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 79 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
736.1.e.a	$736$	$1$	736.e	184.e	$2$	$1$	$1$	$0.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-46}) $	$\Q(\sqrt{2}) $	✓				184.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+q^{23}-q^{25}+2q^{31}-2q^{41}+\cdots$
736.1.e.b	$736$	$1$	736.e	184.e	$2$	$2$	$2$	$0.367$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None			✓		184.1.e.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots$
736.1.p.a	$736$	$1$	736.p	736.p	$8$	$4$	$1$	$0.367$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-23}) $	None		✓			736.1.p.a	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q+\zeta_{8}q^{2}+(-1+\zeta_{8})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
736.1.p.b	$736$	$1$	736.p	736.p	$8$	$8$	$2$	$0.367$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-23}) $	None		✓	✓		736.1.p.b	$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}+(\zeta_{24}-\zeta_{24}^{8})q^{3}+\zeta_{24}^{10}q^{4}+\cdots$
736.2.a.a	$736$	$2$	736.a	1.a	$1$	$2$	$2$	$5.877$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			736.2.a.a	$1$	$1$	$0$	$-2$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-2+\beta )q^{5}+(2-\beta )q^{7}+\cdots$
736.2.a.b	$736$	$2$	736.a	1.a	$1$	$2$	$2$	$5.877$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			736.2.a.b	$1$	$1$	$0$	$0$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{5}+(-3-\beta )q^{7}+(-3+\cdots)q^{11}+\cdots$
736.2.a.c	$736$	$2$	736.a	1.a	$1$	$2$	$2$	$5.877$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓			736.2.a.b	$1$	$0$	$0$	$0$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1+\beta )q^{5}+(3-\beta )q^{7}+(3+\beta )q^{11}+\cdots$
736.2.a.d	$736$	$2$	736.a	1.a	$1$	$2$	$2$	$5.877$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			736.2.a.a	$1$	$1$	$0$	$2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(-2-\beta )q^{7}+\cdots$
736.2.a.e	$736$	$2$	736.a	1.a	$1$	$3$	$3$	$5.877$	3.3.316.1	$_{}$	None	None	✓	✓	✓		736.2.a.e	$1$	$1$	$0$	$-4$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
736.2.a.f	$736$	$2$	736.a	1.a	$1$	$3$	$3$	$5.877$	3.3.316.1	$_{}$	None	None	✓	✓			736.2.a.e	$1$	$0$	$0$	$4$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
736.2.a.g	$736$	$2$	736.a	1.a	$1$	$4$	$4$	$5.877$	4.4.13768.1	$_{}$	None	None	✓	✓	✓		736.2.a.g	$1$	$0$	$0$	$-2$	$6$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(2-\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\cdots$
736.2.a.h	$736$	$2$	736.a	1.a	$1$	$4$	$4$	$5.877$	4.4.13768.1	$_{}$	None	None	✓	✓	✓		736.2.a.g	$1$	$0$	$0$	$2$	$6$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(2-\beta _{3})q^{5}+(-1+\beta _{1})q^{7}+\cdots$
736.2.b.a	$736$	$2$	736.b	8.b	$2$	$2$	$2$	$5.877$	$\Q(\sqrt{-2}) $	$_{}$	None	None					184.2.b.a	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{3}-\beta q^{5}+4q^{7}-5q^{9}+\beta q^{11}+\cdots$
736.2.b.b	$736$	$2$	736.b	8.b	$2$	$8$	$8$	$5.877$	8.0.5198736512.1	$_{}$	None	None					184.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{5}q^{5}-\beta _{3}q^{7}+(-\beta _{3}+\beta _{6}+\cdots)q^{9}+\cdots$
736.2.b.c	$736$	$2$	736.b	8.b	$2$	$12$	$12$	$5.877$	12.0.$\cdots$.1	$_{}$	None	None			✓		184.2.b.c	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{11}q^{5}+(-1+\beta _{1})q^{7}+\cdots$
736.2.c.a	$736$	$2$	736.c	92.b	$2$	$24$	$24$	$5.877$		$_{}$	None	None		✓	✓	✓	736.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
