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 207 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
2880.1.c.a	$2880$	$1$	2880.c	15.d	$2$	$4$	$4$	$1.437$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None			✓	✓	1440.1.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{5}+\zeta_{8}^{2}q^{13}+(\zeta_{8}-\zeta_{8}^{3})q^{17}+\cdots$
2880.1.i.a	$2880$	$1$	2880.i	120.i	$2$	$4$	$4$	$1.437$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-10}) $	None		✓			2880.1.i.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-\zeta_{8}^{2}q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
2880.1.i.b	$2880$	$1$	2880.i	120.i	$2$	$4$	$4$	$1.437$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-10}) $	None		✓			2880.1.i.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{8}^{2}q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots$
2880.1.j.a	$2880$	$1$	2880.j	20.d	$2$	$1$	$1$	$1.437$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓				80.1.h.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}+q^{25}+2q^{29}+2q^{41}-q^{49}+\cdots$
2880.1.j.b	$2880$	$1$	2880.j	20.d	$2$	$2$	$2$	$1.437$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{15}) $			✓		180.1.f.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{5}-2 i q^{17}-q^{25}-q^{49}-2 i q^{53}+\cdots$
2880.1.p.a	$2880$	$1$	2880.p	40.e	$2$	$2$	$2$	$1.437$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{5}) $		✓			2880.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{5}-2 q^{11}-q^{25}-2 i q^{29}+\cdots$
2880.1.p.b	$2880$	$1$	2880.p	40.e	$2$	$2$	$2$	$1.437$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{5}) $		✓			2880.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{5}+2 q^{11}-q^{25}-2 i q^{29}+\cdots$
2880.1.r.a	$2880$	$1$	2880.r	80.k	$4$	$4$	$2$	$1.437$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None			✓	✓	720.1.r.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{17}+(-1+\cdots)q^{19}+\cdots$
2880.1.bh.a	$2880$	$1$	2880.bh	5.c	$4$	$2$	$1$	$1.437$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					1440.1.bh.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}+(-i-1)q^{13}+(i-1)q^{17}+\cdots$
2880.1.bh.b	$2880$	$1$	2880.bh	5.c	$4$	$2$	$1$	$1.437$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					160.1.p.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{5}+(i+1)q^{13}+(-i+1)q^{17}+\cdots$
2880.1.bh.c	$2880$	$1$	2880.bh	5.c	$4$	$2$	$1$	$1.437$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None					1440.1.bh.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}+(-i-1)q^{13}+(-i+1)q^{17}+\cdots$
2880.1.bk.a	$2880$	$1$	2880.bk	60.l	$4$	$4$	$2$	$1.437$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None					720.1.bk.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{5}+(-1-\zeta_{8}^{2})q^{13}-\zeta_{8}q^{17}+\cdots$
2880.1.bk.b	$2880$	$1$	2880.bk	60.l	$4$	$4$	$2$	$1.437$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None					180.1.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{5}+(1+\zeta_{8}^{2})q^{13}+\zeta_{8}^{2}q^{25}+\cdots$
2880.1.bu.a	$2880$	$1$	2880.bu	180.p	$6$	$2$	$1$	$1.437$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None					180.1.p.a	$4$	$0$	$0$	$-1$	$1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
2880.1.bu.b	$2880$	$1$	2880.bu	180.p	$6$	$2$	$1$	$1.437$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None					180.1.p.a	$4$	$0$	$0$	$1$	$1$	$1$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
2880.1.bu.c	$2880$	$1$	2880.bu	180.p	$6$	$4$	$2$	$1.437$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None			✓		720.1.bu.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{5}q^{3}-\zeta_{12}^{2}q^{5}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{7}+\cdots$
2880.1.cd.a	$2880$	$1$	2880.cd	45.h	$6$	$8$	$4$	$1.437$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-5}) $	None			✓	✓	1440.1.cd.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{3}+\zeta_{24}^{2}q^{5}+(-\zeta_{24}^{3}+\cdots)q^{7}+\cdots$
2880.1.ec.a	$2880$	$1$	2880.ec	320.ah	$16$	$16$	$2$	$1.437$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	2880.1.ec.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{7}q^{2}+\zeta_{32}^{14}q^{4}-\zeta_{32}q^{5}+\cdots$
2880.2.a.a	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				30.2.a.a	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots$
2880.2.a.b	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				120.2.a.a	$1$	$1$	$0$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots$
2880.2.a.c	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				480.2.a.a	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots$
