2}+\beta _{5})q^{7}+\cdots$
1332.2.j.f	$1332$	$2$	1332.j	37.c	$3$	$6$	$3$	$10.636$	6.0.27379323.1	$_{}$	None	None					444.2.i.c	$2$	$0$	$0$	$0$	$1$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{5}-\beta _{4}q^{7}+\beta _{3}q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
1332.2.j.g	$1332$	$2$	1332.j	37.c	$3$	$12$	$6$	$10.636$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		1332.2.j.g	$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{6})q^{5}+(-\beta _{4}-\beta _{5}-\beta _{7})q^{7}+\cdots$
1332.2.k.a	$1332$	$2$	1332.k	333.g	$3$	$2$	$1$	$10.636$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1332.2.k.a	$2$	$0$	$0$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-3q^{9}+\cdots$
1332.2.k.b	$1332$	$2$	1332.k	333.g	$3$	$74$	$37$	$10.636$		$_{}$	None	None		✓	✓		1332.2.k.b	$2$	$0$	$0$	$-1$	$-3$	$2$			$\mathrm{SU}(2)[C_{3}]$
1332.2.l.a	$1332$	$2$	1332.l	333.h	$3$	$2$	$1$	$10.636$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1332.2.k.a	$2$	$1$	$0$	$-3$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}-q^{5}+3\zeta_{6}q^{9}-5\zeta_{6}q^{11}+\cdots$
1332.2.l.b	$1332$	$2$	1332.l	333.h	$3$	$74$	$37$	$10.636$		$_{}$	None	None		✓	✓		1332.2.k.b	$2$	$0$	$0$	$5$	$6$	$-1$			$\mathrm{SU}(2)[C_{3}]$
1332.2.p.a	$1332$	$2$	1332.p	111.g	$4$	$28$	$14$	$10.636$		$_{}$	None	None		✓	✓	✓	1332.2.p.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1332.2.q.a	$1332$	$2$	1332.q	333.k	$6$	$76$	$38$	$10.636$		$_{}$	None	None		✓	✓	✓	1332.2.q.a	$2$	$0$	$0$	$-2$	$0$	$1$			$\mathrm{SU}(2)[C_{6}]$

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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.