Newform search results

Results (1-50 of 143 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
85.2.a.a	$85$	$2$	85.a	1.a	$1$	$1$	$1$	$0.679$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(2\)	\(-1\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}-q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
85.2.a.b	$85$	$2$	85.a	1.a	$1$	$2$	$2$	$0.679$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(-4\)	\(-2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(-2-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
85.2.a.c	$85$	$2$	85.a	1.a	$1$	$2$	$2$	$0.679$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}+q^{5}+(-3+\cdots)q^{6}+\cdots\)
85.2.b.a	$85$	$2$	85.b	5.b	$2$	$8$	$8$	$0.679$	8.0.619810816.2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
85.2.c.a	$85$	$2$	85.c	85.c	$2$	$8$	$8$	$0.679$	8.0.\(\cdots\).11	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(-2+\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
85.2.d.a	$85$	$2$	85.d	17.b	$2$	$6$	$6$	$0.679$	6.0.350464.1	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{5}q^{3}+(\beta _{1}-\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
85.2.e.a	$85$	$2$	85.e	17.c	$4$	$12$	$6$	$0.679$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{10}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
85.2.j.a	$85$	$2$	85.j	85.j	$4$	$2$	$1$	$0.679$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(-2\)	\(-4\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}+(-1+i)q^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
85.2.j.b	$85$	$2$	85.j	85.j	$4$	$2$	$1$	$0.679$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(2\)	\(-2\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+q^{2}+(1-i)q^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
85.2.j.c	$85$	$2$	85.j	85.j	$4$	$12$	$6$	$0.679$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}+(-\beta _{2}-\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
85.2.l.a	$85$	$2$	85.l	17.d	$8$	$24$	$6$	$0.679$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{8}]$
85.2.m.a	$85$	$2$	85.m	85.m	$8$	$24$	$6$	$0.679$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{8}]$
85.2.o.a	$85$	$2$	85.o	85.o	$16$	$56$	$7$	$0.679$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
85.2.r.a	$85$	$2$	85.r	85.r	$16$	$56$	$7$	$0.679$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
85.3.f.a	$85$	$3$	85.f	85.f	$4$	$32$	$16$	$2.316$		None		$2$	$0$	\(4\)	\(0\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
85.3.g.a	$85$	$3$	85.g	85.g	$4$	$16$	$8$	$2.316$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(-16\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{3}+\beta _{4})q^{2}-\beta _{1}q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
85.3.g.b	$85$	$3$	85.g	85.g	$4$	$16$	$8$	$2.316$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{12}q^{2}-\beta _{9}q^{3}+(1+4\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
85.3.h.a	$85$	$3$	85.h	5.c	$4$	$32$	$16$	$2.316$		None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-16\)			$\mathrm{SU}(2)[C_{4}]$
85.3.i.a	$85$	$3$	85.i	85.i	$4$	$32$	$16$	$2.316$		None		$2$	$0$	\(-4\)	\(-4\)	\(-14\)	\(8\)			$\mathrm{SU}(2)[C_{4}]$
85.3.k.a	$85$	$3$	85.k	85.k	$8$	$64$	$16$	$2.316$		None		$2$	$0$	\(0\)	\(-4\)	\(-12\)	\(8\)			$\mathrm{SU}(2)[C_{8}]$
85.3.n.a	$85$	$3$	85.n	85.n	$8$	$64$	$16$	$2.316$		None		$2$	$0$	\(-8\)	\(-4\)	\(12\)	\(-16\)			$\mathrm{SU}(2)[C_{8}]$
85.3.p.a	$85$	$3$	85.p	85.p	$16$	$128$	$16$	$2.316$		None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
85.3.q.a	$85$	$3$	85.q	17.e	$16$	$96$	$12$	$2.316$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
85.4.a.a	$85$	$4$	85.a	1.a	$1$	$1$	$1$	$5.015$	\(\Q\)	None	✓	$1$	$1$	\(3\)	\(-7\)	\(5\)	\(-22\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}-7q^{3}+q^{4}+5q^{5}-21q^{6}+\cdots\)
