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 217 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
160.1.p.a	$160$	$1$	160.p	5.c	$4$	$2$	$1$	$0.080$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓	✓	✓	160.1.p.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{5}+i q^{9}+(i-1)q^{13}+(-i-1)q^{17}+\cdots$
160.2.a.a	$160$	$2$	160.a	1.a	$1$	$1$	$1$	$1.278$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	160.2.a.a	$1$	$1$	$0$	$-2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
160.2.a.b	$160$	$2$	160.a	1.a	$1$	$1$	$1$	$1.278$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	160.2.a.a	$1$	$0$	$0$	$2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
160.2.a.c	$160$	$2$	160.a	1.a	$1$	$2$	$2$	$1.278$	$\Q(\sqrt{2})$	$_{}$	None	None	✓	✓	✓	✓	160.2.a.c	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}-\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots$
160.2.c.a	$160$	$2$	160.c	5.b	$2$	$2$	$2$	$1.278$	$\Q(\sqrt{-1})$	$_{}$	$\Q(\sqrt{-1})$	None		✓			160.2.c.a	$4$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta+1)q^{5}+3 q^{9}+2\beta q^{13}-4\beta q^{17}+\cdots$
160.2.c.b	$160$	$2$	160.c	5.b	$2$	$4$	$4$	$1.278$	$\Q(i, \sqrt{5})$	$_{}$	$\Q(\sqrt{-5})$	None		✓	✓		160.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots$
160.2.d.a	$160$	$2$	160.d	8.b	$2$	$4$	$4$	$1.278$	$\Q(\zeta_{12})$	$_{}$	None	None			✓	✓	40.2.d.a	$2$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{2}+\beta_1)q^{3}+\beta_1 q^{5}+(\beta_{3}+1)q^{7}+\cdots$
160.2.f.a	$160$	$2$	160.f	40.f	$2$	$4$	$4$	$1.278$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None			✓	✓	40.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots$
160.2.n.a	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	$\Q(\sqrt{-1})$	$_{}$	None	None		✓			160.2.n.a	$2$	$1$	$0$	$-4$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i-2)q^{3}+(i-2)q^{5}+(2 i-2)q^{7}+\cdots$
160.2.n.b	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	$\Q(\sqrt{-1})$	$_{}$	None	None		✓			160.2.n.b	$2$	$0$	$0$	$-2$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{3}+(-2 i+1)q^{5}+(i-1)q^{7}+\cdots$
160.2.n.c	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	$\Q(\sqrt{-1})$	$_{}$	None	None		✓			160.2.n.c	$2$	$0$	$0$	$-2$	$2$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{3}+(2 i+1)q^{5}+(-3 i+3)q^{7}+\cdots$
160.2.n.d	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	$\Q(\sqrt{-1})$	$_{}$	None	None		✓			160.2.n.c	$2$	$0$	$0$	$2$	$2$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(2 i+1)q^{5}+(3 i-3)q^{7}+\cdots$
160.2.n.e	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	$\Q(\sqrt{-1})$	$_{}$	None	None		✓			160.2.n.b	$2$	$0$	$0$	$2$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(-2 i+1)q^{5}+(-i+1)q^{7}+\cdots$
160.2.n.f	$160$	$2$	160.n	20.e	$4$	$2$	$1$	$1.278$	$\Q(\sqrt{-1})$	$_{}$	None	None		✓			160.2.n.a	$2$	$0$	$0$	$4$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i+2)q^{3}+(i-2)q^{5}+(-2 i+2)q^{7}+\cdots$
160.2.o.a	$160$	$2$	160.o	40.k	$4$	$8$	$4$	$1.278$	$\Q(\zeta_{20})$	$_{}$	None	None			✓	✓	40.2.k.a	$4$	$0$	$0$	$4$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta_{3} q^{3}+\beta_{5} q^{5}-\beta_{6} q^{7}+(-\beta_{3}+\beta_{2}+\beta_1-1)q^{9}+\cdots$
160.2.u.a	$160$	$2$	160.u	160.u	$8$	$88$	$22$	$1.278$		$_{}$	None	None		✓	✓	✓	160.2.u.a	$2$	$0$	$-4$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{8}]$
160.2.x.a	$160$	$2$	160.x	32.g	$8$	$64$	$16$	$1.278$		$_{}$	None	None		✓	✓	✓	160.2.x.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
