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 142 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
522.2.a.a	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓	✓			522.2.a.a	$1$	$0$	$-1$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots$
522.2.a.b	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓				58.2.a.b	$1$	$1$	$-1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
522.2.a.c	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓				174.2.a.d	$1$	$1$	$-1$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
522.2.a.d	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓		✓	✓	174.2.a.e	$1$	$0$	$-1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
522.2.a.e	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓	✓			522.2.a.e	$1$	$0$	$-1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+4q^{7}-q^{8}-2q^{10}+\cdots$
522.2.a.f	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓	✓	✓	✓	522.2.a.f	$1$	$1$	$-1$	$0$	$3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-5q^{7}-q^{8}-3q^{10}+\cdots$
522.2.a.g	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓	✓	✓	✓	522.2.a.f	$1$	$1$	$1$	$0$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}-5q^{7}+q^{8}-3q^{10}+\cdots$
522.2.a.h	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓		✓	✓	174.2.a.a	$1$	$1$	$1$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}-3q^{7}+q^{8}-3q^{10}+\cdots$
522.2.a.i	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓				174.2.a.c	$1$	$0$	$1$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+4q^{11}+\cdots$
522.2.a.j	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓	✓			522.2.a.e	$1$	$0$	$1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+4q^{7}+q^{8}-2q^{10}+\cdots$
522.2.a.k	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓				58.2.a.a	$1$	$0$	$1$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-2q^{7}+q^{8}+3q^{10}+\cdots$
522.2.a.l	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓	✓			522.2.a.a	$1$	$0$	$1$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots$
522.2.a.m	$522$	$2$	522.a	1.a	$1$	$1$	$1$	$4.168$	$\Q$	None	✓				174.2.a.b	$1$	$0$	$1$	$0$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+5q^{7}+q^{8}+3q^{10}+\cdots$
522.2.d.a	$522$	$2$	522.d	29.b	$2$	$2$	$2$	$4.168$	$\Q(\sqrt{-1}) $	None					58.2.b.a	$2$	$0$	$0$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}-q^{5}-2 q^{7}-i q^{8}+\cdots$
522.2.d.b	$522$	$2$	522.d	29.b	$2$	$2$	$2$	$4.168$	$\Q(\sqrt{-1}) $	None					174.2.d.a	$2$	$0$	$0$	$0$	$-2$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}-q^{5}+3 q^{7}-i q^{8}+\cdots$
522.2.d.c	$522$	$2$	522.d	29.b	$2$	$4$	$4$	$4.168$	$\Q(i, \sqrt{13})$	None		✓			522.2.d.c	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+\beta _{3}q^{5}+q^{7}-\beta _{1}q^{8}+\cdots$
522.2.d.d	$522$	$2$	522.d	29.b	$2$	$4$	$4$	$4.168$	$\Q(i, \sqrt{33})$	None					174.2.d.b	$2$	$0$	$0$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{4}+\beta _{3}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{8}+\cdots$
522.2.e.a	$522$	$2$	522.e	9.c	$3$	$2$	$1$	$4.168$	$\Q(\sqrt{-3}) $	None		✓			522.2.e.a	$2$	$1$	$-1$	$-3$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
