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 60 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
3654.2.a.a	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.f	$1$	$1$	$-1$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}+4q^{10}+\cdots$
3654.2.a.b	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.j	$1$	$0$	$-1$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots$
3654.2.a.c	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.k	$1$	$0$	$-1$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots$
3654.2.a.d	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.i	$1$	$0$	$-1$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots$
3654.2.a.e	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓	✓			3654.2.a.e	$1$	$1$	$-1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{11}-3q^{13}+\cdots$
3654.2.a.f	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.e	$1$	$0$	$-1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-4q^{13}+\cdots$
3654.2.a.g	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓	✓			3654.2.a.g	$1$	$1$	$-1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}+2q^{13}+\cdots$
3654.2.a.h	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.h	$1$	$0$	$-1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{13}-q^{14}+\cdots$
3654.2.a.i	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓	✓	✓	✓	3654.2.a.i	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-q^{13}+\cdots$
3654.2.a.j	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.d	$1$	$1$	$-1$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots$
3654.2.a.k	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓	✓			3654.2.a.k	$1$	$0$	$-1$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots$
3654.2.a.l	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				406.2.a.d	$1$	$0$	$-1$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots$
3654.2.a.m	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.g	$1$	$0$	$-1$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots$
3654.2.a.n	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				406.2.a.c	$1$	$1$	$1$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots$
3654.2.a.o	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓	✓			3654.2.a.k	$1$	$0$	$1$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots$
3654.2.a.p	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.b	$1$	$1$	$1$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots$
3654.2.a.q	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓	✓			3654.2.a.g	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}+2q^{13}+\cdots$
3654.2.a.r	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.c	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{13}-q^{14}+\cdots$
3654.2.a.s	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓	✓			3654.2.a.e	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}-3q^{13}+\cdots$
3654.2.a.t	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				406.2.a.a	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}+4q^{11}-q^{14}+\cdots$
3654.2.a.u	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓	✓	✓	✓	3654.2.a.i	$1$	$1$	$1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-q^{13}+\cdots$
3654.2.a.v	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				1218.2.a.a	$1$	$1$	$1$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots$
3654.2.a.w	$3654$	$2$	3654.a	1.a	$1$	$1$	$1$	$29.177$	$\Q$	None	✓				406.2.a.b	$1$	$0$	$1$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots$
3654.2.a.x	$3654$	$2$	3654.a	1.a	$1$	$2$	$2$	$29.177$	$\Q(\sqrt{17}) $	None	✓				1218.2.a.n	$1$	$1$	$-2$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots$
3654.2.a.y	$3654$	$2$	3654.a	1.a	$1$	$2$	$2$	$29.177$	$\Q(\sqrt{3}) $	None	✓		✓		406.2.a.e	$1$	$1$	$-2$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{7}-q^{8}+\cdots$
3654.2.a.z	$3654$	$2$	3654.a	1.a	$1$	$2$	$2$	$29.177$	$\Q(\sqrt{2}) $	None	✓				1218.2.a.m	$1$	$0$	$-2$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{5}+q^{7}-q^{8}+\cdots$
3654.2.a.ba	$3654$	$2$	3654.a	1.a	$1$	$2$	$2$	$29.177$	$\Q(\sqrt{5}) $	None	✓				1218.2.a.l	$1$	$0$	$2$	$0$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}+q^{8}+\cdots$
3654.2.a.bb	$3654$	$2$	3654.a	1.a	$1$	$3$	$3$	$29.177$	3.3.2920.1	None	✓		✓		1218.2.a.r	$1$	$0$	$-3$	$0$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+q^{7}-q^{8}+\cdots$
