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 170 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
1584.1.j.a	$1584$	$1$	1584.j	11.b	$2$	$1$	$1$	$0.791$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓		✓	✓	44.1.d.a	$2$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+q^{11}-q^{23}+q^{31}-q^{37}+\cdots$
1584.1.bf.a	$1584$	$1$	1584.bf	99.h	$6$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None					396.1.m.b	$4$	$0$	$0$	$-2$	$-2$	$0$		$1$		$q-q^{3}+\zeta_{6}^{2}q^{5}+q^{9}+\zeta_{6}q^{11}-2\zeta_{6}^{2}q^{15}+\cdots$
1584.1.bf.b	$1584$	$1$	1584.bf	99.h	$6$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None					99.1.h.a	$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\zeta_{6}q^{11}+\cdots$
1584.1.bf.c	$1584$	$1$	1584.bf	99.h	$6$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None					396.1.m.a	$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
1584.1.bk.a	$1584$	$1$	1584.bk	396.o	$6$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			1584.1.bk.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+q^{9}-\zeta_{6}q^{11}-\zeta_{6}^{2}q^{23}-\zeta_{6}q^{25}+\cdots$
1584.1.bk.b	$1584$	$1$	1584.bk	396.o	$6$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			1584.1.bk.b	$4$	$0$	$0$	$-1$	$-3$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$
1584.1.bk.c	$1584$	$1$	1584.bk	396.o	$6$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			1584.1.bk.c	$4$	$0$	$0$	$-1$	$3$	$0$		$1$		$q-\zeta_{6}q^{3}+(1+\zeta_{6})q^{5}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
1584.1.bk.d	$1584$	$1$	1584.bk	396.o	$6$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			1584.1.bk.b	$4$	$0$	$0$	$1$	$-3$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$
1584.1.bk.e	$1584$	$1$	1584.bk	396.o	$6$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			1584.1.bk.c	$4$	$0$	$0$	$1$	$3$	$0$		$1$		$q+\zeta_{6}q^{3}+(1+\zeta_{6})q^{5}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots$
1584.1.bk.f	$1584$	$1$	1584.bk	396.o	$6$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		✓			1584.1.bk.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+q^{9}+\zeta_{6}q^{11}+\zeta_{6}^{2}q^{23}-\zeta_{6}q^{25}+\cdots$
1584.2.a.a	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				264.2.a.d	$1$	$0$	$0$	$0$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots$
1584.2.a.b	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				99.2.a.a	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+2q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots$
1584.2.a.c	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				132.2.a.a	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}-q^{11}+6q^{13}+4q^{17}+\cdots$
1584.2.a.d	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				264.2.a.a	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{11}+2q^{13}-6q^{17}+4q^{23}+\cdots$
1584.2.a.e	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				132.2.a.b	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}+q^{11}-2q^{13}-4q^{17}+\cdots$
1584.2.a.f	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				66.2.a.b	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}-q^{11}-6q^{13}-2q^{17}+\cdots$
1584.2.a.g	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				11.2.a.a	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+q^{11}+4q^{13}+2q^{17}+\cdots$
1584.2.a.h	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				66.2.a.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots$
1584.2.a.i	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				198.2.a.b	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots$
1584.2.a.j	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				264.2.a.c	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{11}+2q^{17}-8q^{19}-2q^{23}+\cdots$
1584.2.a.k	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				198.2.a.b	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots$
1584.2.a.l	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				792.2.a.c	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-q^{11}-6q^{13}-6q^{17}+2q^{19}+\cdots$
1584.2.a.m	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				792.2.a.c	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+q^{11}-6q^{13}+6q^{17}+2q^{19}+\cdots$
1584.2.a.n	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				264.2.a.b	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-q^{11}+6q^{13}-6q^{17}+\cdots$
1584.2.a.o	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				33.2.a.a	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots$
1584.2.a.p	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				44.2.a.a	$1$	$1$	$0$	$0$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-2q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots$
1584.2.a.q	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				88.2.a.a	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots$
