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 98 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
2070.2.a.a	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓	✓	✓	✓	2070.2.a.a	$1$	$0$	$-1$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
2070.2.a.b	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓				690.2.a.k	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots$
2070.2.a.c	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓				690.2.a.j	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots$
2070.2.a.d	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓	✓			2070.2.a.d	$1$	$1$	$-1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
2070.2.a.e	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓				690.2.a.g	$1$	$1$	$-1$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots$
2070.2.a.f	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓	✓	✓	✓	2070.2.a.f	$1$	$0$	$-1$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots$
2070.2.a.g	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓				690.2.a.i	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots$
2070.2.a.h	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓				690.2.a.h	$1$	$0$	$-1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+6q^{13}+\cdots$
2070.2.a.i	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓	✓			2070.2.a.i	$1$	$1$	$-1$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
2070.2.a.j	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓	✓			2070.2.a.d	$1$	$0$	$1$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
2070.2.a.k	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓				690.2.a.c	$1$	$0$	$1$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
2070.2.a.l	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓	✓	✓	✓	2070.2.a.f	$1$	$1$	$1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
2070.2.a.m	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓		✓	✓	690.2.a.f	$1$	$1$	$1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-4q^{11}+\cdots$
2070.2.a.n	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓	✓			2070.2.a.i	$1$	$0$	$1$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
2070.2.a.o	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓				690.2.a.d	$1$	$0$	$1$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots$
2070.2.a.p	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓	✓	✓	✓	2070.2.a.a	$1$	$1$	$1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
2070.2.a.q	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓		✓	✓	690.2.a.a	$1$	$1$	$1$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
2070.2.a.r	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓				690.2.a.e	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots$
2070.2.a.s	$2070$	$2$	2070.a	1.a	$1$	$1$	$1$	$16.529$	$\Q$	None	✓				690.2.a.b	$1$	$0$	$1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots$
2070.2.a.t	$2070$	$2$	2070.a	1.a	$1$	$2$	$2$	$16.529$	$\Q(\sqrt{17})$	None	✓				690.2.a.l	$1$	$0$	$-2$	$0$	$-2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots$
2070.2.a.u	$2070$	$2$	2070.a	1.a	$1$	$2$	$2$	$16.529$	$\Q(\sqrt{5})$	None	✓				230.2.a.c	$1$	$0$	$-2$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots$
2070.2.a.v	$2070$	$2$	2070.a	1.a	$1$	$2$	$2$	$16.529$	$\Q(\sqrt{2})$	None	✓	✓	✓	✓	2070.2.a.v	$1$	$1$	$-2$	$0$	$-2$	$4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(2+\beta )q^{7}-q^{8}+\cdots$
2070.2.a.w	$2070$	$2$	2070.a	1.a	$1$	$2$	$2$	$16.529$	$\Q(\sqrt{13})$	None	✓		✓		230.2.a.b	$1$	$0$	$2$	$0$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}+q^{8}+\cdots$
2070.2.a.x	$2070$	$2$	2070.a	1.a	$1$	$2$	$2$	$16.529$	$\Q(\sqrt{21})$	None	✓		✓		230.2.a.a	$1$	$0$	$2$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+q^{10}+\cdots$
2070.2.a.y	$2070$	$2$	2070.a	1.a	$1$	$2$	$2$	$16.529$	$\Q(\sqrt{2})$	None	✓	✓	✓	✓	2070.2.a.v	$1$	$0$	$2$	$0$	$2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(2+\beta )q^{7}+q^{8}+\cdots$
2070.2.a.z	$2070$	$2$	2070.a	1.a	$1$	$3$	$3$	$16.529$	3.3.1101.1	None	✓		✓		230.2.a.d	$1$	$0$	$-3$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots$
2070.2.d.a	$2070$	$2$	2070.d	5.b	$2$	$4$	$4$	$16.529$	$\Q(\zeta_{8})$	None					690.2.d.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{2}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}-2\zeta_{8}^{2}q^{7}+\cdots$
2070.2.d.b	$2070$	$2$	2070.d	5.b	$2$	$4$	$4$	$16.529$	$\Q(i, \sqrt{5})$	None					690.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}-\beta _{3}q^{5}-4\beta _{1}q^{7}-\beta _{1}q^{8}+\cdots$
