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 53 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
5220.2.a.a	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				1740.2.a.f	$1$	$2$	$0$	$0$	$-1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-5q^{7}-5q^{11}-5q^{13}-7q^{17}+\cdots$
5220.2.a.b	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				1740.2.a.g	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}+3q^{11}+q^{13}+3q^{17}+\cdots$
5220.2.a.c	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				1740.2.a.b	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-3q^{11}-2q^{13}+4q^{17}+\cdots$
5220.2.a.d	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓	✓			5220.2.a.d	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+q^{11}-2q^{17}-2q^{19}+\cdots$
5220.2.a.e	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				580.2.a.b	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+4q^{11}-6q^{13}+4q^{17}+\cdots$
5220.2.a.f	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓	✓			5220.2.a.f	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-3q^{11}-q^{13}+3q^{17}+\cdots$
5220.2.a.g	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				1740.2.a.h	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-4q^{11}+2q^{13}+4q^{19}+\cdots$
5220.2.a.h	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				1740.2.a.c	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+4q^{11}+2q^{13}+8q^{17}+\cdots$
5220.2.a.i	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				1740.2.a.d	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}-3q^{11}+3q^{13}-q^{17}+\cdots$
5220.2.a.j	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓	✓			5220.2.a.j	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}+q^{11}-5q^{13}+3q^{17}+\cdots$
5220.2.a.k	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓	✓			5220.2.a.d	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-q^{11}+2q^{17}-2q^{19}+\cdots$
5220.2.a.l	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				1740.2.a.e	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+3q^{11}-q^{13}-3q^{17}+\cdots$
5220.2.a.m	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓	✓			5220.2.a.f	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+3q^{11}-q^{13}-3q^{17}+\cdots$
5220.2.a.n	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				580.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{11}-2q^{13}-2q^{19}+8q^{23}+\cdots$
5220.2.a.o	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓				1740.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+6q^{11}+6q^{13}-4q^{17}+2q^{19}+\cdots$
5220.2.a.p	$5220$	$2$	5220.a	1.a	$1$	$1$	$1$	$41.682$	$\Q$	None	✓	✓			5220.2.a.j	$1$	$1$	$0$	$0$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}-q^{11}-5q^{13}-3q^{17}+\cdots$
5220.2.a.q	$5220$	$2$	5220.a	1.a	$1$	$2$	$2$	$41.682$	$\Q(\sqrt{17}) $	None	✓				1740.2.a.k	$1$	$0$	$0$	$0$	$-2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-2-\beta )q^{7}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
5220.2.a.r	$5220$	$2$	5220.a	1.a	$1$	$2$	$2$	$41.682$	$\Q(\sqrt{57}) $	None	✓				1740.2.a.n	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+(2-\beta )q^{11}+2q^{13}+\cdots$
5220.2.a.s	$5220$	$2$	5220.a	1.a	$1$	$2$	$2$	$41.682$	$\Q(\sqrt{33}) $	None	✓				1740.2.a.i	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-\beta q^{7}+(-2-\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