160.2.z.a	$160$	$2$	160.z	160.z	$8$	$88$	$22$	$1.278$		$_{}$	None	None		✓	✓	✓	160.2.z.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{8}]$
160.2.ba.a	$160$	$2$	160.ba	160.aa	$8$	$88$	$22$	$1.278$		$_{}$	None	None		✓	✓	✓	160.2.u.a	$2$	$0$	$-4$	$-4$	$-4$	$-8$			$\mathrm{SU}(2)[C_{8}]$
160.3.b.a	$160$	$3$	160.b	4.b	$2$	$4$	$4$	$4.360$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			160.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+4\beta _{2})q^{7}+\cdots$
160.3.b.b	$160$	$3$	160.b	4.b	$2$	$4$	$4$	$4.360$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			160.3.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots$
160.3.e.a	$160$	$3$	160.e	40.e	$2$	$1$	$1$	$4.360$	$\Q$	$_{}$	$\Q(\sqrt{-10})$	None	✓				40.3.e.a	$2$	$0$	$0$	$0$	$-5$	$6$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-5q^{5}+6q^{7}+9q^{9}+18q^{11}+6q^{13}+\cdots$
160.3.e.b	$160$	$3$	160.e	40.e	$2$	$1$	$1$	$4.360$	$\Q$	$_{}$	$\Q(\sqrt{-10})$	None	✓				40.3.e.a	$2$	$0$	$0$	$0$	$5$	$-6$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+5q^{5}-6q^{7}+9q^{9}+18q^{11}-6q^{13}+\cdots$
160.3.e.c	$160$	$3$	160.e	40.e	$2$	$8$	$8$	$4.360$	8.0. $\cdots$ .2	$_{}$	None	None			✓		40.3.e.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
160.3.g.a	$160$	$3$	160.g	8.d	$2$	$8$	$8$	$4.360$	8.0. $\cdots$ .1	$_{}$	None	None			✓	✓	40.3.g.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{6}q^{7}+(3+\beta _{3}+\cdots)q^{9}+\cdots$
160.3.h.a	$160$	$3$	160.h	20.d	$2$	$6$	$6$	$4.360$	6.0.1827904.1	$_{}$	None	None		✓			160.3.h.a	$2$	$0$	$0$	$-4$	$-2$	$-12$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{3}-\beta _{4}q^{5}+(-2-\beta _{3}+\cdots)q^{7}+\cdots$
160.3.h.b	$160$	$3$	160.h	20.d	$2$	$6$	$6$	$4.360$	6.0.1827904.1	$_{}$	None	None		✓			160.3.h.a	$2$	$0$	$0$	$4$	$-2$	$12$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{4})q^{5}+\cdots$
160.3.m.a	$160$	$3$	160.m	40.i	$4$	$20$	$10$	$4.360$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None			✓	✓	40.3.i.a	$4$	$0$	$0$	$0$	$0$	$4$		$2^{34}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{8}q^{3}+\beta _{9}q^{5}-\beta _{4}q^{7}+(2\beta _{2}-\beta _{13}+\cdots)q^{9}+\cdots$
160.3.p.a	$160$	$3$	160.p	5.c	$4$	$2$	$1$	$4.360$	$\Q(\sqrt{-1})$	$_{}$	$\Q(\sqrt{-1})$	None		✓			160.3.p.a	$4$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(3 i-4)q^{5}+9 i q^{9}+(17 i-17)q^{13}+\cdots$
160.3.p.b	$160$	$3$	160.p	5.c	$4$	$2$	$1$	$4.360$	$\Q(\sqrt{-1})$	$_{}$	$\Q(\sqrt{-1})$	None		✓			160.3.p.b	$4$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(3 i+4)q^{5}+9 i q^{9}+(-7 i+7)q^{13}+\cdots$
160.3.p.c	$160$	$3$	160.p	5.c	$4$	$4$	$2$	$4.360$	$\Q(i, \sqrt{15})$	$_{}$	None	None		✓			160.3.p.c	$4$	$0$	$0$	$0$	$-20$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}-5q^{5}+\beta _{3}q^{7}+21\beta _{1}q^{9}+\cdots$
160.3.p.d	$160$	$3$	160.p	5.c	$4$	$4$	$2$	$4.360$	$\Q(i, \sqrt{7})$	$_{}$	None	None		✓			160.3.p.d	$4$	$0$	$0$	$0$	$12$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}+(3+4\beta _{1})q^{5}-3\beta _{3}q^{7}+5\beta _{1}q^{9}+\cdots$
160.3.p.e	$160$	$3$	160.p	5.c	$4$	$6$	$3$	$4.360$	6.0.3534400.1	$_{}$	None	None		✓			160.3.p.e	$2$	$0$	$0$	$0$	$4$	$-8$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(-2-2\beta _{3}+\cdots)q^{7}+\cdots$
160.3.p.f	$160$	$3$	160.p	5.c	$4$	$6$	$3$	$4.360$	6.0.3534400.1	$_{}$	None	None		✓			160.3.p.e	$2$	$0$	$0$	$0$	$4$	$8$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(2+2\beta _{3}+\cdots)q^{7}+\cdots$
