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 144 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
3840.1.c.a	$3840$	$1$	3840.c	15.d	$2$	$1$	$1$	$1.916$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $	✓				120.1.i.a	$4$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-q^{3}-q^{5}+q^{9}+q^{15}+q^{25}-q^{27}+\cdots$
3840.1.c.b	$3840$	$1$	3840.c	15.d	$2$	$1$	$1$	$1.916$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $	✓				120.1.i.a	$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-q^{3}+q^{5}+q^{9}-q^{15}+q^{25}-q^{27}+\cdots$
3840.1.c.c	$3840$	$1$	3840.c	15.d	$2$	$1$	$1$	$1.916$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $	✓				120.1.i.a	$4$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+q^{3}-q^{5}+q^{9}-q^{15}+q^{25}+q^{27}+\cdots$
3840.1.c.d	$3840$	$1$	3840.c	15.d	$2$	$1$	$1$	$1.916$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $	✓				120.1.i.a	$4$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{5}+q^{9}+q^{15}+q^{25}+q^{27}+\cdots$
3840.1.c.e	$3840$	$1$	3840.c	15.d	$2$	$2$	$2$	$1.916$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{30}) $					1920.1.i.e	$8$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}-i q^{5}+2 i q^{7}+q^{9}+i q^{15}+\cdots$
3840.1.c.f	$3840$	$1$	3840.c	15.d	$2$	$2$	$2$	$1.916$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{6}) $					1920.1.i.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}-i q^{5}-q^{9}-q^{15}-2 q^{23}+\cdots$
3840.1.c.g	$3840$	$1$	3840.c	15.d	$2$	$2$	$2$	$1.916$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{6}) $					1920.1.i.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{3}-i q^{5}-q^{9}+q^{15}+2 q^{23}+\cdots$
3840.1.c.h	$3840$	$1$	3840.c	15.d	$2$	$2$	$2$	$1.916$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{30}) $					1920.1.i.e	$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}-i q^{5}-2 i q^{7}+q^{9}-i q^{15}+\cdots$
3840.1.i.a	$3840$	$1$	3840.i	120.i	$2$	$4$	$4$	$1.916$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None					480.1.c.a	$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{8}q^{3}-q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
3840.1.i.b	$3840$	$1$	3840.i	120.i	$2$	$4$	$4$	$1.916$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None					480.1.c.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}q^{3}+q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
3840.1.bj.a	$3840$	$1$	3840.bj	60.l	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None					1920.1.u.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}^{3}q^{3}-\zeta_{8}q^{5}+(-1+\zeta_{8}^{2})q^{7}+\cdots$
3840.1.bj.b	$3840$	$1$	3840.bj	60.l	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None					960.1.u.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{3}q^{5}+(-1+\zeta_{8}^{2})q^{7}+\cdots$
3840.1.bj.c	$3840$	$1$	3840.bj	60.l	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None					960.1.u.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots$
3840.1.bj.d	$3840$	$1$	3840.bj	60.l	$4$	$4$	$2$	$1.916$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None					1920.1.u.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}q^{5}+(1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
3840.1.bu.a	$3840$	$1$	3840.bu	480.au	$8$	$8$	$2$	$1.916$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None					480.1.bu.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}q^{3}+\zeta_{16}^{3}q^{5}+\zeta_{16}^{2}q^{9}-\zeta_{16}^{4}q^{15}+\cdots$
3840.1.bu.b	$3840$	$1$	3840.bu	480.au	$8$	$8$	$2$	$1.916$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None					480.1.bu.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}q^{3}+\zeta_{16}^{3}q^{5}+\zeta_{16}^{2}q^{9}+\zeta_{16}^{4}q^{15}+\cdots$
3840.1.cl.a	$3840$	$1$	3840.cl	960.bl	$16$	$16$	$2$	$1.916$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-15}) $	None			✓	✓	960.1.cl.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{3}q^{3}+\zeta_{32}q^{5}+\zeta_{32}^{6}q^{9}-\zeta_{32}^{4}q^{15}+\cdots$
3840.1.dy.a	$3840$	$1$	3840.dy	3840.cy	$64$	$64$	$2$	$1.916$	$\Q(\zeta_{128})$	$D_{64}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	3840.1.dy.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{128}^{29}q^{2}-\zeta_{128}q^{3}+\zeta_{128}^{58}q^{4}+\cdots$
3840.2.a.a	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				960.2.k.a	$1$	$1$	$0$	$-1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
3840.2.a.b	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.a	$1$	$0$	$0$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
3840.2.a.c	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.b	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
3840.2.a.d	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				120.2.k.a	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+q^{15}+\cdots$
3840.2.a.e	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				960.2.k.b	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+6q^{13}+q^{15}+2q^{19}+\cdots$
3840.2.a.f	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.c	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
3840.2.a.g	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.d	$1$	$0$	$0$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}+6q^{11}+6q^{13}+\cdots$
3840.2.a.h	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.c	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
3840.2.a.i	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.d	$1$	$0$	$0$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}+6q^{11}-6q^{13}+\cdots$
3840.2.a.j	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				960.2.k.b	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-6q^{13}-q^{15}+2q^{19}+\cdots$
3840.2.a.k	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.a	$1$	$0$	$0$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
3840.2.a.l	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.b	$1$	$1$	$0$	$-1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
3840.2.a.m	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				120.2.k.a	$1$	$1$	$0$	$-1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-q^{15}+\cdots$
3840.2.a.n	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				960.2.k.a	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
3840.2.a.o	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.d	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}+6q^{13}+\cdots$
3840.2.a.p	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.c	$1$	$0$	$0$	$1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
3840.2.a.q	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				960.2.k.b	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+6q^{13}-q^{15}-2q^{19}+\cdots$
3840.2.a.r	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				120.2.k.a	$1$	$1$	$0$	$1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots$
3840.2.a.s	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.a	$1$	$1$	$0$	$1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
3840.2.a.t	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.b	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
3840.2.a.u	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				960.2.k.a	$1$	$1$	$0$	$1$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
3840.2.a.v	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				960.2.k.a	$1$	$0$	$0$	$1$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
3840.2.a.w	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				120.2.k.a	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+q^{15}+\cdots$
3840.2.a.x	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.a	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
3840.2.a.y	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.b	$1$	$0$	$0$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
3840.2.a.z	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				960.2.k.b	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-6q^{13}+q^{15}-2q^{19}+\cdots$
3840.2.a.ba	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.d	$1$	$1$	$0$	$1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots$
3840.2.a.bb	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	$_{}$	None	None	✓				1920.2.k.c	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
3840.2.a.bc	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1920.2.k.i	$1$	$1$	$0$	$-2$	$-2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots$
3840.2.a.bd	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1920.2.k.j	$1$	$0$	$0$	$-2$	$-2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
3840.2.a.be	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				960.2.k.e	$1$	$1$	$0$	$-2$	$-2$	$4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
3840.2.a.bf	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				960.2.k.e	$1$	$0$	$0$	$-2$	$2$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$

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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.