LMFDB - Newform search results

Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 56 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9408.2.a.a	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots$
9408.2.a.b	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+q^{9}-4q^{11}-4q^{13}+\cdots$
9408.2.a.d	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots$
9408.2.a.g	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots$
9408.2.a.k	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}-2q^{11}+q^{13}+\cdots$
9408.2.a.m	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
9408.2.a.p	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots$
9408.2.a.r	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-6q^{11}+2q^{13}+4q^{19}+\cdots$
9408.2.a.t	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots$
9408.2.a.v	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+4q^{13}-4q^{17}+4q^{19}+\cdots$
9408.2.a.y	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+2q^{11}+5q^{13}+2q^{17}+\cdots$
9408.2.a.ba	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots$
9408.2.a.bb	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-q^{11}-q^{15}+8q^{17}+\cdots$
9408.2.a.bc	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots$
9408.2.a.bd	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots$
9408.2.a.bf	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots$
9408.2.a.bg	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}-q^{13}+\cdots$
9408.2.a.bl	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$3$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{9}-q^{11}-4q^{13}+\cdots$
9408.2.a.bm	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$3$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots$
9408.2.a.bq	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots$
9408.2.a.br	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots$
9408.2.a.bt	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{9}-q^{11}+4q^{13}+\cdots$
9408.2.a.bu	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots$
9408.2.a.bv	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
9408.2.a.by	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots$
9408.2.a.bz	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}+q^{13}+\cdots$
9408.2.a.cf	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots$
9408.2.a.cg	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-q^{11}-q^{15}-8q^{17}+\cdots$
9408.2.a.ch	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-2q^{11}-2q^{13}-4q^{17}+\cdots$
9408.2.a.ci	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-2q^{11}+q^{13}+2q^{17}+\cdots$
9408.2.a.cl	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+4q^{13}-4q^{17}-4q^{19}+\cdots$
9408.2.a.cm	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+2q^{11}-5q^{13}-2q^{17}+\cdots$
9408.2.a.co	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+6q^{11}+2q^{13}-4q^{19}+\cdots$
9408.2.a.cq	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots$
9408.2.a.ct	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
9408.2.a.cu	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots$
9408.2.a.cv	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}-q^{13}+\cdots$
9408.2.a.cw	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots$
9408.2.a.cy	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots$
9408.2.a.db	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots$
9408.2.a.dd	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots$
9408.2.a.dg	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots$
9408.2.a.di	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+q^{9}+2q^{11}+\cdots$
9408.2.a.dk	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}-\beta q^{15}+\cdots$
9408.2.a.dm	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+\beta q^{11}-\beta q^{13}+\beta q^{17}+\cdots$
9408.2.a.do	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{9}+(2-\beta )q^{11}+2q^{13}+\cdots$
9408.2.a.dr	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$4$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots$
9408.2.a.dt	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+q^{9}-2q^{11}+\cdots$
9408.2.a.du	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots$
9408.2.a.dy	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-3\beta q^{13}+\cdots$

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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.