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 64 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
1716.1.m.a	$1716$	$1$	1716.m	1716.m	$2$	$1$	$1$	$0.856$	$\Q$	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-429}) $	$\Q(\sqrt{3}) $	✓	✓			1716.1.m.a	$4$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
1716.1.m.b	$1716$	$1$	1716.m	1716.m	$2$	$1$	$1$	$0.856$	$\Q$	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-429}) $	$\Q(\sqrt{3}) $	✓	✓			1716.1.m.a	$4$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
1716.1.m.c	$1716$	$1$	1716.m	1716.m	$2$	$1$	$1$	$0.856$	$\Q$	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-429}) $	$\Q(\sqrt{3}) $	✓	✓			1716.1.m.a	$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
1716.1.m.d	$1716$	$1$	1716.m	1716.m	$2$	$1$	$1$	$0.856$	$\Q$	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-429}) $	$\Q(\sqrt{3}) $	✓	✓			1716.1.m.a	$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
1716.1.m.e	$1716$	$1$	1716.m	1716.m	$2$	$4$	$4$	$0.856$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-143}) $	None		✓			1716.1.m.e	$4$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q+\zeta_{10}^{2}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
1716.1.m.f	$1716$	$1$	1716.m	1716.m	$2$	$4$	$4$	$0.856$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-143}) $	None		✓			1716.1.m.e	$4$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-\zeta_{10}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{2}q^{6}+\cdots$
1716.1.m.g	$1716$	$1$	1716.m	1716.m	$2$	$4$	$4$	$0.856$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			1716.1.m.g	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
1716.1.m.h	$1716$	$1$	1716.m	1716.m	$2$	$4$	$4$	$0.856$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			1716.1.m.g	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{3}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
1716.1.m.i	$1716$	$1$	1716.m	1716.m	$2$	$4$	$4$	$0.856$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-143}) $	None		✓			1716.1.m.e	$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q-\zeta_{10}^{2}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
1716.1.m.j	$1716$	$1$	1716.m	1716.m	$2$	$4$	$4$	$0.856$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-143}) $	None		✓			1716.1.m.e	$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q+\zeta_{10}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{2}q^{6}+\cdots$
1716.1.bt.a	$1716$	$1$	1716.bt	1716.at	$10$	$16$	$4$	$0.856$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-39}) $	None		✓			1716.1.bt.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{40}^{15}q^{2}+\zeta_{40}^{14}q^{3}-\zeta_{40}^{10}q^{4}+\cdots$
1716.1.bt.b	$1716$	$1$	1716.bt	1716.at	$10$	$16$	$4$	$0.856$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-39}) $	None		✓			1716.1.bt.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{11}q^{2}+\zeta_{40}^{14}q^{3}-\zeta_{40}^{2}q^{4}+\cdots$
1716.2.a.a	$1716$	$2$	1716.a	1.a	$1$	$1$	$1$	$13.702$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1716.2.a.a	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}-q^{11}+q^{13}-2q^{17}+\cdots$
1716.2.a.b	$1716$	$2$	1716.a	1.a	$1$	$1$	$1$	$13.702$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1716.2.a.b	$1$	$1$	$0$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
1716.2.a.c	$1716$	$2$	1716.a	1.a	$1$	$1$	$1$	$13.702$	$\Q$	$_{}$	None	None	✓	✓			1716.2.a.c	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}-q^{11}+q^{13}+6q^{17}+\cdots$
1716.2.a.d	$1716$	$2$	1716.a	1.a	$1$	$2$	$2$	$13.702$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	1716.2.a.d	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta )q^{5}+q^{9}+q^{11}-q^{13}+\cdots$
