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 134 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
165.1.l.a	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		✓			165.1.l.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+i q^{4}+i q^{5}+q^{9}-i q^{11}+\cdots$
165.1.l.b	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		✓			165.1.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{3}+i q^{4}-i q^{5}-q^{9}+i q^{11}+\cdots$
165.2.a.a	$165$	$2$	165.a	1.a	$1$	$2$	$2$	$1.318$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	165.2.a.a	$1$	$1$	$-2$	$-2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots$
165.2.a.b	$165$	$2$	165.a	1.a	$1$	$2$	$2$	$1.318$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	165.2.a.b	$1$	$0$	$0$	$2$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}+2q^{7}+\cdots$
165.2.a.c	$165$	$2$	165.a	1.a	$1$	$3$	$3$	$1.318$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	165.2.a.c	$1$	$0$	$-1$	$3$	$3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
165.2.c.a	$165$	$2$	165.c	5.b	$2$	$6$	$6$	$1.318$	6.0.350464.1	$_{}$	None	None		✓			165.2.c.a	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}-\beta _{5})q^{2}+\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots$
165.2.c.b	$165$	$2$	165.c	5.b	$2$	$6$	$6$	$1.318$	6.0.350464.1	$_{}$	None	None		✓			165.2.c.b	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots$
165.2.d.a	$165$	$2$	165.d	165.d	$2$	$2$	$2$	$1.318$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			165.2.d.a	$4$	$0$	$0$	$-1$	$3$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}+2q^{4}+(1+\beta )q^{5}+(-3+\beta )q^{9}+\cdots$
165.2.d.b	$165$	$2$	165.d	165.d	$2$	$2$	$2$	$1.318$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		✓			165.2.d.a	$4$	$0$	$0$	$1$	$-3$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{3}+2q^{4}+(-2+\beta )q^{5}+(-3+\cdots)q^{9}+\cdots$
165.2.d.c	$165$	$2$	165.d	165.d	$2$	$16$	$16$	$1.318$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		165.2.d.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
165.2.f.a	$165$	$2$	165.f	33.d	$2$	$8$	$8$	$1.318$	8.0.619810816.2	$_{}$	None	None		✓			165.2.f.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{3}-\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots$
165.2.f.b	$165$	$2$	165.f	33.d	$2$	$8$	$8$	$1.318$	8.0.619810816.2	$_{}$	None	None		✓			165.2.f.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
165.2.j.a	$165$	$2$	165.j	55.e	$4$	$24$	$12$	$1.318$		$_{}$	None	None		✓	✓	✓	165.2.j.a	$4$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{4}]$
165.2.k.a	$165$	$2$	165.k	15.e	$4$	$4$	$2$	$1.318$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			165.2.k.a	$2$	$1$	$-4$	$-4$	$-8$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$
165.2.k.b	$165$	$2$	165.k	15.e	$4$	$4$	$2$	$1.318$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			165.2.k.a	$2$	$0$	$4$	$0$	$8$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
165.2.k.c	$165$	$2$	165.k	15.e	$4$	$16$	$8$	$1.318$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			165.2.k.c	$2$	$0$	$-4$	$-2$	$-8$	$8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}-\beta _{15}q^{3}+(-\beta _{1}-\beta _{3}-\beta _{13}+\cdots)q^{4}+\cdots$