1584.2.a.r	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				99.2.a.a	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+2q^{7}-q^{11}-2q^{13}-2q^{17}+\cdots$
1584.2.a.s	$1584$	$2$	1584.a	1.a	$1$	$1$	$1$	$12.648$	$\Q$	$_{}$	None	None	✓				66.2.a.c	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+2q^{7}+q^{11}+4q^{13}+2q^{17}+\cdots$
1584.2.a.t	$1584$	$2$	1584.a	1.a	$1$	$2$	$2$	$12.648$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		88.2.a.b	$1$	$0$	$0$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(2-2\beta )q^{7}-q^{11}+\cdots$
1584.2.a.u	$1584$	$2$	1584.a	1.a	$1$	$2$	$2$	$12.648$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		792.2.a.i	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2-\beta )q^{7}-q^{11}+(2-\beta )q^{13}+\cdots$
1584.2.a.v	$1584$	$2$	1584.a	1.a	$1$	$2$	$2$	$12.648$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		792.2.a.i	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(2+\beta )q^{13}+\cdots$
1584.2.b.a	$1584$	$2$	1584.b	33.d	$2$	$2$	$2$	$12.648$	$\Q(\sqrt{-2}) $	$_{}$	None	None					198.2.b.a	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+(-3-\beta )q^{11}-3\beta q^{13}+\cdots$
1584.2.b.b	$1584$	$2$	1584.b	33.d	$2$	$2$	$2$	$12.648$	$\Q(\sqrt{-2}) $	$_{}$	None	None					396.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+3\beta q^{7}+(-3+\beta )q^{11}+6q^{17}+\cdots$
1584.2.b.c	$1584$	$2$	1584.b	33.d	$2$	$2$	$2$	$12.648$	$\Q(\sqrt{-2}) $	$_{}$	None	None					396.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-3\beta q^{7}+(3+\beta )q^{11}-6q^{17}+\cdots$
1584.2.b.d	$1584$	$2$	1584.b	33.d	$2$	$2$	$2$	$12.648$	$\Q(\sqrt{-2}) $	$_{}$	None	None					198.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+(3-\beta )q^{11}+3\beta q^{13}+6q^{17}+\cdots$
1584.2.b.e	$1584$	$2$	1584.b	33.d	$2$	$4$	$4$	$12.648$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None					99.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{3}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots$
1584.2.b.f	$1584$	$2$	1584.b	33.d	$2$	$6$	$6$	$12.648$	6.0.12781568.1	$_{}$	None	None					792.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}+\beta _{4})q^{11}+\cdots$
1584.2.b.g	$1584$	$2$	1584.b	33.d	$2$	$6$	$6$	$12.648$	6.0.12781568.1	$_{}$	None	None					792.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots$
1584.2.d.a	$1584$	$2$	1584.d	12.b	$2$	$2$	$2$	$12.648$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1584.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-2\beta q^{7}-q^{11}+\beta q^{17}-2\beta q^{19}+\cdots$
1584.2.d.b	$1584$	$2$	1584.d	12.b	$2$	$2$	$2$	$12.648$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			1584.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+2\beta q^{7}+q^{11}+\beta q^{17}+2\beta q^{19}+\cdots$
1584.2.d.c	$1584$	$2$	1584.d	12.b	$2$	$8$	$8$	$12.648$	8.0.1768034304.5	$_{}$	None	None		✓			1584.2.d.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{5}-\beta _{4}q^{7}-q^{11}+(-1+\beta _{3}+\cdots)q^{13}+\cdots$
1584.2.d.d	$1584$	$2$	1584.d	12.b	$2$	$8$	$8$	$12.648$	8.0.1768034304.5	$_{}$	None	None		✓			1584.2.d.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{5}+\beta _{4}q^{7}+q^{11}+(-1+\beta _{3}+\cdots)q^{13}+\cdots$
1584.2.o.a	$1584$	$2$	1584.o	44.c	$2$	$2$	$2$	$12.648$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None					176.2.e.a	$4$	$0$	$0$	$0$	$-6$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{5}-\beta q^{11}+\beta q^{23}+4q^{25}+3\beta q^{31}+\cdots$
1584.2.o.b	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			1584.2.o.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+\beta _{2}q^{7}+(-3+\beta _{1})q^{11}+\cdots$
1584.2.o.c	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	$\Q(\sqrt{6}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-33}) $	None		✓			1584.2.o.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{7}-\beta _{3}q^{11}+\beta _{2}q^{17}+3\beta _{1}q^{19}+\cdots$
1584.2.o.d	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			1584.2.o.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{11}-3\beta _{1}q^{13}+\cdots$
1584.2.o.e	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None					176.2.e.b	$4$	$0$	$0$	$0$	$6$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(1+\beta _{3})q^{5}+(2\beta _{1}-\beta _{2})q^{11}+(\beta _{1}+\cdots)q^{23}+\cdots$
1584.2.o.f	$1584$	$2$	1584.o	44.c	$2$	$4$	$4$	$12.648$	$\Q(i, \sqrt{10})$	$_{}$	None	None					528.2.o.a	$4$	$0$	$0$	$0$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\cdots$
1584.2.o.g	$1584$	$2$	1584.o	44.c	$2$	$8$	$8$	$12.648$	8.0.454201344.7	$_{}$	None	None			✓		528.2.o.b	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{5}+\beta _{6}q^{7}+(\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots$

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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.