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 51 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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7744.2.a.c	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$2$	$0$	$-2$	$-1$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}+2q^{15}+\cdots$
7744.2.a.f	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$-1$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+2q^{7}+q^{9}+q^{13}+2q^{15}+\cdots$
7744.2.a.m	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$3$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{7}-2q^{9}-4q^{13}+\cdots$
7744.2.a.n	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-1$	$3$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-q^{3}+3q^{5}-2q^{9}-3q^{15}+9q^{23}+\cdots$
7744.2.a.o	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$3$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+4q^{7}-2q^{9}-2q^{13}+\cdots$
7744.2.a.q	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$2$	$0$	$0$	$-3$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-4q^{7}-3q^{9}+3q^{13}-3q^{17}+\cdots$
7744.2.a.r	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-3$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}-3q^{9}-3q^{13}+3q^{17}+\cdots$
7744.2.a.t	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{5}-3q^{9}-4q^{13}-8q^{17}-q^{25}+\cdots$
7744.2.a.u	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{5}-3q^{9}+4q^{13}+8q^{17}-q^{25}+\cdots$
7744.2.a.w	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-1$	$-4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}-2q^{9}-4q^{13}+\cdots$
7744.2.a.x	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-1$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}-2q^{9}+4q^{13}+\cdots$
7744.2.a.z	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-1$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+4q^{7}-2q^{9}+4q^{13}+\cdots$
7744.2.a.ba	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$3$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-4q^{7}-2q^{9}-2q^{13}+\cdots$
7744.2.a.bh	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$3$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{5}-2q^{7}+q^{9}+5q^{13}+\cdots$
7744.2.a.bi	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$3$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{5}+2q^{7}+q^{9}-5q^{13}+\cdots$
7744.2.a.bk	$7744$	$2$	7744.a	1.a	$1$	$1$	$1$	$61.836$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$3$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+3q^{5}+2q^{7}+6q^{9}+9q^{15}+\cdots$
7744.2.a.bn	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-3$	$-2$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}+2q^{7}+\cdots$
7744.2.a.bp	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-3$	$1$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+\beta q^{5}+(-1+3\beta )q^{7}+\cdots$
7744.2.a.bq	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$-6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+\beta q^{5}+(-3-\beta )q^{7}+\cdots$
7744.2.a.bt	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+\beta q^{5}+(3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
7744.2.a.bw	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-1$	$-3$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+2q^{13}+\cdots$
7744.2.a.by	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-1$	$-3$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots$
7744.2.a.ca	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2\beta q^{5}+(-2+4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
7744.2.a.cb	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-1$	$1$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{5}-\beta q^{7}+(-2+\beta )q^{9}+\cdots$
7744.2.a.ch	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1-2\beta )q^{5}-3q^{9}+(-2-3\beta )q^{13}+\cdots$
7744.2.a.ci	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1-2\beta )q^{5}-3q^{9}+(2+3\beta )q^{13}+\cdots$
7744.2.a.cj	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$0$	$6$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+3q^{5}-2\beta q^{7}+2q^{9}-6q^{13}+\cdots$
7744.2.a.ck	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$0$	$6$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+3q^{5}+2\beta q^{7}+2q^{9}+6q^{13}+\cdots$
7744.2.a.cm	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$1$	$-3$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+2q^{13}+\cdots$
7744.2.a.cn	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{33}) $	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$1$	$-3$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{3}+(-2+\beta )q^{5}+(5+\beta )q^{9}+(8+\cdots)q^{15}+\cdots$
7744.2.a.cp	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{5}+(2-4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
7744.2.a.cq	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$1$	$1$	$-1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{5}-\beta q^{7}+(-2+\beta )q^{9}+\cdots$
7744.2.a.ct	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
7744.2.a.cu	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$2$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}+(1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
7744.2.a.cw	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$4$	$-2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2+\beta )q^{5}+(-1-\beta )q^{7}+\cdots$
7744.2.a.cx	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$4$	$2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+\cdots$
7744.2.a.cz	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$3$	$-2$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2+2\beta )q^{5}+2q^{7}+\cdots$
7744.2.a.db	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$3$	$1$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}+(-1+3\beta )q^{7}+\cdots$
7744.2.a.dc	$7744$	$2$	7744.a	1.a	$1$	$2$	$2$	$61.836$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$4$	$-6$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{5}-2\beta q^{7}+q^{9}+3\beta q^{13}+\cdots$
7744.2.a.dd	$7744$	$2$	7744.a	1.a	$1$	$3$	$3$	$61.836$	3.3.404.1	None	✓	$1$	$0$	$0$	$0$	$3$	$-4$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots$
7744.2.a.de	$7744$	$2$	7744.a	1.a	$1$	$3$	$3$	$61.836$	3.3.404.1	None	✓	$1$	$0$	$0$	$0$	$3$	$-4$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots$
7744.2.a.df	$7744$	$2$	7744.a	1.a	$1$	$3$	$3$	$61.836$	3.3.404.1	None	✓	$1$	$0$	$0$	$0$	$3$	$4$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots$
7744.2.a.dg	$7744$	$2$	7744.a	1.a	$1$	$3$	$3$	$61.836$	3.3.404.1	None	✓	$1$	$0$	$0$	$0$	$3$	$4$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots$
7744.2.a.dh	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.5225.1	None	✓	$1$	$0$	$0$	$-2$	$-1$	$-1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$
7744.2.a.dm	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.22000.1	None	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-2-3\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots$
7744.2.a.dn	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.7488.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+(5+2\beta _{1}+\cdots)q^{9}+\cdots$
7744.2.a.do	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.7488.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+(5+2\beta _{1}+\cdots)q^{9}+\cdots$
7744.2.a.dp	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.4400.1	None	✓	$2$	$0$	$0$	$0$	$6$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+\beta _{1}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
7744.2.a.dr	$7744$	$2$	7744.a	1.a	$1$	$4$	$4$	$61.836$	4.4.5225.1	None	✓	$1$	$0$	$0$	$2$	$-1$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$
7744.2.a.dt	$7744$	$2$	7744.a	1.a	$1$	$6$	$6$	$61.836$	6.6.19898000.1	None	✓	$1$	$0$	$0$	$-5$	$0$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$

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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.