3654.2.a.bc	$3654$	$2$	3654.a	1.a	$1$	$3$	$3$	$29.177$	3.3.568.1	None	✓		✓		406.2.a.f	$1$	$1$	$3$	$0$	$-5$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2+\beta _{1})q^{5}-q^{7}+q^{8}+\cdots$
3654.2.a.bd	$3654$	$2$	3654.a	1.a	$1$	$3$	$3$	$29.177$	3.3.1304.1	None	✓				1218.2.a.q	$1$	$0$	$3$	$0$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+q^{7}+q^{8}+\cdots$
3654.2.a.be	$3654$	$2$	3654.a	1.a	$1$	$3$	$3$	$29.177$	3.3.229.1	None	✓		✓		1218.2.a.p	$1$	$0$	$3$	$0$	$0$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}+\cdots$
3654.2.a.bf	$3654$	$2$	3654.a	1.a	$1$	$3$	$3$	$29.177$	3.3.568.1	None	✓				1218.2.a.o	$1$	$0$	$3$	$0$	$0$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{7}+q^{8}+\beta _{1}q^{10}+\cdots$
3654.2.a.bg	$3654$	$2$	3654.a	1.a	$1$	$4$	$4$	$29.177$	4.4.11348.1	None	✓		✓		406.2.a.g	$1$	$1$	$-4$	$0$	$1$	$4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}-q^{8}+\beta _{1}q^{10}+\cdots$
3654.2.a.bh	$3654$	$2$	3654.a	1.a	$1$	$5$	$5$	$29.177$	5.5.3060944.1	None	✓	✓	✓		3654.2.a.bh	$1$	$0$	$-5$	$0$	$-2$	$5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{3}q^{5}+q^{7}-q^{8}-\beta _{3}q^{10}+\cdots$
3654.2.a.bi	$3654$	$2$	3654.a	1.a	$1$	$5$	$5$	$29.177$	5.5.3241536.1	None	✓	✓	✓	✓	3654.2.a.bi	$1$	$0$	$-5$	$0$	$0$	$-5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}-q^{8}-\beta _{3}q^{10}+\cdots$
3654.2.a.bj	$3654$	$2$	3654.a	1.a	$1$	$5$	$5$	$29.177$	5.5.3241536.1	None	✓	✓	✓	✓	3654.2.a.bi	$1$	$0$	$5$	$0$	$0$	$-5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{3}q^{5}-q^{7}+q^{8}-\beta _{3}q^{10}+\cdots$
3654.2.a.bk	$3654$	$2$	3654.a	1.a	$1$	$5$	$5$	$29.177$	5.5.3060944.1	None	✓	✓	✓		3654.2.a.bh	$1$	$0$	$5$	$0$	$2$	$5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{3}q^{5}+q^{7}+q^{8}-\beta _{3}q^{10}+\cdots$
3654.2.f.a	$3654$	$2$	3654.f	21.c	$2$	$40$	$40$	$29.177$		None		✓			3654.2.f.a	$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
3654.2.f.b	$3654$	$2$	3654.f	21.c	$2$	$40$	$40$	$29.177$		None		✓			3654.2.f.b	$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
3654.2.g.a	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	$\Q(\sqrt{-1}) $	None					1218.2.g.e	$2$	$1$	$0$	$0$	$-8$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}-4 q^{5}+q^{7}-i q^{8}+\cdots$
3654.2.g.b	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	$\Q(\sqrt{-1}) $	None		✓			3654.2.g.b	$2$	$0$	$0$	$0$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}-2 q^{5}-q^{7}+i q^{8}+\cdots$
3654.2.g.c	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	$\Q(\sqrt{-1}) $	None					1218.2.g.d	$2$	$0$	$0$	$0$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}-2 q^{5}+q^{7}+i q^{8}+\cdots$
3654.2.g.d	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	$\Q(\sqrt{-1}) $	None					406.2.c.a	$2$	$1$	$0$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}-q^{5}+q^{7}-i q^{8}+\cdots$
3654.2.g.e	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	$\Q(\sqrt{-1}) $	None					1218.2.g.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}-q^{7}+i q^{8}-4 i q^{11}+\cdots$
3654.2.g.f	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	$\Q(\sqrt{-1}) $	None					1218.2.g.c	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}-q^{7}-i q^{8}-3 i q^{11}+\cdots$
3654.2.g.g	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	$\Q(\sqrt{-1}) $	None		✓			3654.2.g.b	$2$	$0$	$0$	$0$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+2 q^{5}-q^{7}+i q^{8}+\cdots$
3654.2.g.h	$3654$	$2$	3654.g	29.b	$2$	$2$	$2$	$29.177$	$\Q(\sqrt{-1}) $	None					1218.2.g.a	$2$	$0$	$0$	$0$	$8$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+4 q^{5}+q^{7}+i q^{8}+\cdots$
3654.2.g.i	$3654$	$2$	3654.g	29.b	$2$	$4$	$4$	$29.177$	$\Q(i, \sqrt{33})$	None		✓			3654.2.g.i	$2$	$0$	$0$	$0$	$-8$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}-2q^{5}+q^{7}+\beta _{2}q^{8}+\cdots$
3654.2.g.j	$3654$	$2$	3654.g	29.b	$2$	$4$	$4$	$29.177$	$\Q(i, \sqrt{5})$	None					1218.2.g.h	$2$	$0$	$0$	$0$	$-4$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+(-1+\beta _{3})q^{5}+q^{7}+\cdots$
3654.2.g.k	$3654$	$2$	3654.g	29.b	$2$	$4$	$4$	$29.177$	$\Q(i, \sqrt{57})$	None					1218.2.g.g	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+q^{7}+\beta _{2}q^{8}+(-\beta _{1}+\cdots)q^{11}+\cdots$

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