522.2.e.b	$522$	$2$	522.e	9.c	$3$	$2$	$1$	$4.168$	$\Q(\sqrt{-3}) $	None		✓			522.2.e.b	$2$	$0$	$-1$	$3$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
522.2.e.c	$522$	$2$	522.e	9.c	$3$	$2$	$1$	$4.168$	$\Q(\sqrt{-3}) $	None		✓			522.2.e.c	$2$	$0$	$-1$	$3$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
522.2.e.d	$522$	$2$	522.e	9.c	$3$	$2$	$1$	$4.168$	$\Q(\sqrt{-3}) $	None		✓			522.2.e.d	$2$	$0$	$1$	$3$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
522.2.e.e	$522$	$2$	522.e	9.c	$3$	$4$	$2$	$4.168$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			522.2.e.e	$2$	$0$	$2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
522.2.e.f	$522$	$2$	522.e	9.c	$3$	$6$	$3$	$4.168$	$\Q(\zeta_{18})$	None		✓			522.2.e.f	$2$	$0$	$3$	$0$	$-6$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_1+1)q^{2}+(\beta_{5}+\beta_{2})q^{3}+\cdots$
522.2.e.g	$522$	$2$	522.e	9.c	$3$	$8$	$4$	$4.168$	8.0.2091141441.1	None		✓			522.2.e.g	$2$	$0$	$-4$	$-1$	$2$	$8$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
522.2.e.h	$522$	$2$	522.e	9.c	$3$	$12$	$6$	$4.168$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			522.2.e.h	$2$	$0$	$-6$	$2$	$-2$	$8$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{2}+(\beta _{1}+\beta _{9})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots$
522.2.e.i	$522$	$2$	522.e	9.c	$3$	$18$	$9$	$4.168$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓		522.2.e.i	$2$	$0$	$9$	$1$	$4$	$-3$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{5}q^{2}-\beta _{7}q^{3}+(-1+\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots$
522.2.g.a	$522$	$2$	522.g	87.f	$4$	$8$	$4$	$4.168$	$\Q(\zeta_{24})$	None		✓			522.2.g.a	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta_1 q^{2}+\beta_{3} q^{4}+(\beta_{6}+\beta_{5}+\beta_1)q^{5}+\cdots$
522.2.g.b	$522$	$2$	522.g	87.f	$4$	$12$	$6$	$4.168$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓	✓		522.2.g.b	$4$	$0$	$0$	$0$	$0$	$8$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}-\beta _{3}q^{4}-\beta _{4}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
522.2.h.a	$522$	$2$	522.h	261.i	$6$	$4$	$2$	$4.168$	$\Q(\zeta_{12})$	None		✓			522.2.h.a	$4$	$0$	$0$	$0$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
522.2.h.b	$522$	$2$	522.h	261.i	$6$	$56$	$28$	$4.168$		None		✓	✓		522.2.h.b	$4$	$0$	$0$	$0$	$-8$	$2$			$\mathrm{SU}(2)[C_{6}]$
522.2.k.a	$522$	$2$	522.k	29.d	$7$	$6$	$1$	$4.168$	$\Q(\zeta_{14})$	None					174.2.g.b	$2$	$0$	$-1$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\zeta_{14}^{4}q^{2}-\zeta_{14}q^{4}+(-1+\zeta_{14}+\cdots)q^{5}+\cdots$
522.2.k.b	$522$	$2$	522.k	29.d	$7$	$6$	$1$	$4.168$	$\Q(\zeta_{14})$	None		✓			522.2.k.b	$2$	$0$	$-1$	$0$	$-3$	$-6$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\zeta_{14}^{4}q^{2}-\zeta_{14}q^{4}+(-1+\zeta_{14}+\cdots)q^{5}+\cdots$
522.2.k.c	$522$	$2$	522.k	29.d	$7$	$6$	$1$	$4.168$	$\Q(\zeta_{14})$	None					58.2.d.a	$2$	$0$	$-1$	$0$	$4$	$-5$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\zeta_{14}^{4}q^{2}-\zeta_{14}q^{4}+(\zeta_{14}^{3}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots$
522.2.k.d	$522$	$2$	522.k	29.d	$7$	$6$	$1$	$4.168$	$\Q(\zeta_{14})$	None					174.2.g.a	$2$	$0$	$1$	$0$	$1$	$6$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\zeta_{14}^{4}q^{2}-\zeta_{14}q^{4}+(-1+\zeta_{14}+\cdots)q^{5}+\cdots$
