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 71 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
3696.1.bb.a	$3696$	$1$	3696.bb	231.h	$2$	$1$	$1$	$1.845$	$\Q$	$D_{3}$	$\Q(\sqrt{-231}) $	None	✓				231.1.h.a	$2$	$0$	$0$	$-1$	$-1$	$-1$		$1$		$q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
3696.1.bb.b	$3696$	$1$	3696.bb	231.h	$2$	$1$	$1$	$1.845$	$\Q$	$D_{3}$	$\Q(\sqrt{-231}) $	None	✓				231.1.h.a	$2$	$0$	$0$	$-1$	$-1$	$1$		$1$		$q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
3696.1.bb.c	$3696$	$1$	3696.bb	231.h	$2$	$1$	$1$	$1.845$	$\Q$	$D_{3}$	$\Q(\sqrt{-231}) $	None	✓				231.1.h.a	$2$	$0$	$0$	$1$	$1$	$-1$		$1$		$q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
3696.1.bb.d	$3696$	$1$	3696.bb	231.h	$2$	$1$	$1$	$1.845$	$\Q$	$D_{3}$	$\Q(\sqrt{-231}) $	None	✓				231.1.h.a	$2$	$0$	$0$	$1$	$1$	$1$		$1$		$q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
3696.1.bm.a	$3696$	$1$	3696.bm	3696.am	$4$	$4$	$2$	$1.845$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-231}) $	None		✓			3696.1.bm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{6}+\cdots$
3696.1.bm.b	$3696$	$1$	3696.bm	3696.am	$4$	$4$	$2$	$1.845$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-231}) $	None		✓			3696.1.bm.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{6}+\cdots$
3696.1.bm.c	$3696$	$1$	3696.bm	3696.am	$4$	$8$	$4$	$1.845$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-231}) $	None		✓			3696.1.bm.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{10}q^{4}+\cdots$
3696.1.bm.d	$3696$	$1$	3696.bm	3696.am	$4$	$8$	$4$	$1.845$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-231}) $	None		✓			3696.1.bm.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{3}q^{3}-\zeta_{24}^{2}q^{4}+\cdots$
3696.1.cn.a	$3696$	$1$	3696.cn	924.z	$6$	$4$	$2$	$1.845$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-33}) $	None		✓			3696.1.cn.a	$8$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
3696.1.cn.b	$3696$	$1$	3696.cn	924.z	$6$	$4$	$2$	$1.845$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-33}) $	None		✓			3696.1.cn.a	$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
3696.1.dl.a	$3696$	$1$	3696.dl	924.ak	$10$	$8$	$2$	$1.845$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-21}) $	None		✓			3696.1.dl.a	$8$	$0$	$0$	$-2$	$0$	$2$		$1$		$q-\zeta_{20}^{6}q^{3}+(-\zeta_{20}+\zeta_{20}^{5})q^{5}-\zeta_{20}^{4}q^{7}+\cdots$
3696.1.dl.b	$3696$	$1$	3696.dl	924.ak	$10$	$8$	$2$	$1.845$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-21}) $	None		✓			3696.1.dl.a	$8$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+\zeta_{20}^{6}q^{3}+(-\zeta_{20}+\zeta_{20}^{5})q^{5}+\zeta_{20}^{4}q^{7}+\cdots$
3696.2.a.a	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.e	$1$	$1$	$0$	$-1$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots$
3696.2.a.b	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				924.2.a.f	$1$	$0$	$0$	$-1$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}-7q^{13}+\cdots$
3696.2.a.c	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.f	$1$	$1$	$0$	$-1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}-3q^{13}+\cdots$
3696.2.a.d	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				924.2.a.e	$1$	$0$	$0$	$-1$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}+3q^{13}+\cdots$
3696.2.a.e	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.g	$1$	$1$	$0$	$-1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots$
3696.2.a.f	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.i	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-5q^{13}+\cdots$
3696.2.a.g	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.h	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
3696.2.a.h	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				924.2.a.g	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
3696.2.a.i	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				462.2.a.f	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+q^{11}+2q^{13}-2q^{19}+\cdots$
3696.2.a.j	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				462.2.a.d	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+q^{11}+6q^{13}+4q^{17}+\cdots$
3696.2.a.k	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.j	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-5q^{13}+\cdots$
3696.2.a.l	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.k	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+3q^{13}+\cdots$
3696.2.a.m	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				462.2.a.g	$1$	$1$	$0$	$-1$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}-2q^{13}+\cdots$
3696.2.a.n	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.l	$1$	$0$	$0$	$-1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}+6q^{13}+\cdots$
3696.2.a.o	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				924.2.a.h	$1$	$1$	$0$	$-1$	$3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
3696.2.a.p	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				462.2.a.e	$1$	$0$	$0$	$1$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$
3696.2.a.q	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.a	$1$	$0$	$0$	$1$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
3696.2.a.r	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				924.2.a.a	$1$	$1$	$0$	$1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
3696.2.a.s	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				462.2.a.a	$1$	$1$	$0$	$1$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
3696.2.a.t	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				231.2.a.a	$1$	$0$	$0$	$1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}+q^{9}+q^{11}+6q^{13}+\cdots$
3696.2.a.u	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				924.2.a.c	$1$	$0$	$0$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-3q^{13}+\cdots$
3696.2.a.v	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.b	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-3q^{13}+\cdots$
3696.2.a.w	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				924.2.a.b	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
3696.2.a.x	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.c	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+q^{11}+2q^{13}-8q^{17}+\cdots$
3696.2.a.y	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				462.2.a.b	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+q^{11}-2q^{13}-4q^{17}+\cdots$
3696.2.a.z	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				924.2.a.d	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
3696.2.a.ba	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				1848.2.a.d	$1$	$0$	$0$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}+q^{9}-q^{11}-6q^{13}+\cdots$
3696.2.a.bb	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	$_{}$	None	None	✓				462.2.a.c	$1$	$0$	$0$	$1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
3696.2.a.bc	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				462.2.a.h	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
3696.2.a.bd	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓		✓		1848.2.a.s	$1$	$0$	$0$	$-2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{7}+q^{9}-q^{11}-\beta q^{13}+\cdots$
3696.2.a.be	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				231.2.a.c	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots$
3696.2.a.bf	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓		✓		1848.2.a.o	$1$	$1$	$0$	$2$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots$
3696.2.a.bg	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				1848.2.a.m	$1$	$1$	$0$	$2$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots$
3696.2.a.bh	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				1848.2.a.n	$1$	$1$	$0$	$2$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots$
3696.2.a.bi	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				1848.2.a.p	$1$	$0$	$0$	$2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{7}+q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots$
3696.2.a.bj	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		1848.2.a.r	$1$	$0$	$0$	$2$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-q^{11}+\cdots$
3696.2.a.bk	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				1848.2.a.q	$1$	$0$	$0$	$2$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+q^{11}+\cdots$
3696.2.a.bl	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓		✓		231.2.a.b	$1$	$0$	$0$	$2$	$6$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots$

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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.