5220.2.a.t	$5220$	$2$	5220.a	1.a	$1$	$2$	$2$	$41.682$	$\Q(\sqrt{33}) $	None	✓				1740.2.a.l	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{7}+(-2+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
5220.2.a.u	$5220$	$2$	5220.a	1.a	$1$	$2$	$2$	$41.682$	$\Q(\sqrt{17}) $	None	✓				1740.2.a.m	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2\beta q^{7}+(2-\beta )q^{11}+6q^{13}+\cdots$
5220.2.a.v	$5220$	$2$	5220.a	1.a	$1$	$2$	$2$	$41.682$	$\Q(\sqrt{17}) $	None	✓				1740.2.a.j	$1$	$1$	$0$	$0$	$2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta )q^{7}+(1-2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots$
5220.2.a.w	$5220$	$2$	5220.a	1.a	$1$	$3$	$3$	$41.682$	3.3.148.1	None	✓		✓		580.2.a.d	$1$	$1$	$0$	$0$	$-3$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+(1-\beta _{2})q^{7}+(-1+\beta _{2})q^{11}+\cdots$
5220.2.a.x	$5220$	$2$	5220.a	1.a	$1$	$3$	$3$	$41.682$	3.3.564.1	None	✓		✓		580.2.a.c	$1$	$1$	$0$	$0$	$3$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta _{2})q^{7}+(-3-\beta _{2})q^{11}+\cdots$
5220.2.a.y	$5220$	$2$	5220.a	1.a	$1$	$7$	$7$	$41.682$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	5220.2.a.y	$1$	$0$	$0$	$0$	$-7$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{5}+\beta _{2}q^{7}-\beta _{5}q^{11}-\beta _{6}q^{13}+\cdots$
5220.2.a.z	$5220$	$2$	5220.a	1.a	$1$	$7$	$7$	$41.682$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	5220.2.a.y	$1$	$0$	$0$	$0$	$7$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{5}+\beta _{2}q^{7}+\beta _{5}q^{11}-\beta _{6}q^{13}+\cdots$
5220.2.b.a	$5220$	$2$	5220.b	145.d	$2$	$4$	$4$	$41.682$	$\Q(\sqrt{-5}, \sqrt{-29})$	$\Q(\sqrt{-435}) $		✓			5220.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{11}+(-3\beta _{1}+\cdots)q^{23}+\cdots$
5220.2.b.b	$5220$	$2$	5220.b	145.d	$2$	$4$	$4$	$41.682$	$\Q(\sqrt{-5}, \sqrt{-29})$	$\Q(\sqrt{-435}) $		✓			5220.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{11}+(3\beta _{1}+\beta _{2}+\cdots)q^{23}+\cdots$
5220.2.b.c	$5220$	$2$	5220.b	145.d	$2$	$14$	$14$	$41.682$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None					1740.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{9}q^{7}-\beta _{5}q^{11}-\beta _{6}q^{13}+\cdots$
5220.2.b.d	$5220$	$2$	5220.b	145.d	$2$	$14$	$14$	$41.682$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None					1740.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{9}q^{7}+\beta _{5}q^{11}-\beta _{6}q^{13}+\cdots$
5220.2.b.e	$5220$	$2$	5220.b	145.d	$2$	$16$	$16$	$41.682$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					580.2.f.a	$4$	$0$	$0$	$0$	$2$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{5}+\beta _{10}q^{7}+\beta _{8}q^{11}+\beta _{4}q^{13}+\cdots$
5220.2.b.f	$5220$	$2$	5220.b	145.d	$2$	$24$	$24$	$41.682$		None		✓	✓		5220.2.b.f	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
5220.2.g.a	$5220$	$2$	5220.g	5.b	$2$	$2$	$2$	$41.682$	$\Q(\sqrt{-1}) $	None					1740.2.g.b	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+2)q^{5}+2 i q^{7}-5 q^{11}+4 i q^{17}+\cdots$
5220.2.g.b	$5220$	$2$	5220.g	5.b	$2$	$2$	$2$	$41.682$	$\Q(\sqrt{-1}) $	None					1740.2.g.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-i+2)q^{5}+2 i q^{7}+q^{11}-4 i q^{13}+\cdots$
5220.2.g.c	$5220$	$2$	5220.g	5.b	$2$	$4$	$4$	$41.682$	$\Q(\sqrt{-2}, \sqrt{3})$	None					580.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+(1+\beta _{2}+\cdots)q^{11}+\cdots$
5220.2.g.d	$5220$	$2$	5220.g	5.b	$2$	$10$	$10$	$41.682$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None					580.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{5}+(\beta _{1}-\beta _{8}-\beta _{9})q^{7}+(\beta _{2}-\beta _{7}+\cdots)q^{11}+\cdots$