736.2.h.a	$736$	$2$	736.h	184.h	$2$	$4$	$4$	$5.877$	$\Q(i, \sqrt{14})$	$_{}$	None	None					184.2.h.a	$4$	$0$	$0$	$8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{3}+\beta _{3}q^{5}+q^{9}+\beta _{2}q^{11}-4\beta _{1}q^{13}+\cdots$
736.2.h.b	$736$	$2$	736.h	184.h	$2$	$6$	$6$	$5.877$	6.0.8869743.1	$_{}$	$\Q(\sqrt{-23}) $	None					184.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{3}+(3+\beta _{2}-\beta _{5})q^{9}+(-\beta _{1}+\cdots)q^{13}+\cdots$
736.2.h.c	$736$	$2$	736.h	184.h	$2$	$12$	$12$	$5.877$	12.0.$\cdots$.2	$_{}$	None	None			✓		184.2.h.c	$4$	$0$	$0$	$-4$	$0$	$0$		$2^{10}\cdot 23$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}-\beta _{8}q^{5}-\beta _{4}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$
736.2.m.a	$736$	$2$	736.m	32.g	$8$	$4$	$1$	$5.877$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			736.2.m.a	$2$	$0$	$4$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(1+\zeta_{8}^{2})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+2\zeta_{8}^{2}q^{4}+\cdots$
736.2.m.b	$736$	$2$	736.m	32.g	$8$	$164$	$41$	$5.877$		$_{}$	None	None		✓			736.2.m.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
736.2.m.c	$736$	$2$	736.m	32.g	$8$	$184$	$46$	$5.877$		$_{}$	None	None		✓	✓		736.2.m.c	$2$	$0$	$-4$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{8}]$
736.2.n.a	$736$	$2$	736.n	736.n	$8$	$24$	$6$	$5.877$		$_{}$	$\Q(\sqrt{-23}) $	None		✓			736.2.n.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{8}]$
736.2.n.b	$736$	$2$	736.n	736.n	$8$	$352$	$88$	$5.877$		$_{}$	None	None		✓	✓		736.2.n.b	$4$	$0$	$-8$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
736.2.q.a	$736$	$2$	736.q	23.c	$11$	$10$	$1$	$5.877$	$\Q(\zeta_{22})$	$_{}$	None	None		✓			736.2.q.a	$2$	$1$	$0$	$-6$	$-6$	$-13$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-2+2\zeta_{22}-2\zeta_{22}^{2}+\zeta_{22}^{3}-\zeta_{22}^{4}+\cdots)q^{3}+\cdots$
736.2.q.b	$736$	$2$	736.q	23.c	$11$	$10$	$1$	$5.877$	$\Q(\zeta_{22})$	$_{}$	None	None		✓			736.2.q.a	$2$	$0$	$0$	$6$	$-6$	$13$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(2-2\zeta_{22}+2\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}+\cdots)q^{3}+\cdots$
736.2.q.c	$736$	$2$	736.q	23.c	$11$	$20$	$2$	$5.877$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			736.2.q.c	$4$	$0$	$0$	$0$	$-14$	$0$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\beta _{1}-\beta _{15})q^{3}+(-1+\beta _{10}+2\beta _{16}+\cdots)q^{5}+\cdots$
736.2.q.d	$736$	$2$	736.q	23.c	$11$	$20$	$2$	$5.877$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			736.2.q.d	$4$	$0$	$0$	$0$	$26$	$0$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(\beta _{1}+\beta _{3}+\beta _{5}-\beta _{6}-\beta _{13}-\beta _{15}+\cdots)q^{3}+\cdots$
736.2.q.e	$736$	$2$	736.q	23.c	$11$	$60$	$6$	$5.877$		$_{}$	None	None		✓			736.2.q.e	$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{11}]$
736.2.q.f	$736$	$2$	736.q	23.c	$11$	$60$	$6$	$5.877$		$_{}$	None	None		✓			736.2.q.e	$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{11}]$
736.2.q.g	$736$	$2$	736.q	23.c	$11$	$60$	$6$	$5.877$		$_{}$	None	None		✓			736.2.q.g	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{11}]$
736.2.r.a	$736$	$2$	736.r	184.j	$22$	$220$	$22$	$5.877$		$_{}$	None	None			✓	✓	184.2.j.a	$4$	$0$	$0$	$18$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