1716.2.a.e	$1716$	$2$	1716.a	1.a	$1$	$2$	$2$	$13.702$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	1716.2.a.e	$1$	$1$	$0$	$2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}-2\beta q^{7}+q^{9}+\cdots$
1716.2.a.f	$1716$	$2$	1716.a	1.a	$1$	$3$	$3$	$13.702$	3.3.1620.1	$_{}$	None	None	✓	✓	✓	✓	1716.2.a.f	$1$	$0$	$0$	$-3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}-q^{11}+\cdots$
1716.2.a.g	$1716$	$2$	1716.a	1.a	$1$	$3$	$3$	$13.702$	3.3.564.1	$_{}$	None	None	✓	✓	✓	✓	1716.2.a.g	$1$	$0$	$0$	$3$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots$
1716.2.a.h	$1716$	$2$	1716.a	1.a	$1$	$3$	$3$	$13.702$	3.3.404.1	$_{}$	None	None	✓	✓	✓		1716.2.a.h	$1$	$0$	$0$	$3$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+2\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
1716.2.a.i	$1716$	$2$	1716.a	1.a	$1$	$4$	$4$	$13.702$	4.4.90996.1	$_{}$	None	None	✓	✓	✓	✓	1716.2.a.i	$1$	$0$	$0$	$-4$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{9}+q^{11}+\cdots$
1716.2.d.a	$1716$	$2$	1716.d	33.d	$2$	$48$	$48$	$13.702$		$_{}$	None	None		✓	✓	✓	1716.2.d.a	$4$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1716.2.e.a	$1716$	$2$	1716.e	13.b	$2$	$10$	$10$	$13.702$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓			1716.2.e.a	$2$	$0$	$0$	$-10$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{8}q^{5}+(-\beta _{8}-\beta _{9})q^{7}+q^{9}+\cdots$
1716.2.e.b	$1716$	$2$	1716.e	13.b	$2$	$10$	$10$	$13.702$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓			1716.2.e.b	$2$	$0$	$0$	$10$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{6}q^{5}+\beta _{9}q^{7}+q^{9}-\beta _{3}q^{11}+\cdots$
1716.2.p.a	$1716$	$2$	1716.p	429.e	$2$	$56$	$56$	$13.702$		$_{}$	None	None		✓	✓	✓	1716.2.p.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1716.2.q.a	$1716$	$2$	1716.q	13.c	$3$	$2$	$1$	$13.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1716.2.q.a	$2$	$0$	$0$	$-1$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
1716.2.q.b	$1716$	$2$	1716.q	13.c	$3$	$12$	$6$	$13.702$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1716.2.q.b	$2$	$0$	$0$	$-6$	$0$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{5}q^{3}-\beta _{3}q^{5}-\beta _{4}q^{7}+(-1-\beta _{5}+\cdots)q^{9}+\cdots$
1716.2.q.c	$1716$	$2$	1716.q	13.c	$3$	$12$	$6$	$13.702$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1716.2.q.c	$2$	$0$	$0$	$6$	$-6$	$1$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+(-1-\beta _{5}+\cdots)q^{9}+\cdots$
1716.2.q.d	$1716$	$2$	1716.q	13.c	$3$	$12$	$6$	$13.702$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1716.2.q.d	$2$	$0$	$0$	$6$	$2$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{3}-\beta _{9}q^{5}+(\beta _{3}-\beta _{10})q^{7}+\cdots$
1716.2.q.e	$1716$	$2$	1716.q	13.c	$3$	$14$	$7$	$13.702$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓	✓		1716.2.q.e	$2$	$0$	$0$	$-7$	$-6$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1})q^{3}-\beta _{9}q^{5}+(-\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots$
1716.2.v.a	$1716$	$2$	1716.v	143.g	$4$	$4$	$2$	$13.702$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1716.2.v.a	$2$	$0$	$0$	$4$	$4$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{3}+(\beta_{3}+\beta_{2}+\beta_1+1)q^{5}+\cdots$
1716.2.v.b	$1716$	$2$	1716.v	143.g	$4$	$4$	$2$	$13.702$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1716.2.v.a	$2$	$0$	$0$	$4$	$4$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{3}+(\beta_{3}+\beta_{2}+\beta_1+1)q^{5}+\cdots$