160.3.v.a	$160$	$3$	160.v	160.v	$8$	$184$	$46$	$4.360$		$_{}$	None	None		✓	✓	✓	160.3.v.a	$2$	$0$	$-4$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{8}]$
160.3.w.a	$160$	$3$	160.w	32.h	$8$	$128$	$32$	$4.360$		$_{}$	None	None		✓	✓	✓	160.3.w.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
160.3.y.a	$160$	$3$	160.y	160.y	$8$	$184$	$46$	$4.360$		$_{}$	None	None		✓	✓	✓	160.3.y.a	$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{8}]$
160.3.bb.a	$160$	$3$	160.bb	160.ab	$8$	$184$	$46$	$4.360$		$_{}$	None	None		✓	✓	✓	160.3.v.a	$2$	$0$	$-4$	$-4$	$-4$	$-8$			$\mathrm{SU}(2)[C_{8}]$
160.4.a.a	$160$	$4$	160.a	1.a	$1$	$1$	$1$	$9.440$	$\Q$	$_{}$	None	None	✓	✓			160.4.a.a	$1$	$0$	$0$	$-2$	$-5$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-5q^{5}+6q^{7}-23q^{9}+60q^{11}+\cdots$
160.4.a.b	$160$	$4$	160.a	1.a	$1$	$1$	$1$	$9.440$	$\Q$	$_{}$	None	None	✓	✓			160.4.a.a	$1$	$1$	$0$	$2$	$-5$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-5q^{5}-6q^{7}-23q^{9}-60q^{11}+\cdots$
160.4.a.c	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	$\Q(\sqrt{6})$	$_{}$	None	None	✓	✓	✓	✓	160.4.a.c	$1$	$1$	$0$	$-8$	$10$	$-8$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-4+\beta )q^{3}+5q^{5}+(-4-5\beta )q^{7}+\cdots$
160.4.a.d	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	$\Q(\sqrt{5})$	$_{}$	None	None	✓	✓	✓		160.4.a.d	$2$	$1$	$0$	$0$	$-10$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta q^{3}-5q^{5}+7\beta q^{7}-7q^{9}+2\beta q^{11}+\cdots$
160.4.a.e	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	$\Q(\sqrt{13})$	$_{}$	None	None	✓	✓	✓		160.4.a.e	$2$	$0$	$0$	$0$	$-10$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta q^{3}-5q^{5}-\beta q^{7}+5^{2}q^{9}-6\beta q^{11}+\cdots$
160.4.a.f	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	$\Q(\sqrt{10})$	$_{}$	None	None	✓	✓			160.4.a.f	$2$	$0$	$0$	$0$	$10$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}+5q^{5}+3\beta q^{7}+13q^{9}-2\beta q^{11}+\cdots$
160.4.a.g	$160$	$4$	160.a	1.a	$1$	$2$	$2$	$9.440$	$\Q(\sqrt{6})$	$_{}$	None	None	✓	✓			160.4.a.c	$1$	$0$	$0$	$8$	$10$	$8$	$+$	$2$	$\mathrm{SU}(2)$	$q+(4+\beta )q^{3}+5q^{5}+(4-5\beta )q^{7}+(13+\cdots)q^{9}+\cdots$
160.4.c.a	$160$	$4$	160.c	5.b	$2$	$2$	$2$	$9.440$	$\Q(\sqrt{-1})$	$_{}$	$\Q(\sqrt{-1})$	None		✓			160.4.c.a	$4$	$0$	$0$	$0$	$-22$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta-11)q^{5}+27 q^{9}-46\beta q^{13}+\cdots$
160.4.c.b	$160$	$4$	160.c	5.b	$2$	$4$	$4$	$9.440$	$\Q(i, \sqrt{29})$	$_{}$	None	None		✓			160.4.c.b	$4$	$0$	$0$	$0$	$-12$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-3+\beta _{1})q^{5}+\beta _{2}q^{7}+11q^{9}+\cdots$
160.4.c.c	$160$	$4$	160.c	5.b	$2$	$4$	$4$	$9.440$	$\Q(i, \sqrt{5})$	$_{}$	$\Q(\sqrt{-5})$	None		✓			160.4.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}+2\beta _{3})q^{3}-5\beta _{2}q^{5}+(-6\beta _{1}+\cdots)q^{7}+\cdots$
160.4.c.d	$160$	$4$	160.c	5.b	$2$	$8$	$8$	$9.440$	8.0. $\cdots$ .22	$_{}$	None	None		✓	✓		160.4.c.d	$4$	$0$	$0$	$0$	$32$	$0$		$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(4-\beta _{4})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
160.4.d.a	$160$	$4$	160.d	8.b	$2$	$12$	$12$	$9.440$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None			✓	✓	40.4.d.a	$2$	$0$	$0$	$0$	$0$	$-28$		$2^{30}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-2+\beta _{4})q^{7}+(-9+\cdots)q^{9}+\cdots$

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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.