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 (1-50 of 54 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9075.2.a.c	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	$\Q$	None	✓	$1$	$2$	$-1$	$-1$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}-4q^{7}+3q^{8}+\cdots$
9075.2.a.i	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{7}+q^{9}+2q^{12}-q^{13}+\cdots$
9075.2.a.j	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{7}+q^{9}+2q^{12}+2q^{13}+\cdots$
9075.2.a.k	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{7}+q^{9}+2q^{12}-2q^{13}+\cdots$
9075.2.a.l	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{12}+q^{13}+\cdots$
9075.2.a.o	$9075$	$2$	9075.a	1.a	$1$	$1$	$1$	$72.464$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}+4q^{7}-3q^{8}+\cdots$
9075.2.a.y	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{5}) $	None	✓	$1$	$2$	$-1$	$-2$	$0$	$-6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
9075.2.a.z	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$-2$	$0$	$-6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
9075.2.a.bf	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{15}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+\beta q^{7}+q^{9}+2q^{12}+\cdots$
9075.2.a.bg	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}-2\beta q^{7}+\cdots$
9075.2.a.bh	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+2q^{7}-\beta q^{8}+\cdots$
9075.2.a.bj	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-\beta q^{8}+\cdots$
9075.2.a.bk	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-\beta q^{7}+\cdots$
9075.2.a.bl	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+\beta q^{7}+q^{9}-2q^{12}+\cdots$
9075.2.a.bm	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{15}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+\beta q^{7}+q^{9}-2q^{12}+\cdots$
9075.2.a.bn	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-2\beta q^{7}+\cdots$
9075.2.a.bo	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-2\beta q^{7}+\cdots$
9075.2.a.bp	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-\beta q^{8}+q^{9}+\cdots$
9075.2.a.br	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-\beta q^{7}+\cdots$
9075.2.a.bv	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$-2$	$0$	$6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
9075.2.a.by	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$2$	$0$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
9075.2.a.bz	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$2$	$0$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
9075.2.a.cb	$9075$	$2$	9075.a	1.a	$1$	$2$	$2$	$72.464$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$3$	$2$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots$
9075.2.a.cd	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.568.1	None	✓	$1$	$0$	$-2$	$3$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(3+\beta _{2})q^{4}+\cdots$
9075.2.a.ce	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.469.1	None	✓	$1$	$0$	$-1$	$-3$	$0$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
9075.2.a.cf	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.148.1	None	✓	$1$	$0$	$-1$	$-3$	$0$	$0$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
9075.2.a.cg	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.148.1	None	✓	$1$	$0$	$-1$	$3$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
9075.2.a.ci	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.469.1	None	✓	$1$	$0$	$1$	$-3$	$0$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
9075.2.a.cj	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.568.1	None	✓	$1$	$0$	$2$	$-3$	$0$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
9075.2.a.ck	$9075$	$2$	9075.a	1.a	$1$	$3$	$3$	$72.464$	3.3.148.1	None	✓	$1$	$0$	$3$	$3$	$0$	$8$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
9075.2.a.cm	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.725.1	None	✓	$1$	$0$	$-3$	$-4$	$0$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
9075.2.a.co	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	$\Q(\zeta_{15})^+$	None	✓	$1$	$0$	$-1$	$4$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots$
9075.2.a.cp	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.5725.1	None	✓	$1$	$0$	$-1$	$4$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots$
9075.2.a.cq	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.5725.1	None	✓	$1$	$0$	$-1$	$4$	$0$	$8$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots$
9075.2.a.cr	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	$\Q(\zeta_{24})^+$	None	✓	$2$	$0$	$0$	$-4$	$0$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}-\beta _{2}q^{6}-\beta _{1}q^{7}-2\beta _{2}q^{8}+\cdots$
9075.2.a.cs	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$0$	$0$	$-4$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}-2\beta _{3}q^{7}+\cdots$
9075.2.a.cw	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	$\Q(\sqrt{3}, \sqrt{11})$	None	✓	$2$	$0$	$0$	$-4$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots$
9075.2.a.cx	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	$\Q(\sqrt{3}, \sqrt{5})$	None	✓	$2$	$0$	$0$	$-4$	$0$	$0$	$+$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}-q^{3}+(2+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
9075.2.a.db	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	$\Q(\sqrt{3}, \sqrt{11})$	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{3})q^{4}+\beta _{1}q^{6}+\cdots$
9075.2.a.dc	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.8112.1	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(2-\beta _{3})q^{4}-\beta _{2}q^{6}+\cdots$
9075.2.a.dd	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	$\Q(\sqrt{3}, \sqrt{5})$	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}+q^{3}+(2+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
9075.2.a.de	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.5725.1	None	✓	$1$	$0$	$1$	$-4$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots$
9075.2.a.dj	$9075$	$2$	9075.a	1.a	$1$	$4$	$4$	$72.464$	4.4.725.1	None	✓	$1$	$0$	$5$	$-4$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1}-\beta _{2})q^{2}-q^{3}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots$
9075.2.a.dk	$9075$	$2$	9075.a	1.a	$1$	$5$	$5$	$72.464$	5.5.9444552.1	None	✓	$1$	$0$	$-1$	$-5$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
9075.2.a.dl	$9075$	$2$	9075.a	1.a	$1$	$5$	$5$	$72.464$	5.5.9444552.1	None	✓	$1$	$0$	$-1$	$5$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
9075.2.a.dm	$9075$	$2$	9075.a	1.a	$1$	$5$	$5$	$72.464$	5.5.9444552.1	None	✓	$1$	$0$	$1$	$-5$	$0$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
9075.2.a.dn	$9075$	$2$	9075.a	1.a	$1$	$5$	$5$	$72.464$	5.5.9444552.1	None	✓	$1$	$0$	$1$	$5$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
9075.2.a.dp	$9075$	$2$	9075.a	1.a	$1$	$6$	$6$	$72.464$	6.6.860280160.1	None	✓	$1$	$0$	$-1$	$6$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
9075.2.a.dq	$9075$	$2$	9075.a	1.a	$1$	$6$	$6$	$72.464$	6.6.437199552.1	None	✓	$2$	$0$	$0$	$6$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
9075.2.a.ds	$9075$	$2$	9075.a	1.a	$1$	$6$	$6$	$72.464$	6.6.860280160.1	None	✓	$1$	$0$	$1$	$6$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$

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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.