2070.2.d.c	$2070$	$2$	2070.d	5.b	$2$	$4$	$4$	$16.529$	$\Q(i, \sqrt{5})$	None					230.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-q^{4}+(1+2\beta _{2})q^{5}+3\beta _{1}q^{7}+\cdots$
2070.2.d.d	$2070$	$2$	2070.d	5.b	$2$	$6$	$6$	$16.529$	6.0.5161984.1	None					690.2.d.d	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-q^{4}+\beta _{4}q^{5}+2\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots$
2070.2.d.e	$2070$	$2$	2070.d	5.b	$2$	$6$	$6$	$16.529$	6.0.350464.1	None					690.2.d.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$
2070.2.d.f	$2070$	$2$	2070.d	5.b	$2$	$8$	$8$	$16.529$	8.0. $\cdots$ .3	None					230.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(\beta _{3}+\beta _{6})q^{5}+(\beta _{2}-\beta _{5}+\cdots)q^{7}+\cdots$
2070.2.d.g	$2070$	$2$	2070.d	5.b	$2$	$8$	$8$	$16.529$	$\Q(\zeta_{24})$	None		✓			2070.2.d.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}-q^{4}+\beta_{5} q^{5}-\beta_1 q^{8}+\cdots$
2070.2.d.h	$2070$	$2$	2070.d	5.b	$2$	$16$	$16$	$16.529$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		2070.2.d.h	$4$	$0$	$0$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}-q^{4}-\beta _{11}q^{5}+\beta _{12}q^{7}+\cdots$
2070.2.e.a	$2070$	$2$	2070.e	69.c	$2$	$16$	$16$	$16.529$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			2070.2.e.a	$2$	$0$	$0$	$0$	$-16$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}-q^{4}-q^{5}-\beta _{5}q^{7}+\beta _{8}q^{8}+\cdots$
2070.2.e.b	$2070$	$2$	2070.e	69.c	$2$	$16$	$16$	$16.529$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			2070.2.e.a	$2$	$0$	$0$	$0$	$16$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}-q^{4}+q^{5}-\beta _{5}q^{7}-\beta _{8}q^{8}+\cdots$
2070.2.h.a	$2070$	$2$	2070.h	345.h	$2$	$24$	$24$	$16.529$		None		✓			2070.2.h.a	$4$	$0$	$-24$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2070.2.h.b	$2070$	$2$	2070.h	345.h	$2$	$24$	$24$	$16.529$		None		✓			2070.2.h.a	$4$	$0$	$24$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2070.2.j.a	$2070$	$2$	2070.j	15.e	$4$	$4$	$2$	$16.529$	$\Q(\zeta_{8})$	None		✓			2070.2.j.a	$2$	$0$	$0$	$0$	$-8$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2-\zeta_{8}^{2})q^{5}+\cdots$
2070.2.j.b	$2070$	$2$	2070.j	15.e	$4$	$4$	$2$	$16.529$	$\Q(\zeta_{8})$	None		✓			2070.2.j.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots$
2070.2.j.c	$2070$	$2$	2070.j	15.e	$4$	$4$	$2$	$16.529$	$\Q(\zeta_{8})$	None		✓			2070.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
2070.2.j.d	$2070$	$2$	2070.j	15.e	$4$	$4$	$2$	$16.529$	$\Q(\zeta_{8})$	None		✓			2070.2.j.d	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
2070.2.j.e	$2070$	$2$	2070.j	15.e	$4$	$4$	$2$	$16.529$	$\Q(\zeta_{8})$	None		✓			2070.2.j.e	$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
2070.2.j.f	$2070$	$2$	2070.j	15.e	$4$	$4$	$2$	$16.529$	$\Q(\zeta_{8})$	None		✓			2070.2.j.a	$2$	$0$	$0$	$0$	$8$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2-\zeta_{8}^{2})q^{5}+\cdots$
2070.2.j.g	$2070$	$2$	2070.j	15.e	$4$	$12$	$6$	$16.529$	12.0. $\cdots$ .1	None		✓			2070.2.j.g	$4$	$0$	$0$	$0$	$0$	$-24$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{7}q^{4}-\beta _{11}q^{5}+(-2+2\beta _{7}+\cdots)q^{7}+\cdots$
2070.2.j.h	$2070$	$2$	2070.j	15.e	$4$	$16$	$8$	$16.529$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			2070.2.j.h	$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}-\beta _{7}q^{4}+(-\beta _{4}+\beta _{10})q^{5}+\cdots$
2070.2.j.i	$2070$	$2$	2070.j	15.e	$4$	$16$	$8$	$16.529$	16.0. $\cdots$ .1	None		✓			2070.2.j.i	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{2}-\beta _{10}q^{4}+\beta _{15}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
2070.2.j.j	$2070$	$2$	2070.j	15.e	$4$	$20$	$10$	$16.529$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		2070.2.j.j	$4$	$0$	$0$	$0$	$0$	$-16$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{13}q^{2}+\beta _{5}q^{4}+(-\beta _{12}-\beta _{16}+\cdots)q^{5}+\cdots$
2070.3.b.a	$2070$	$3$	2070.b	15.d	$2$	$88$	$88$	$56.403$		None		✓	✓	✓	2070.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2070.3.c.a	$2070$	$3$	2070.c	23.b	$2$	$16$	$16$	$56.403$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					230.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+2q^{4}-\beta _{2}q^{5}+(\beta _{1}+\beta _{7}+\cdots)q^{7}+\cdots$

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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.