1716.2.v.c	$1716$	$2$	1716.v	143.g	$4$	$20$	$10$	$13.702$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			1716.2.v.c	$4$	$0$	$0$	$20$	$-12$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{3}+(-1+\beta _{6}-\beta _{9})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots$
1716.2.v.d	$1716$	$2$	1716.v	143.g	$4$	$28$	$14$	$13.702$		$_{}$	None	None		✓	✓		1716.2.v.d	$4$	$0$	$0$	$-28$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
1716.2.x.a	$1716$	$2$	1716.x	39.f	$4$	$96$	$48$	$13.702$		$_{}$	None	None		✓	✓	✓	1716.2.x.a	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
1716.2.z.a	$1716$	$2$	1716.z	11.c	$5$	$4$	$1$	$13.702$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			1716.2.z.a	$2$	$0$	$0$	$1$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+(1-3\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots$
1716.2.z.b	$1716$	$2$	1716.z	11.c	$5$	$4$	$1$	$13.702$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			1716.2.z.b	$2$	$0$	$0$	$1$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots$
1716.2.z.c	$1716$	$2$	1716.z	11.c	$5$	$4$	$1$	$13.702$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			1716.2.z.c	$2$	$0$	$0$	$1$	$4$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}^{2}q^{3}+(1+\zeta_{10}+\zeta_{10}^{2})q^{5}+\cdots$
1716.2.z.d	$1716$	$2$	1716.z	11.c	$5$	$16$	$4$	$13.702$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1716.2.z.d	$2$	$0$	$0$	$4$	$-2$	$1$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{10}q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{6}+\beta _{10}+\cdots)q^{5}+\cdots$
1716.2.z.e	$1716$	$2$	1716.z	11.c	$5$	$20$	$5$	$13.702$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1716.2.z.e	$2$	$0$	$0$	$-5$	$2$	$-9$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{3}+\beta _{1}q^{5}+(-1+\beta _{3}-\beta _{6}+\cdots)q^{7}+\cdots$
1716.2.z.f	$1716$	$2$	1716.z	11.c	$5$	$20$	$5$	$13.702$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1716.2.z.f	$2$	$0$	$0$	$5$	$4$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{8}q^{3}+(1-\beta _{4}+\beta _{8}+\beta _{16})q^{5}+\cdots$
1716.2.z.g	$1716$	$2$	1716.z	11.c	$5$	$28$	$7$	$13.702$		$_{}$	None	None		✓	✓		1716.2.z.g	$2$	$0$	$0$	$-7$	$-2$	$-5$			$\mathrm{SU}(2)[C_{5}]$
1716.2.be.a	$1716$	$2$	1716.be	13.e	$6$	$20$	$10$	$13.702$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1716.2.be.a	$2$	$0$	$0$	$-10$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{11})q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
1716.2.be.b	$1716$	$2$	1716.be	13.e	$6$	$24$	$12$	$13.702$		$_{}$	None	None		✓	✓		1716.2.be.b	$2$	$0$	$0$	$12$	$0$	$-12$			$\mathrm{SU}(2)[C_{6}]$
1716.3.f.a	$1716$	$3$	1716.f	3.b	$2$	$80$	$80$	$46.758$		$_{}$	None	None		✓	✓	✓	1716.3.f.a	$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1716.3.g.a	$1716$	$3$	1716.g	143.d	$2$	$56$	$56$	$46.758$		$_{}$	None	None		✓	✓	✓	1716.3.g.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1716.3.j.a	$1716$	$3$	1716.j	39.d	$2$	$92$	$92$	$46.758$		$_{}$	None	None		✓	✓	✓	1716.3.j.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1716.3.k.a	$1716$	$3$	1716.k	11.b	$2$	$48$	$48$	$46.758$		$_{}$	None	None		✓	✓	✓	1716.3.k.a	$2$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{2}]$
1716.3.s.a	$1716$	$3$	1716.s	13.d	$4$	$96$	$48$	$46.758$		$_{}$	None	None		✓	✓	✓	1716.3.s.a	$2$	$0$	$0$	$0$	$-24$	$16$			$\mathrm{SU}(2)[C_{4}]$
1716.4.a.a	$1716$	$4$	1716.a	1.a	$1$	$1$	$1$	$101.247$	$\Q$	$_{}$	None	None	✓	✓			1716.4.a.a	$1$	$2$	$0$	$-3$	$-9$	$-25$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-9q^{5}-5^{2}q^{7}+9q^{9}-11q^{11}+\cdots$

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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.