LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 57 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2960.1.o.a	$2960$	$1$	2960.o	740.g	$2$	$4$	$4$	$1.477$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-185}) $	None	✓	✓			2960.1.o.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+(1+\beta _{2})q^{9}+\cdots$
2960.1.o.b	$2960$	$1$	2960.o	740.g	$2$	$4$	$4$	$1.477$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-185}) $	None	✓	✓			2960.1.o.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\beta _{1}q^{3}+q^{5}+\beta _{3}q^{7}+(1+\beta _{2})q^{9}+\cdots$
2960.1.bu.a	$2960$	$1$	2960.bu	740.p	$4$	$2$	$1$	$1.477$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2960.1.bu.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}-iq^{9}+iq^{13}+q^{25}+(1+i+\cdots)q^{29}+\cdots$
2960.1.bz.a	$2960$	$1$	2960.bz	740.s	$4$	$2$	$1$	$1.477$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2960.1.bu.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{5}-iq^{9}+q^{13}-q^{25}+(-1+\cdots)q^{29}+\cdots$
2960.1.cj.a	$2960$	$1$	2960.cj	185.j	$4$	$2$	$1$	$1.477$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None					740.1.t.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+iq^{5}-iq^{7}+iq^{11}-iq^{15}+\cdots$
2960.1.cj.b	$2960$	$1$	2960.cj	185.j	$4$	$2$	$1$	$1.477$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None					740.1.t.a	$2$	$0$	$0$	$2$	$2$	$0$		$1$		$q+q^{3}+q^{5}+iq^{7}+iq^{11}+q^{15}+\cdots$
2960.1.cw.a	$2960$	$1$	2960.cw	740.w	$6$	$2$	$1$	$1.477$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			2960.1.cw.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}-\zeta_{6}^{2}q^{9}+(-1-\zeta_{6})q^{17}+q^{25}+\cdots$
2960.1.cw.b	$2960$	$1$	2960.cw	740.w	$6$	$2$	$1$	$1.477$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			2960.1.cw.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{9}+(1+\zeta_{6})q^{17}+\cdots$
2960.1.dn.a	$2960$	$1$	2960.dn	2960.cn	$12$	$4$	$1$	$1.477$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	✓	✓	2960.1.dn.a	$4$	$0$	$2$	$2$	$2$	$2$		$1$		$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
2960.1.eo.a	$2960$	$1$	2960.eo	740.aj	$12$	$4$	$1$	$1.477$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2960.1.eo.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{3}q^{5}-\zeta_{12}q^{9}-\zeta_{12}^{2}q^{13}+\cdots$
2960.1.et.a	$2960$	$1$	2960.et	740.am	$12$	$4$	$1$	$1.477$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2960.1.eo.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{2}q^{5}-\zeta_{12}^{5}q^{9}+\zeta_{12}q^{13}+\cdots$
2960.1.ez.a	$2960$	$1$	2960.ez	2960.dz	$12$	$8$	$2$	$1.477$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	2960.1.ez.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}+\zeta_{24}^{5}q^{3}-\zeta_{24}^{2}q^{4}+\cdots$
2960.1.fm.a	$2960$	$1$	2960.fm	2960.em	$12$	$4$	$1$	$1.477$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	✓	✓	2960.1.dn.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots$
2960.1.fx.a	$2960$	$1$	2960.fx	740.as	$18$	$6$	$1$	$1.477$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		✓			2960.1.fx.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{4}q^{5}+\zeta_{18}^{7}q^{9}+(\zeta_{18}^{5}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
2960.1.fx.b	$2960$	$1$	2960.fx	740.as	$18$	$6$	$1$	$1.477$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		✓			2960.1.fx.a	$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q-\zeta_{18}^{6}q^{5}+\zeta_{18}^{7}q^{9}+(-\zeta_{18}^{5}-\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
2960.1.gf.a	$2960$	$1$	2960.gf	740.aw	$36$	$12$	$1$	$1.477$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2960.1.gf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{2}q^{5}-\zeta_{36}^{17}q^{9}-\zeta_{36}q^{13}+\cdots$
2960.1.go.a	$2960$	$1$	2960.go	740.bb	$36$	$12$	$1$	$1.477$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	2960.1.gf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{3}q^{5}-\zeta_{36}^{11}q^{9}-\zeta_{36}^{16}q^{13}+\cdots$
2960.2.a.a	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				740.2.a.c	$1$	$0$	$0$	$-3$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+3q^{7}+6q^{9}-5q^{11}+\cdots$
2960.2.a.b	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				1480.2.a.d	$1$	$1$	$0$	$-2$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots$
2960.2.a.c	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				370.2.a.c	$1$	$1$	$0$	$-2$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-q^{7}+q^{9}-3q^{11}-2q^{15}+\cdots$
2960.2.a.d	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				740.2.a.b	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}-2q^{9}+3q^{11}-4q^{13}+\cdots$
2960.2.a.e	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				185.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+5q^{7}-2q^{9}-3q^{11}+\cdots$
2960.2.a.f	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				1480.2.a.c	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{15}+\cdots$
2960.2.a.g	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				370.2.a.b	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots$
2960.2.a.h	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				740.2.a.a	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}+3q^{11}-6q^{13}+\cdots$
