LMFDB - Newform search results

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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 (47 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	7	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9016.2.a.a	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{5}+6q^{9}+2q^{11}+q^{13}+\cdots$
9016.2.a.b	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+6q^{9}+5q^{13}+6q^{17}-6q^{19}+\cdots$
9016.2.a.c	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$-4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
9016.2.a.d	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots$
9016.2.a.e	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+4q^{11}-6q^{13}+q^{23}+\cdots$
9016.2.a.f	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+q^{9}-4q^{11}-4q^{15}+\cdots$
9016.2.a.g	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}-6q^{11}+3q^{13}+q^{23}+\cdots$
9016.2.a.h	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-3q^{9}+4q^{13}+4q^{17}+2q^{19}+\cdots$
9016.2.a.i	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+6q^{11}+2q^{13}-6q^{17}+6q^{19}+\cdots$
9016.2.a.j	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-2q^{9}-2q^{11}-7q^{13}+\cdots$
9016.2.a.k	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}-2q^{9}-4q^{11}+5q^{13}+\cdots$
9016.2.a.l	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+q^{9}-4q^{11}-4q^{15}+\cdots$
9016.2.a.m	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+6q^{17}-6q^{19}+q^{23}+\cdots$
9016.2.a.n	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+6q^{9}-6q^{11}-q^{13}+q^{23}+\cdots$
9016.2.a.o	$9016$	$2$	9016.a	1.a	$1$	$1$	$1$	$71.993$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+4q^{5}+6q^{9}+2q^{11}-5q^{13}+\cdots$
9016.2.a.p	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}-q^{9}-4q^{11}+3\beta q^{13}+\cdots$
9016.2.a.q	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}-q^{9}-4q^{11}+\beta q^{13}+\cdots$
9016.2.a.r	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{9}+3\beta q^{13}-2\beta q^{17}+2\beta q^{19}+\cdots$
9016.2.a.s	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{5}-q^{9}+2q^{11}-4\beta q^{13}+\cdots$
9016.2.a.t	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}-q^{9}+6q^{11}-2q^{15}+\cdots$
9016.2.a.u	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+\beta q^{5}+5q^{9}-4q^{11}-4\beta q^{13}+\cdots$
9016.2.a.v	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}-q^{9}+2q^{11}+2\beta q^{13}+\cdots$
9016.2.a.w	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$1$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots$
9016.2.a.x	$9016$	$2$	9016.a	1.a	$1$	$2$	$2$	$71.993$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$1$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots$
9016.2.a.y	$9016$	$2$	9016.a	1.a	$1$	$3$	$3$	$71.993$	3.3.568.1	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots$
9016.2.a.z	$9016$	$2$	9016.a	1.a	$1$	$3$	$3$	$71.993$	3.3.148.1	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-2+2\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{9}+\cdots$
9016.2.a.ba	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	$\Q(\zeta_{24})^+$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+2\beta _{3}q^{5}+(-1+\beta _{2})q^{9}+\cdots$
9016.2.a.bb	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	4.4.9248.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{9}+\cdots$
9016.2.a.bc	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	4.4.34196.1	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{1}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
9016.2.a.bd	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	4.4.170528.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}+(2+\beta _{2})q^{9}+2q^{11}+\cdots$
9016.2.a.be	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	$\Q(\sqrt{7}, \sqrt{15})$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(2-\beta _{3})q^{9}-2q^{11}-\beta _{1}q^{13}+\cdots$
9016.2.a.bf	$9016$	$2$	9016.a	1.a	$1$	$4$	$4$	$71.993$	4.4.8468.1	None	✓	$1$	$1$	$0$	$3$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(\beta _{2}-\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{9}+\cdots$
9016.2.a.bg	$9016$	$2$	9016.a	1.a	$1$	$5$	$5$	$71.993$	5.5.3385684.1	None	✓	$1$	$0$	$0$	$3$	$-2$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+(3-\beta _{4})q^{9}+\cdots$
9016.2.a.bh	$9016$	$2$	9016.a	1.a	$1$	$6$	$6$	$71.993$	6.6.79480832.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{1}q^{5}+(1+\beta _{2}-\beta _{3})q^{9}+\cdots$
9016.2.a.bi	$9016$	$2$	9016.a	1.a	$1$	$6$	$6$	$71.993$	6.6.1229312.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{9}+(2+\beta _{5})q^{11}+\cdots$
9016.2.a.bj	$9016$	$2$	9016.a	1.a	$1$	$8$	$8$	$71.993$	8.8.$\cdots$.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q-\beta _{6}q^{3}-\beta _{4}q^{5}-\beta _{3}q^{9}+(-1-\beta _{3}+\cdots)q^{11}+\cdots$
9016.2.a.bk	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$0$	$-4$	$-3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{10}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
9016.2.a.bl	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$0$	$-4$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
9016.2.a.bm	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$-7$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(1+\beta _{1}+\beta _{7}+\cdots)q^{9}+\cdots$
9016.2.a.bn	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$0$	$-2$	$9$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{5})q^{5}+(1+\beta _{4}-\beta _{5}+\cdots)q^{9}+\cdots$
9016.2.a.bo	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$0$	$2$	$-9$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(1+\beta _{4}-\beta _{5}+\cdots)q^{9}+\cdots$
9016.2.a.bp	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$7$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(1+\beta _{1}+\beta _{7}+\cdots)q^{9}+\cdots$
9016.2.a.bq	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
9016.2.a.br	$9016$	$2$	9016.a	1.a	$1$	$11$	$11$	$71.993$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{10}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
9016.2.a.bs	$9016$	$2$	9016.a	1.a	$1$	$14$	$14$	$71.993$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{7})q^{5}+(1+\beta _{4}+\cdots)q^{9}+\cdots$
9016.2.a.bt	$9016$	$2$	9016.a	1.a	$1$	$18$	$18$	$71.993$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{10}q^{5}+(1+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$
9016.2.a.bu	$9016$	$2$	9016.a	1.a	$1$	$18$	$18$	$71.993$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{10}q^{5}+(2+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.