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 62 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
4680.2.a.a	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-5q^{7}-q^{11}+q^{13}+3q^{17}+\cdots$
4680.2.a.b	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	✓			4680.2.a.b	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}-3q^{11}+q^{13}+3q^{17}+\cdots$
4680.2.a.c	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.j	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}+3q^{11}-q^{13}+q^{17}+\cdots$
4680.2.a.d	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.k	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+q^{13}+4q^{17}+6q^{19}+\cdots$
4680.2.a.e	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				520.2.a.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{11}+q^{13}-2q^{17}+2q^{19}+\cdots$
4680.2.a.f	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	✓			4680.2.a.f	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{13}+6q^{17}-8q^{19}-6q^{23}+\cdots$
4680.2.a.g	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.d	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{11}+q^{13}-2q^{17}-4q^{19}+\cdots$
4680.2.a.h	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	✓			4680.2.a.h	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-4q^{11}-q^{13}-8q^{17}+\cdots$
4680.2.a.i	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.e	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-4q^{11}-q^{13}+2q^{19}+\cdots$
4680.2.a.j	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	✓			4680.2.a.j	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}+5q^{11}-q^{13}-3q^{17}+\cdots$
4680.2.a.k	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.f	$1$	$1$	$0$	$0$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-4q^{11}+q^{13}-6q^{17}+\cdots$
4680.2.a.l	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.l	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}+q^{13}-2q^{17}+q^{25}+\cdots$
4680.2.a.m	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.g	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-4q^{11}+q^{13}+6q^{17}+\cdots$
4680.2.a.n	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	✓			4680.2.a.b	$1$	$1$	$0$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots$
4680.2.a.o	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.h	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+5q^{11}+q^{13}-3q^{17}+\cdots$
4680.2.a.p	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.b	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{11}+q^{13}+2q^{17}-4q^{19}+\cdots$
4680.2.a.q	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.i	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{13}-2q^{17}-4q^{23}+q^{25}+\cdots$
4680.2.a.r	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	✓			4680.2.a.f	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{13}-6q^{17}-8q^{19}+6q^{23}+\cdots$
4680.2.a.s	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				1560.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{13}+6q^{17}+4q^{19}+q^{25}+\cdots$
4680.2.a.t	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓				520.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{11}-q^{13}+6q^{17}+4q^{19}+\cdots$
4680.2.a.u	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	✓			4680.2.a.h	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+4q^{11}-q^{13}+8q^{17}+\cdots$
4680.2.a.v	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	✓			4680.2.a.j	$1$	$1$	$0$	$0$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}-5q^{11}-q^{13}+3q^{17}+\cdots$
4680.2.a.w	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{2}) $	None	✓				520.2.a.c	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-3\beta q^{11}-q^{13}+(2+2\beta )q^{17}+\cdots$
4680.2.a.x	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{5}) $	None	✓	✓	✓		4680.2.a.x	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-q^{13}+(2-\beta )q^{17}+2q^{19}+\cdots$
4680.2.a.y	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{17}) $	None	✓		✓		1560.2.a.o	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-\beta q^{7}+(4-\beta )q^{11}+q^{13}+(2+\cdots)q^{17}+\cdots$
4680.2.a.z	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{6}) $	None	✓		✓		520.2.a.f	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+(2-\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
4680.2.a.ba	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{5}) $	None	✓	✓	✓		4680.2.a.x	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-q^{13}+(-2-\beta )q^{17}+\cdots$