736.2.w.a	$736$	$2$	736.w	92.h	$22$	$240$	$24$	$5.877$		$_{}$	None	None		✓	✓	✓	736.2.w.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
736.2.x.a	$736$	$2$	736.x	184.p	$22$	$220$	$22$	$5.877$		$_{}$	None	None			✓	✓	184.2.p.a	$4$	$0$	$0$	$0$	$0$	$22$			$\mathrm{SU}(2)[C_{22}]$
736.2.be.a	$736$	$2$	736.be	736.ae	$88$	$3760$	$94$	$5.877$		$_{}$	None	None		✓	✓	✓	736.2.be.a	$4$	$0$	$-36$	$-36$	$-44$	$-44$			$\mathrm{SU}(2)[C_{88}]$
736.2.bf.a	$736$	$2$	736.bf	736.af	$88$	$3760$	$94$	$5.877$		$_{}$	None	None		✓	✓	✓	736.2.bf.a	$4$	$0$	$-36$	$-36$	$-36$	$-36$			$\mathrm{SU}(2)[C_{88}]$
736.3.d.a	$736$	$3$	736.d	4.b	$2$	$20$	$20$	$20.055$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			736.3.d.a	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{34}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{5}q^{5}+\beta _{8}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
736.3.d.b	$736$	$3$	736.d	4.b	$2$	$24$	$24$	$20.055$		$_{}$	None	None		✓	✓		736.3.d.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
736.3.e.a	$736$	$3$	736.e	184.e	$2$	$2$	$2$	$20.055$	$\Q(\sqrt{23}) $	$_{}$	$\Q(\sqrt{-46}) $	None	✓				184.3.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{5}+9q^{9}-\beta q^{11}-\beta q^{19}-23q^{23}+\cdots$
736.3.e.b	$736$	$3$	736.e	184.e	$2$	$2$	$2$	$20.055$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-46}) $	None	✓				184.3.e.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}+9q^{9}+7\beta q^{11}-13\beta q^{19}+\cdots$
736.3.e.c	$736$	$3$	736.e	184.e	$2$	$6$	$6$	$20.055$	6.0.8869743.1	$_{}$	$\Q(\sqrt{-23}) $	None					184.3.e.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+(-9+\beta _{2}-\beta _{3})q^{9}+(-\beta _{1}+\cdots)q^{13}+\cdots$
736.3.e.d	$736$	$3$	736.e	184.e	$2$	$36$	$36$	$20.055$		$_{}$	None	None			✓		184.3.e.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
736.3.f.a	$736$	$3$	736.f	23.b	$2$	$24$	$24$	$20.055$		$_{}$	None	None		✓			736.3.f.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
736.3.f.b	$736$	$3$	736.f	23.b	$2$	$24$	$24$	$20.055$		$_{}$	None	None		✓			736.3.f.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
736.3.g.a	$736$	$3$	736.g	8.d	$2$	$44$	$44$	$20.055$		$_{}$	None	None			✓	✓	184.3.g.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
736.4.a.a	$736$	$4$	736.a	1.a	$1$	$3$	$3$	$43.425$	3.3.11032.1	$_{}$	None	None	✓	✓			736.4.a.a	$1$	$1$	$0$	$-2$	$0$	$16$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(4+\cdots)q^{7}+\cdots$
736.4.a.b	$736$	$4$	736.a	1.a	$1$	$3$	$3$	$43.425$	3.3.11032.1	$_{}$	None	None	✓	✓			736.4.a.a	$1$	$1$	$0$	$2$	$0$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-4+\cdots)q^{7}+\cdots$
736.4.a.c	$736$	$4$	736.a	1.a	$1$	$4$	$4$	$43.425$	4.4.310848.1	$_{}$	None	None	✓	✓			736.4.a.c	$1$	$1$	$0$	$0$	$-20$	$-44$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-5+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
736.4.a.d	$736$	$4$	736.a	1.a	$1$	$4$	$4$	$43.425$	4.4.310848.1	$_{}$	None	None	✓	✓			736.4.a.c	$1$	$1$	$0$	$0$	$-20$	$44$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-5+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
736.4.a.e	$736$	$4$	736.a	1.a	$1$	$8$	$8$	$43.425$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓		736.4.a.e	$1$	$1$	$0$	$-12$	$-12$	$14$	$-$	$2^{8}$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots$

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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.