165.2.k.d	$165$	$2$	165.k	15.e	$4$	$16$	$8$	$1.318$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			165.2.k.c	$2$	$0$	$4$	$4$	$8$	$8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(\beta _{1}+\beta _{3}+\beta _{13}+\cdots)q^{4}+\cdots$
165.2.m.a	$165$	$2$	165.m	11.c	$5$	$8$	$2$	$1.318$	8.0.13140625.1	$_{}$	None	None		✓			165.2.m.a	$2$	$0$	$0$	$-2$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6})q^{2}+(-1+\cdots)q^{3}+\cdots$
165.2.m.b	$165$	$2$	165.m	11.c	$5$	$8$	$2$	$1.318$	8.0.819390625.1	$_{}$	None	None		✓			165.2.m.b	$2$	$0$	$2$	$2$	$2$	$9$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{4}q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
165.2.m.c	$165$	$2$	165.m	11.c	$5$	$8$	$2$	$1.318$	$\Q(\zeta_{15})$	$_{}$	None	None		✓			165.2.m.c	$2$	$0$	$2$	$2$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{15}-\zeta_{15}^{3}+\zeta_{15}^{4}-\zeta_{15}^{5}+\cdots)q^{2}+\cdots$
165.2.m.d	$165$	$2$	165.m	11.c	$5$	$8$	$2$	$1.318$	8.0.13140625.1	$_{}$	None	None		✓			165.2.m.d	$2$	$0$	$4$	$-2$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots$
165.2.p.a	$165$	$2$	165.p	33.f	$10$	$16$	$4$	$1.318$	16.0.$\cdots$.1	$_{}$	None	None		✓			165.2.p.a	$4$	$0$	$0$	$8$	$0$	$-10$		$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{2}-\beta _{5}+\beta _{6}-\beta _{8}+\cdots)q^{3}+\cdots$
165.2.p.b	$165$	$2$	165.p	33.f	$10$	$48$	$12$	$1.318$		$_{}$	None	None		✓	✓		165.2.p.b	$4$	$0$	$0$	$-4$	$0$	$10$			$\mathrm{SU}(2)[C_{10}]$
165.2.r.a	$165$	$2$	165.r	165.r	$10$	$80$	$20$	$1.318$		$_{}$	None	None		✓	✓	✓	165.2.r.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
165.2.s.a	$165$	$2$	165.s	55.j	$10$	$48$	$12$	$1.318$		$_{}$	None	None		✓	✓	✓	165.2.s.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{10}]$
165.2.v.a	$165$	$2$	165.v	165.v	$20$	$160$	$20$	$1.318$		$_{}$	None	None		✓	✓	✓	165.2.v.a	$8$	$0$	$0$	$-8$	$0$	$-20$			$\mathrm{SU}(2)[C_{20}]$
165.2.w.a	$165$	$2$	165.w	55.l	$20$	$96$	$12$	$1.318$		$_{}$	None	None		✓	✓	✓	165.2.w.a	$4$	$0$	$0$	$0$	$-8$	$-20$			$\mathrm{SU}(2)[C_{20}]$
165.3.b.a	$165$	$3$	165.b	11.b	$2$	$16$	$16$	$4.496$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	165.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
165.3.e.a	$165$	$3$	165.e	3.b	$2$	$28$	$28$	$4.496$		$_{}$	None	None		✓	✓	✓	165.3.e.a	$2$	$0$	$0$	$0$	$0$	$24$			$\mathrm{SU}(2)[C_{2}]$
165.3.g.a	$165$	$3$	165.g	15.d	$2$	$2$	$2$	$4.496$	$\Q(\sqrt{-11}) $	$_{}$	None	None		✓			165.3.g.a	$2$	$0$	$-2$	$-5$	$-10$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(-2-\beta )q^{3}-3q^{4}-5q^{5}+\cdots$
165.3.g.b	$165$	$3$	165.g	15.d	$2$	$2$	$2$	$4.496$	$\Q(\sqrt{-11}) $	$_{}$	None	None		✓			165.3.g.a	$2$	$0$	$2$	$5$	$10$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(3-\beta )q^{3}-3q^{4}+5q^{5}+(3+\cdots)q^{6}+\cdots$
165.3.g.c	$165$	$3$	165.g	15.d	$2$	$36$	$36$	$4.496$		$_{}$	None	None		✓	✓		165.3.g.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
165.3.h.a	$165$	$3$	165.h	55.d	$2$	$24$	$24$	$4.496$		$_{}$	None	None		✓	✓	✓	165.3.h.a	$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{2}]$
165.3.i.a	$165$	$3$	165.i	5.c	$4$	$40$	$20$	$4.496$		$_{}$	None	None		✓	✓	✓	165.3.i.a	$2$	$0$	$8$	$0$	$16$	$0$			$\mathrm{SU}(2)[C_{4}]$