522.2.k.e	$522$	$2$	522.k	29.d	$7$	$6$	$1$	$4.168$	$\Q(\zeta_{14})$	None		✓			522.2.k.b	$2$	$0$	$1$	$0$	$3$	$-6$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\zeta_{14}^{4}q^{2}-\zeta_{14}q^{4}+(1-\zeta_{14}+2\zeta_{14}^{4}+\cdots)q^{5}+\cdots$
522.2.k.f	$522$	$2$	522.k	29.d	$7$	$12$	$2$	$4.168$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			522.2.k.f	$2$	$0$	$-2$	$0$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{9}q^{2}+\beta _{4}q^{4}+(\beta _{1}+\beta _{9})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
522.2.k.g	$522$	$2$	522.k	29.d	$7$	$12$	$2$	$4.168$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					174.2.g.c	$2$	$0$	$-2$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{5}q^{2}+\beta _{6}q^{4}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots$
522.2.k.h	$522$	$2$	522.k	29.d	$7$	$12$	$2$	$4.168$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					58.2.d.b	$2$	$0$	$2$	$0$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{2}q^{2}+\beta _{6}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
522.2.k.i	$522$	$2$	522.k	29.d	$7$	$12$	$2$	$4.168$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			522.2.k.f	$2$	$0$	$2$	$0$	$2$	$8$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{9}q^{2}+\beta _{4}q^{4}+(-\beta _{1}-\beta _{9})q^{5}+\cdots$
522.2.l.a	$522$	$2$	522.l	261.l	$12$	$120$	$30$	$4.168$		None		✓	✓	✓	522.2.l.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
522.2.n.a	$522$	$2$	522.n	29.e	$14$	$12$	$2$	$4.168$	$\Q(\zeta_{28})$	None					58.2.e.a	$2$	$0$	$0$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q-\zeta_{28}^{9}q^{2}-\zeta_{28}^{4}q^{4}+(\zeta_{28}+\zeta_{28}^{2}+\cdots)q^{5}+\cdots$
522.2.n.b	$522$	$2$	522.n	29.e	$14$	$12$	$2$	$4.168$	$\Q(\zeta_{28})$	None					174.2.h.a	$2$	$0$	$0$	$0$	$2$	$8$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q-\zeta_{28}^{9}q^{2}-\zeta_{28}^{4}q^{4}+(-\zeta_{28}+\zeta_{28}^{2}+\cdots)q^{5}+\cdots$
522.2.n.c	$522$	$2$	522.n	29.e	$14$	$24$	$4$	$4.168$		None					174.2.h.b	$2$	$0$	$0$	$0$	$-2$	$-12$			$\mathrm{SU}(2)[C_{14}]$
522.2.n.d	$522$	$2$	522.n	29.e	$14$	$24$	$4$	$4.168$		None		✓			522.2.n.d	$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{14}]$
522.2.q.a	$522$	$2$	522.q	261.q	$21$	$180$	$15$	$4.168$		None		✓			522.2.q.a	$4$	$0$	$-15$	$-2$	$2$	$-5$			$\mathrm{SU}(2)[C_{21}]$
522.2.q.b	$522$	$2$	522.q	261.q	$21$	$180$	$15$	$4.168$		None		✓			522.2.q.b	$4$	$0$	$15$	$2$	$2$	$5$			$\mathrm{SU}(2)[C_{21}]$
522.2.r.a	$522$	$2$	522.r	87.k	$28$	$48$	$4$	$4.168$		None		✓			522.2.r.a	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{28}]$
522.2.r.b	$522$	$2$	522.r	87.k	$28$	$72$	$6$	$4.168$		None		✓	✓		522.2.r.b	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{28}]$
522.2.v.a	$522$	$2$	522.v	261.u	$42$	$360$	$30$	$4.168$		None		✓	✓	✓	522.2.v.a	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{42}]$
522.2.x.a	$522$	$2$	522.x	261.x	$84$	$720$	$30$	$4.168$		None		✓	✓	✓	522.2.x.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{84}]$

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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.