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 165 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
2736.1.b.a	$2736$	$1$	2736.b	228.b	$2$	$4$	$4$	$1.365$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		✓			2736.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
2736.1.b.b	$2736$	$1$	2736.b	228.b	$2$	$8$	$8$	$1.365$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		✓	✓		2736.1.b.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$		$q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{5}-\zeta_{24}^{6}q^{7}+\cdots$
2736.1.o.a	$2736$	$1$	2736.o	19.b	$2$	$1$	$1$	$1.365$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-19}) $	$\Q(\sqrt{57}) $	✓				171.1.c.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+2q^{7}+q^{19}-q^{25}-2q^{43}+3q^{49}+\cdots$
2736.1.o.b	$2736$	$1$	2736.o	19.b	$2$	$1$	$1$	$1.365$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓				76.1.c.a	$2$	$0$	$0$	$0$	$1$	$1$		$1$		$q+q^{5}+q^{7}-q^{11}+q^{17}-q^{19}+2q^{23}+\cdots$
2736.1.o.c	$2736$	$1$	2736.o	19.b	$2$	$2$	$2$	$1.365$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None	✓		✓		684.1.h.b	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta q^{5}-q^{7}-\beta q^{11}+\beta q^{17}+q^{19}+\cdots$
2736.1.bk.a	$2736$	$1$	2736.bk	76.g	$6$	$2$	$1$	$1.365$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2736.1.bk.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{6}-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}-q^{19}+\cdots$
2736.1.bk.b	$2736$	$1$	2736.bk	76.g	$6$	$2$	$1$	$1.365$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			2736.1.bk.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-\zeta_{6}q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots$
2736.1.bs.a	$2736$	$1$	2736.bs	171.o	$6$	$4$	$2$	$1.365$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓	✓	171.1.o.a	$4$	$0$	$0$	$0$	$-2$	$2$		$1$		$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{7}+\cdots$
2736.1.cd.a	$2736$	$1$	2736.cd	19.d	$6$	$2$	$1$	$1.365$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None			✓	✓	171.1.p.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{7}+(-1+\zeta_{6}^{2})q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots$
2736.1.fg.a	$2736$	$1$	2736.fg	19.f	$18$	$6$	$1$	$1.365$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None			✓	✓	684.1.bx.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+(\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots$
2736.1.ga.a	$2736$	$1$	2736.ga	76.l	$18$	$6$	$1$	$1.365$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓			2736.1.ga.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots$
2736.1.ga.b	$2736$	$1$	2736.ga	76.l	$18$	$6$	$1$	$1.365$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓			2736.1.ga.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{18}^{7}-\zeta_{18}^{8})q^{7}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{13}+\cdots$
2736.2.a.a	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				456.2.a.b	$1$	$2$	$0$	$0$	$-4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-4q^{7}-4q^{11}-4q^{13}-6q^{17}+\cdots$
2736.2.a.b	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				1368.2.a.a	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-6q^{11}+2q^{13}-4q^{17}+q^{19}+\cdots$
2736.2.a.c	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				19.2.a.a	$1$	$1$	$0$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{7}+3q^{11}-4q^{13}+3q^{17}+\cdots$
2736.2.a.d	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				114.2.a.b	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{11}+2q^{13}+6q^{17}+q^{19}+\cdots$
2736.2.a.e	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				456.2.a.d	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{13}-2q^{17}+q^{19}-q^{25}+\cdots$
2736.2.a.f	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				342.2.a.a	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{11}-4q^{13}+q^{19}+8q^{23}+\cdots$
2736.2.a.g	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				228.2.a.b	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{11}+2q^{13}-6q^{17}+q^{19}+\cdots$
2736.2.a.h	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				57.2.a.b	$1$	$0$	$0$	$0$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}-3q^{11}-6q^{13}-3q^{17}+\cdots$
2736.2.a.i	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				456.2.a.a	$1$	$0$	$0$	$0$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}-5q^{11}-2q^{13}+q^{17}+\cdots$
2736.2.a.j	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				114.2.a.a	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}+4q^{11}+2q^{17}-q^{19}-2q^{23}+\cdots$
2736.2.a.k	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				152.2.a.b	$1$	$0$	$0$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}+2q^{11}+q^{13}+5q^{17}-q^{19}+\cdots$
2736.2.a.l	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				1368.2.a.e	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{11}-2q^{13}+4q^{17}-q^{19}-2q^{23}+\cdots$