165.3.l.a	$165$	$3$	165.l	165.l	$4$	$4$	$2$	$4.496$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			165.3.l.a	$4$	$0$	$0$	$-12$	$-16$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-3q^{3}+\beta _{2}q^{4}+(-4-3\beta _{2}+\cdots)q^{5}+\cdots$
165.3.l.b	$165$	$3$	165.l	165.l	$4$	$4$	$2$	$4.496$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			165.3.l.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-3\beta _{2}q^{3}-\beta _{2}q^{4}+5\beta _{2}q^{5}+\cdots$
165.3.l.c	$165$	$3$	165.l	165.l	$4$	$4$	$2$	$4.496$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			165.3.l.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(\beta _{1}-3\beta _{2})q^{3}-4\beta _{2}q^{4}+(3\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$
165.3.l.d	$165$	$3$	165.l	165.l	$4$	$4$	$2$	$4.496$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			165.3.l.a	$4$	$0$	$0$	$0$	$16$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+3\beta _{2}q^{3}+\beta _{2}q^{4}+(4+3\beta _{2}+\cdots)q^{5}+\cdots$
165.3.l.e	$165$	$3$	165.l	165.l	$4$	$4$	$2$	$4.496$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None		✓			165.3.l.c	$4$	$0$	$0$	$10$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(3+\beta _{3})q^{3}+4\beta _{2}q^{4}+(-3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
165.3.l.f	$165$	$3$	165.l	165.l	$4$	$4$	$2$	$4.496$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			165.3.l.b	$4$	$0$	$0$	$12$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+3q^{3}-\beta _{2}q^{4}-5\beta _{2}q^{5}+\cdots$
165.3.l.g	$165$	$3$	165.l	165.l	$4$	$64$	$32$	$4.496$		$_{}$	None	None		✓	✓		165.3.l.g	$8$	$0$	$0$	$-16$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
165.3.n.a	$165$	$3$	165.n	55.h	$10$	$96$	$24$	$4.496$		$_{}$	None	None		✓	✓	✓	165.3.n.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{10}]$
165.3.o.a	$165$	$3$	165.o	165.o	$10$	$176$	$44$	$4.496$		$_{}$	None	None		✓	✓	✓	165.3.o.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
165.3.q.a	$165$	$3$	165.q	33.h	$10$	$128$	$32$	$4.496$		$_{}$	None	None		✓	✓	✓	165.3.q.a	$4$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
165.3.t.a	$165$	$3$	165.t	11.d	$10$	$32$	$8$	$4.496$		$_{}$	None	None		✓			165.3.t.a	$2$	$0$	$0$	$0$	$40$	$20$			$\mathrm{SU}(2)[C_{10}]$
165.3.t.b	$165$	$3$	165.t	11.d	$10$	$32$	$8$	$4.496$		$_{}$	None	None		✓			165.3.t.b	$2$	$0$	$0$	$0$	$-40$	$-20$			$\mathrm{SU}(2)[C_{10}]$
165.3.u.a	$165$	$3$	165.u	165.u	$20$	$352$	$44$	$4.496$		$_{}$	None	None		✓	✓	✓	165.3.u.a	$8$	$0$	$0$	$-4$	$0$	$-20$			$\mathrm{SU}(2)[C_{20}]$
165.3.x.a	$165$	$3$	165.x	55.k	$20$	$192$	$24$	$4.496$		$_{}$	None	None		✓	✓	✓	165.3.x.a	$4$	$0$	$0$	$0$	$-8$	$52$			$\mathrm{SU}(2)[C_{20}]$
165.4.a.a	$165$	$4$	165.a	1.a	$1$	$1$	$1$	$9.735$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	165.4.a.a	$1$	$0$	$0$	$-3$	$-5$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-8q^{4}-5q^{5}+2q^{7}+9q^{9}+\cdots$
165.4.a.b	$165$	$4$	165.a	1.a	$1$	$1$	$1$	$9.735$	$\Q$	$_{}$	None	None	✓	✓			165.4.a.b	$1$	$0$	$1$	$3$	$-5$	$36$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}-7q^{4}-5q^{5}+3q^{6}+\cdots$

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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.