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 (38 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	5	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9200.2.a.b	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-4q^{7}+6q^{9}-2q^{11}+5q^{13}+\cdots$
9200.2.a.f	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots$
9200.2.a.j	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+3q^{7}+q^{9}-5q^{11}-5q^{13}+\cdots$
9200.2.a.l	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}-2q^{9}+2q^{11}-7q^{13}+\cdots$
9200.2.a.n	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}-2q^{11}+5q^{13}+4q^{17}+\cdots$
9200.2.a.p	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots$
9200.2.a.r	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}+q^{11}+q^{13}+5q^{19}+\cdots$
9200.2.a.t	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}-2q^{11}+2q^{13}-3q^{17}+\cdots$
9200.2.a.u	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}+q^{11}-q^{13}+5q^{19}+\cdots$
9200.2.a.y	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}-2q^{9}+6q^{11}+q^{13}+\cdots$
9200.2.a.bc	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{7}+q^{9}-5q^{11}+5q^{13}+\cdots$
9200.2.a.bf	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots$
9200.2.a.bg	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{7}+q^{9}-2q^{13}+5q^{17}+\cdots$
9200.2.a.bi	$9200$	$2$	9200.a	1.a	$1$	$1$	$1$	$73.462$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{7}+q^{9}-6q^{13}-7q^{17}+\cdots$
9200.2.a.bn	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$4$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(2+\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
9200.2.a.bo	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-1$	$0$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-3+3\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
9200.2.a.bp	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots$
9200.2.a.bq	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+2q^{11}+\cdots$
9200.2.a.br	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{9}-2\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9200.2.a.bs	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{21}) $	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{7}+(2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
9200.2.a.bt	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{7}+2q^{9}+(3+\beta )q^{11}+\cdots$
9200.2.a.bu	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
9200.2.a.bv	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}-2q^{11}+\cdots$
9200.2.a.bw	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots$
9200.2.a.bz	$9200$	$2$	9200.a	1.a	$1$	$2$	$2$	$73.462$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$-4$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2-\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
9200.2.a.cb	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$0$	$-2$	$0$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-2-2\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots$
9200.2.a.ch	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$0$	$2$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(2-2\beta _{1})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots$
9200.2.a.ci	$9200$	$2$	9200.a	1.a	$1$	$3$	$3$	$73.462$	3.3.229.1	None	✓	$1$	$1$	$0$	$2$	$0$	$7$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(2-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
9200.2.a.cj	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.13448.1	None	✓	$1$	$1$	$0$	$-3$	$0$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{3}+(-1-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots$
9200.2.a.cm	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.53121.1	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
9200.2.a.co	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.53121.1	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots$
9200.2.a.cq	$9200$	$2$	9200.a	1.a	$1$	$4$	$4$	$73.462$	4.4.5744.1	None	✓	$1$	$1$	$0$	$2$	$0$	$6$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(2+\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
9200.2.a.cs	$9200$	$2$	9200.a	1.a	$1$	$5$	$5$	$73.462$	5.5.791953.1	None	✓	$1$	$1$	$0$	$-3$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4})q^{7}+\cdots$
9200.2.a.cu	$9200$	$2$	9200.a	1.a	$1$	$5$	$5$	$73.462$	5.5.13955077.1	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{3}-\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
9200.2.a.cw	$9200$	$2$	9200.a	1.a	$1$	$5$	$5$	$73.462$	5.5.791953.1	None	✓	$1$	$1$	$0$	$3$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{2}-\beta _{4})q^{7}+\cdots$
9200.2.a.cx	$9200$	$2$	9200.a	1.a	$1$	$6$	$6$	$73.462$	6.6.143376304.1	None	✓	$1$	$1$	$0$	$-4$	$0$	$-9$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-2+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
9200.2.a.cz	$9200$	$2$	9200.a	1.a	$1$	$7$	$7$	$73.462$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$0$	$-4$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots$
9200.2.a.dd	$9200$	$2$	9200.a	1.a	$1$	$8$	$8$	$73.462$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$0$	$-7$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots$

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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.