4680.2.a.bb	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{41}) $	None	✓				1560.2.a.m	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-\beta q^{7}+(2+\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
4680.2.a.bc	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{5}) $	None	✓				520.2.a.g	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(-3-\beta )q^{11}-q^{13}-2q^{17}+\cdots$
4680.2.a.bd	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{3}) $	None	✓		✓		520.2.a.e	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2\beta q^{7}+(-1-\beta )q^{11}+q^{13}+\cdots$
4680.2.a.be	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{3}) $	None	✓				520.2.a.d	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2\beta q^{7}+(3+\beta )q^{11}+q^{13}+\cdots$
4680.2.a.bf	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{33}) $	None	✓		✓		1560.2.a.n	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{7}+\beta q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
4680.2.a.bg	$4680$	$2$	4680.a	1.a	$1$	$3$	$3$	$37.370$	3.3.1016.1	None	✓	✓	✓		4680.2.a.bg	$1$	$0$	$0$	$0$	$-3$	$-1$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}-\beta _{2}q^{7}+(2-\beta _{1})q^{11}-q^{13}+\cdots$
4680.2.a.bh	$4680$	$2$	4680.a	1.a	$1$	$3$	$3$	$37.370$	3.3.940.1	None	✓		✓		1560.2.a.q	$1$	$0$	$0$	$0$	$-3$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+\beta _{2}q^{7}+(-2-\beta _{1})q^{11}-q^{13}+\cdots$
4680.2.a.bi	$4680$	$2$	4680.a	1.a	$1$	$3$	$3$	$37.370$	3.3.621.1	None	✓	✓	✓	✓	4680.2.a.bi	$1$	$0$	$0$	$0$	$-3$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+(1+\beta _{2})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots$
4680.2.a.bj	$4680$	$2$	4680.a	1.a	$1$	$3$	$3$	$37.370$	3.3.1016.1	None	✓	✓	✓		4680.2.a.bg	$1$	$0$	$0$	$0$	$3$	$-1$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{5}-\beta _{2}q^{7}+(-2+\beta _{1})q^{11}-q^{13}+\cdots$
4680.2.a.bk	$4680$	$2$	4680.a	1.a	$1$	$3$	$3$	$37.370$	3.3.621.1	None	✓	✓	✓	✓	4680.2.a.bi	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta _{2})q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots$
4680.2.a.bl	$4680$	$2$	4680.a	1.a	$1$	$3$	$3$	$37.370$	3.3.1849.1	None	✓		✓		1560.2.a.p	$1$	$0$	$0$	$0$	$3$	$5$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(2-\beta _{1})q^{7}+(-1-\beta _{2})q^{11}+\cdots$
4680.2.g.a	$4680$	$2$	4680.g	13.b	$2$	$2$	$2$	$37.370$	$\Q(\sqrt{-1}) $	None					1560.2.g.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{5}+4 i q^{7}-4 i q^{11}+(-2 i-3)q^{13}+\cdots$
4680.2.g.b	$4680$	$2$	4680.g	13.b	$2$	$2$	$2$	$37.370$	$\Q(\sqrt{-1}) $	None					1560.2.g.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{5}+2 i q^{7}+4 i q^{11}+(2 i-3)q^{13}+\cdots$
4680.2.g.c	$4680$	$2$	4680.g	13.b	$2$	$2$	$2$	$37.370$	$\Q(\sqrt{-1}) $	None					1560.2.g.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{5}+2 i q^{7}+(2 i-3)q^{13}+6 q^{17}+\cdots$
4680.2.g.d	$4680$	$2$	4680.g	13.b	$2$	$2$	$2$	$37.370$	$\Q(\sqrt{-1}) $	None					1560.2.g.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{5}+6 i q^{11}+(-3 i-2)q^{13}+\cdots$
4680.2.g.e	$4680$	$2$	4680.g	13.b	$2$	$2$	$2$	$37.370$	$\Q(\sqrt{-1}) $	None					1560.2.g.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{5}+3 i q^{7}+3 i q^{11}+(-3 i-2)q^{13}+\cdots$
4680.2.g.f	$4680$	$2$	4680.g	13.b	$2$	$4$	$4$	$37.370$	$\Q(\zeta_{12})$	None					1560.2.g.g	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{5}-\beta_{2} q^{7}+(-\beta_{2}+1)q^{13}+\cdots$
4680.2.g.g	$4680$	$2$	4680.g	13.b	$2$	$4$	$4$	$37.370$	$\Q(i, \sqrt{17})$	None					1560.2.g.h	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
4680.2.g.h	$4680$	$2$	4680.g	13.b	$2$	$4$	$4$	$37.370$	$\Q(i, \sqrt{41})$	None					1560.2.g.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots$
4680.2.g.i	$4680$	$2$	4680.g	13.b	$2$	$6$	$6$	$37.370$	6.0.3356224.1	None					1560.2.g.i	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-2\beta _{1}+\beta _{4})q^{7}+(-2\beta _{4}+\cdots)q^{11}+\cdots$
4680.2.g.j	$4680$	$2$	4680.g	13.b	$2$	$6$	$6$	$37.370$	6.0.350464.1	None					520.2.k.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}+(\beta _{3}-\beta _{4}+\beta _{5})q^{7}+(\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots$
4680.2.g.k	$4680$	$2$	4680.g	13.b	$2$	$8$	$8$	$37.370$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					520.2.k.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+(-\beta _{2}-\beta _{4}+\beta _{5})q^{7}+\beta _{4}q^{11}+\cdots$
4680.2.g.l	$4680$	$2$	4680.g	13.b	$2$	$12$	$12$	$37.370$	12.0.$\cdots$.1	None		✓			4680.2.g.l	$4$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{6}q^{11}+(-1-\beta _{7}+\cdots)q^{13}+\cdots$

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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.