2736.2.a.m	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				1368.2.a.e	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{11}-2q^{13}-4q^{17}-q^{19}+2q^{23}+\cdots$
2736.2.a.n	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				38.2.a.a	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-6q^{11}+5q^{13}-3q^{17}-q^{19}+\cdots$
2736.2.a.o	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				114.2.a.c	$1$	$1$	$0$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-4q^{13}-6q^{17}-q^{19}-6q^{23}+\cdots$
2736.2.a.p	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				152.2.a.a	$1$	$1$	$0$	$0$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}-3q^{11}-4q^{13}-5q^{17}+\cdots$
2736.2.a.q	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				76.2.a.a	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}+5q^{11}-4q^{13}+3q^{17}+\cdots$
2736.2.a.r	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				342.2.a.a	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{11}-4q^{13}+q^{19}-8q^{23}+\cdots$
2736.2.a.s	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				57.2.a.c	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+6q^{13}+6q^{17}+q^{19}+4q^{23}+\cdots$
2736.2.a.t	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				228.2.a.a	$1$	$1$	$0$	$0$	$3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}-5q^{11}-6q^{13}+5q^{17}+\cdots$
2736.2.a.u	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				456.2.a.c	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+3q^{7}-q^{11}-2q^{13}+5q^{17}+\cdots$
2736.2.a.v	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				57.2.a.a	$1$	$0$	$0$	$0$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+5q^{7}+q^{11}+2q^{13}+q^{17}+\cdots$
2736.2.a.w	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				38.2.a.b	$1$	$0$	$0$	$0$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-3q^{7}+2q^{11}-q^{13}-3q^{17}+\cdots$
2736.2.a.x	$2736$	$2$	2736.a	1.a	$1$	$1$	$1$	$21.847$	$\Q$	$_{}$	None	None	✓				1368.2.a.a	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+6q^{11}+2q^{13}+4q^{17}+q^{19}+\cdots$
2736.2.a.y	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓		✓		228.2.a.c	$1$	$1$	$0$	$0$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(-1+\cdots)q^{11}+\cdots$
2736.2.a.z	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				456.2.a.f	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}-\beta q^{7}+(4-\beta )q^{11}-2\beta q^{13}+\cdots$
2736.2.a.ba	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓		✓		684.2.a.e	$2$	$1$	$0$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-3q^{7}-\beta q^{11}+2q^{13}-3\beta q^{17}+\cdots$
2736.2.a.bb	$2736$	$2$	2736.a	1.a	$1$	$2$	$2$	$21.847$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓				456.2.a.e	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(2-\beta )q^{7}+(2-\beta )q^{11}+6q^{13}+\cdots$
2736.2.a.bc	$2736$	$2$	2736.a	1.a	$1$	$3$	$3$	$21.847$	3.3.892.1	$_{}$	None	None	✓				1368.2.a.m	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots$
2736.2.a.bd	$2736$	$2$	2736.a	1.a	$1$	$3$	$3$	$21.847$	3.3.961.1	$_{}$	None	None	✓		✓		152.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots$
2736.2.a.be	$2736$	$2$	2736.a	1.a	$1$	$3$	$3$	$21.847$	3.3.892.1	$_{}$	None	None	✓				1368.2.a.m	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(3+\cdots)q^{11}+\cdots$
2736.2.a.bf	$2736$	$2$	2736.a	1.a	$1$	$4$	$4$	$21.847$	4.4.13068.1	$_{}$	None	None	✓		✓	✓	171.2.a.e	$2$	$0$	$0$	$0$	$0$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots$
2736.2.d.a	$2736$	$2$	2736.d	12.b	$2$	$12$	$12$	$21.847$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			2736.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{4}+\beta _{9})q^{5}+(\beta _{1}+\beta _{3}-\beta _{8})q^{7}+\cdots$
2736.2.d.b	$2736$	$2$	2736.d	12.b	$2$	$24$	$24$	$21.847$		$_{}$	None	None		✓	✓		2736.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2736.2.f.a	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	$\Q(\sqrt{-2}) $	$_{}$	None	None					342.2.b.a	$2$	$1$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots$
2736.2.f.b	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	$\Q(\sqrt{-2}) $	$_{}$	None	None					342.2.b.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-2q^{7}-\beta q^{11}+\beta q^{17}+(-1+\cdots)q^{19}+\cdots$
2736.2.f.c	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	$\Q(\sqrt{-2}) $	$_{}$	None	None					1368.2.f.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-2q^{7}+3\beta q^{11}-2\beta q^{13}+\cdots$
2736.2.f.d	$2736$	$2$	2736.f	57.d	$2$	$2$	$2$	$21.847$	$\Q(\sqrt{-2}) $	$_{}$	None	None					1368.2.f.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-2q^{7}+3\beta q^{11}+2\beta q^{13}+\cdots$

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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.