2880.2.a.d	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				160.2.a.a	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots$
2880.2.a.e	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				360.2.a.c	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-2q^{11}-4q^{13}+2q^{17}+\cdots$
2880.2.a.f	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				20.2.a.a	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-2q^{13}+6q^{17}-4q^{19}+\cdots$
2880.2.a.g	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				1440.2.a.b	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+2q^{11}-2q^{17}+4q^{19}+\cdots$
2880.2.a.h	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				90.2.a.a	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+6q^{11}+4q^{13}-6q^{17}+\cdots$
2880.2.a.i	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				480.2.a.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{11}-2q^{13}+2q^{17}+8q^{19}+\cdots$
2880.2.a.j	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				480.2.a.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{11}-2q^{13}+2q^{17}-8q^{19}+\cdots$
2880.2.a.k	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				90.2.a.a	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-6q^{11}+4q^{13}-6q^{17}+\cdots$
2880.2.a.l	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				1440.2.a.b	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-2q^{11}-2q^{17}-4q^{19}+\cdots$
2880.2.a.m	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				20.2.a.a	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-2q^{13}+6q^{17}+4q^{19}+\cdots$
2880.2.a.n	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				360.2.a.c	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+2q^{11}-4q^{13}+2q^{17}+\cdots$
2880.2.a.o	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				160.2.a.a	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+4q^{11}+6q^{13}-2q^{17}+\cdots$
2880.2.a.p	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				480.2.a.a	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots$
2880.2.a.q	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				30.2.a.a	$1$	$1$	$0$	$0$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots$
2880.2.a.r	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				120.2.a.a	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots$
2880.2.a.s	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				480.2.a.c	$1$	$0$	$0$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}+2q^{13}+6q^{17}+4q^{23}+\cdots$
2880.2.a.t	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				40.2.a.a	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots$
2880.2.a.u	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				90.2.a.a	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-6q^{11}+4q^{13}+6q^{17}+\cdots$
2880.2.a.v	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				1440.2.a.b	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-2q^{11}+2q^{17}+4q^{19}+\cdots$
2880.2.a.w	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				360.2.a.c	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+2q^{11}-4q^{13}-2q^{17}+\cdots$
2880.2.a.x	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				120.2.a.b	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{11}-6q^{13}+6q^{17}+4q^{19}+\cdots$
2880.2.a.y	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				15.2.a.a	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots$
2880.2.a.z	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				480.2.a.d	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{13}-6q^{17}-4q^{19}+8q^{23}+\cdots$
2880.2.a.ba	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				480.2.a.d	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{13}-6q^{17}+4q^{19}-8q^{23}+\cdots$
2880.2.a.bb	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				120.2.a.b	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{11}-6q^{13}+6q^{17}-4q^{19}+\cdots$
2880.2.a.bc	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				15.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots$
2880.2.a.bd	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				360.2.a.c	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-2q^{11}-4q^{13}-2q^{17}+\cdots$
2880.2.a.be	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				1440.2.a.b	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+2q^{11}+2q^{17}-4q^{19}+\cdots$
2880.2.a.bf	$2880$	$2$	2880.a	1.a	$1$	$1$	$1$	$22.997$	$\Q$	$_{}$	None	None	✓				90.2.a.a	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+6q^{11}+4q^{13}+6q^{17}+\cdots$

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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.