85.4.a.b	$85$	$4$	85.a	1.a	$1$	$1$	$1$	$5.015$	\(\Q\)	None	✓	$1$	$1$	\(3\)	\(-5\)	\(-5\)	\(-22\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}-5q^{3}+q^{4}-5q^{5}-15q^{6}+\cdots\)
85.4.a.c	$85$	$4$	85.a	1.a	$1$	$1$	$1$	$5.015$	\(\Q\)	None	✓	$1$	$0$	\(3\)	\(10\)	\(5\)	\(-22\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+10q^{3}+q^{4}+5q^{5}+30q^{6}+\cdots\)
85.4.a.d	$85$	$4$	85.a	1.a	$1$	$2$	$2$	$5.015$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-4\)	\(-2\)	\(10\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{2}+(-1+\beta )q^{3}+(-1+\cdots)q^{4}+\cdots\)
85.4.a.e	$85$	$4$	85.a	1.a	$1$	$3$	$3$	$5.015$	3.3.1304.1	None	✓	$1$	$1$	\(-6\)	\(-4\)	\(-15\)	\(8\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
85.4.a.f	$85$	$4$	85.a	1.a	$1$	$3$	$3$	$5.015$	3.3.568.1	None	✓	$1$	$0$	\(3\)	\(9\)	\(-15\)	\(34\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-3\beta _{1})q^{3}+(-1+\cdots)q^{4}+\cdots\)
85.4.a.g	$85$	$4$	85.a	1.a	$1$	$5$	$5$	$5.015$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(-1\)	\(25\)	\(10\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(6-2\beta _{1}+\beta _{3})q^{4}+\cdots\)
85.4.b.a	$85$	$4$	85.b	5.b	$2$	$24$	$24$	$5.015$		None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
85.4.c.a	$85$	$4$	85.c	85.c	$2$	$24$	$24$	$5.015$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
85.4.d.a	$85$	$4$	85.d	17.b	$2$	$2$	$2$	$5.015$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+8iq^{3}-7q^{4}+5iq^{5}+8iq^{6}+\cdots\)
85.4.d.b	$85$	$4$	85.d	17.b	$2$	$16$	$16$	$5.015$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2^{4}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{12}q^{3}+(6-\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
85.4.e.a	$85$	$4$	85.e	17.c	$4$	$36$	$18$	$5.015$		None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
85.4.j.a	$85$	$4$	85.j	85.j	$4$	$48$	$24$	$5.015$		None		$4$	$0$	\(0\)	\(0\)	\(20\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
85.4.l.a	$85$	$4$	85.l	17.d	$8$	$72$	$18$	$5.015$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{8}]$
85.4.m.a	$85$	$4$	85.m	85.m	$8$	$104$	$26$	$5.015$		None		$4$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)			$\mathrm{SU}(2)[C_{8}]$
85.4.o.a	$85$	$4$	85.o	85.o	$16$	$200$	$25$	$5.015$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
85.4.r.a	$85$	$4$	85.r	85.r	$16$	$200$	$25$	$5.015$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
85.5.f.a	$85$	$5$	85.f	85.f	$4$	$68$	$34$	$8.786$		None		$2$	$0$	\(0\)	\(0\)	\(-44\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
85.5.g.a	$85$	$5$	85.g	85.g	$4$	$68$	$34$	$8.786$		None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
85.5.h.a	$85$	$5$	85.h	5.c	$4$	$64$	$32$	$8.786$		None		$2$	$0$	\(0\)	\(20\)	\(0\)	\(160\)			$\mathrm{SU}(2)[C_{4}]$
85.5.i.a	$85$	$5$	85.i	85.i	$4$	$68$	$34$	$8.786$		None		$2$	$0$	\(0\)	\(-4\)	\(28\)	\(-64\)			$\mathrm{SU}(2)[C_{4}]$
85.5.k.a	$85$	$5$	85.k	85.k	$8$	$136$	$34$	$8.786$		None		$2$	$0$	\(0\)	\(-4\)	\(32\)	\(-64\)			$\mathrm{SU}(2)[C_{8}]$
85.5.n.a	$85$	$5$	85.n	85.n	$8$	$136$	$34$	$8.786$		None		$2$	$0$	\(-8\)	\(-4\)	\(-112\)	\(56\)			$\mathrm{SU}(2)[C_{8}]$
85.5.p.a	$85$	$5$	85.p	85.p	$16$	$272$	$34$	$8.786$		None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
85.5.q.a	$85$	$5$	85.q	17.e	$16$	$192$	$24$	$8.786$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
85.6.a.a	$85$	$6$	85.a	1.a	$1$	$5$	$5$	$13.633$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(-7\)	\(-36\)	\(125\)	\(-204\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(-8+\beta _{1}-\beta _{3})q^{3}+\cdots\)
85.6.a.b	$85$	$6$	85.a	1.a	$1$	$7$	$7$	$13.633$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(9\)	\(18\)	\(-175\)	\(50\)	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(3+\beta _{2})q^{3}+(20+2\beta _{1}+\cdots)q^{4}+\cdots\)