2960.2.a.i	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				185.2.a.b	$1$	$0$	$0$	$1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+3q^{7}-2q^{9}+5q^{11}+\cdots$
2960.2.a.j	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				370.2.a.a	$1$	$1$	$0$	$2$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots$
2960.2.a.k	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				185.2.a.c	$1$	$0$	$0$	$2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots$
2960.2.a.l	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				1480.2.a.b	$1$	$1$	$0$	$2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots$
2960.2.a.m	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				370.2.a.d	$1$	$0$	$0$	$2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots$
2960.2.a.n	$2960$	$2$	2960.a	1.a	$1$	$1$	$1$	$23.636$	$\Q$	$_{}$	None	None	✓				1480.2.a.a	$1$	$0$	$0$	$3$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+5q^{7}+6q^{9}+3q^{11}+\cdots$
2960.2.a.o	$2960$	$2$	2960.a	1.a	$1$	$2$	$2$	$23.636$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓				370.2.a.f	$1$	$0$	$0$	$-4$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+(2-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots$
2960.2.a.p	$2960$	$2$	2960.a	1.a	$1$	$2$	$2$	$23.636$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				740.2.a.d	$1$	$0$	$0$	$2$	$2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(-3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
2960.2.a.q	$2960$	$2$	2960.a	1.a	$1$	$2$	$2$	$23.636$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				370.2.a.e	$1$	$0$	$0$	$2$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
2960.2.a.r	$2960$	$2$	2960.a	1.a	$1$	$3$	$3$	$23.636$	3.3.316.1	$_{}$	None	None	✓				1480.2.a.e	$1$	$1$	$0$	$-1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+\beta _{1}q^{7}+\beta _{2}q^{9}+(1+\cdots)q^{11}+\cdots$
2960.2.a.s	$2960$	$2$	2960.a	1.a	$1$	$3$	$3$	$23.636$	3.3.568.1	$_{}$	None	None	✓		✓		1480.2.a.f	$1$	$1$	$0$	$-1$	$3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+\beta _{1}q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots$
2960.2.a.t	$2960$	$2$	2960.a	1.a	$1$	$3$	$3$	$23.636$	3.3.148.1	$_{}$	None	None	✓				740.2.a.e	$1$	$0$	$0$	$0$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+(-2\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
2960.2.a.u	$2960$	$2$	2960.a	1.a	$1$	$3$	$3$	$23.636$	3.3.892.1	$_{}$	None	None	✓				370.2.a.g	$1$	$0$	$0$	$0$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(3+2\beta _{1})q^{9}+\cdots$
2960.2.a.v	$2960$	$2$	2960.a	1.a	$1$	$4$	$4$	$23.636$	4.4.286164.1	$_{}$	None	None	✓		✓		740.2.a.f	$1$	$0$	$0$	$-3$	$4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+q^{5}+(1+\beta _{1})q^{7}+\cdots$
2960.2.a.w	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.973904.1	$_{}$	None	None	✓		✓		185.2.a.e	$1$	$1$	$0$	$-3$	$-5$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-q^{5}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
2960.2.a.x	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.998068.1	$_{}$	None	None	✓		✓		1480.2.a.j	$1$	$1$	$0$	$-1$	$-5$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}-q^{5}+\beta _{2}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
2960.2.a.y	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.6397264.1	$_{}$	None	None	✓				1480.2.a.i	$1$	$0$	$0$	$0$	$-5$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots$
2960.2.a.z	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.935504.1	$_{}$	None	None	✓				1480.2.a.h	$1$	$0$	$0$	$1$	$-5$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}-\beta _{3}q^{7}+(\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots$
2960.2.a.ba	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.368464.1	$_{}$	None	None	✓		✓		185.2.a.d	$1$	$1$	$0$	$1$	$5$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+q^{5}+(-1-\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots$
2960.2.a.bb	$2960$	$2$	2960.a	1.a	$1$	$5$	$5$	$23.636$	5.5.583504.1	$_{}$	None	None	✓				1480.2.a.g	$1$	$0$	$0$	$5$	$5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{2}-\beta _{4})q^{7}+\cdots$
2960.2.a.bc	$2960$	$2$	2960.a	1.a	$1$	$6$	$6$	$23.636$	6.6.693982032.1	$_{}$	None	None	✓		✓		1480.2.a.k	$1$	$0$	$0$	$-1$	$6$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(-1-\beta _{2})q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots$
2960.2.p.a	$2960$	$2$	2960.p	37.b	$2$	$2$	$2$	$23.636$	$\Q(\sqrt{-1}) $	$_{}$	None	None					740.2.h.a	$2$	$1$	$0$	$-6$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3q^{3}+iq^{5}+q^{7}+6q^{9}-3q^{11}+\cdots$
2960.2.p.b	$2960$	$2$	2960.p	37.b	$2$	$2$	$2$	$23.636$	$\Q(\sqrt{-1}) $	$_{}$	None	None					1480.2.p.a	$2$	$1$	$0$	$-4$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{3}+iq^{5}-4q^{7}+q^{9}-4q^{11}+\cdots$
2960.2.p.c	$2960$	$2$	2960.p	37.b	$2$	$2$	$2$	$23.636$	$\Q(\sqrt{-1}) $	$_{}$	None	None					185.2.c.a	$2$	$1$	$0$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+iq^{5}-q^{7}-2q^{9}+3q^{11}+\cdots$
2960.2.p.d	$2960$	$2$	2960.p	37.b	$2$	$2$	$2$	$23.636$	$\Q(\sqrt{-1}) $	$_{}$	None	None					370.2.d.b	$2$	$0$	$0$	$0$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{5}-5q^{7}-3q^{9}-3q^{11}-2iq^{13}+\cdots$

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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.