5220.2.g.e	$5220$	$2$	5220.g	5.b	$2$	$12$	$12$	$41.682$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					1740.2.g.d	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{5}-\beta _{5}q^{7}+(-\beta _{8}+\beta _{9}+\beta _{10}+\cdots)q^{11}+\cdots$
5220.2.g.f	$5220$	$2$	5220.g	5.b	$2$	$12$	$12$	$41.682$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					1740.2.g.c	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}-\beta _{8}q^{7}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots$
5220.2.g.g	$5220$	$2$	5220.g	5.b	$2$	$14$	$14$	$41.682$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			5220.2.g.g	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{5}+\beta _{4}q^{7}+\beta _{6}q^{11}-\beta _{12}q^{13}+\cdots$
5220.2.g.h	$5220$	$2$	5220.g	5.b	$2$	$14$	$14$	$41.682$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			5220.2.g.g	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{5}+\beta _{4}q^{7}-\beta _{6}q^{11}-\beta _{12}q^{13}+\cdots$
5220.2.l.a	$5220$	$2$	5220.l	29.b	$2$	$2$	$2$	$41.682$	$\Q(\sqrt{-1}) $	None					1740.2.l.a	$2$	$0$	$0$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+q^{7}-3 i q^{11}+7 q^{13}-7 i q^{17}+\cdots$
5220.2.l.b	$5220$	$2$	5220.l	29.b	$2$	$2$	$2$	$41.682$	$\Q(\sqrt{-1}) $	None					1740.2.l.b	$2$	$0$	$0$	$0$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+4 q^{7}+3 i q^{11}-2 i q^{17}+\cdots$
5220.2.l.c	$5220$	$2$	5220.l	29.b	$2$	$2$	$2$	$41.682$	$\Q(\sqrt{-7}) $	None					580.2.d.a	$2$	$0$	$0$	$0$	$2$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}-2q^{7}-\beta q^{11}-2q^{13}+\beta q^{19}+\cdots$
5220.2.l.d	$5220$	$2$	5220.l	29.b	$2$	$4$	$4$	$41.682$	$\Q(\sqrt{-2}, \sqrt{11})$	None					580.2.d.c	$2$	$0$	$0$	$0$	$-4$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+(-1+\beta _{3})q^{7}-\beta _{1}q^{11}+(-2\beta _{1}+\cdots)q^{17}+\cdots$
5220.2.l.e	$5220$	$2$	5220.l	29.b	$2$	$4$	$4$	$41.682$	$\Q(\sqrt{-5}, \sqrt{-13})$	None		✓			5220.2.l.e	$2$	$0$	$0$	$0$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+(1-\beta _{3})q^{7}+(-\beta _{1}-\beta _{2})q^{11}+\cdots$
5220.2.l.f	$5220$	$2$	5220.l	29.b	$2$	$4$	$4$	$41.682$	$\Q(\sqrt{-5}, \sqrt{-13})$	None		✓			5220.2.l.e	$2$	$0$	$0$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}+(1-\beta _{3})q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots$
5220.2.l.g	$5220$	$2$	5220.l	29.b	$2$	$4$	$4$	$41.682$	4.0.7168.1	None					580.2.d.b	$2$	$0$	$0$	$0$	$4$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}+(2+\beta _{3})q^{7}-\beta _{2}q^{11}+4\beta _{3}q^{13}+\cdots$
5220.2.l.h	$5220$	$2$	5220.l	29.b	$2$	$6$	$6$	$41.682$	6.0.399424.1	None					1740.2.l.c	$2$	$0$	$0$	$0$	$-6$	$-6$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+(-1-\beta _{2})q^{7}+(-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots$
5220.2.l.i	$5220$	$2$	5220.l	29.b	$2$	$6$	$6$	$41.682$	6.0.16516096.2	None		✓			5220.2.l.i	$2$	$0$	$0$	$0$	$-6$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{4})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots$
5220.2.l.j	$5220$	$2$	5220.l	29.b	$2$	$6$	$6$	$41.682$	6.0.16516096.2	None		✓			5220.2.l.i	$2$	$0$	$0$	$0$	$6$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{4})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots$

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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.