Newform search results

Results (1-50 of 206 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.2.a.a	$105$	$2$	105.a	1.a	$1$	$1$	$1$	$0.838$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
105.2.a.b	$105$	$2$	105.a	1.a	$1$	$2$	$2$	$0.838$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+3q^{4}-q^{5}+\beta q^{6}+q^{7}+\cdots\)
105.2.b.a	$105$	$2$	105.b	21.c	$2$	$2$	$2$	$0.838$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-q^{5}-3q^{6}+\cdots\)
105.2.b.b	$105$	$2$	105.b	21.c	$2$	$2$	$2$	$0.838$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+q^{5}+3q^{6}+\cdots\)
105.2.b.c	$105$	$2$	105.b	21.c	$2$	$4$	$4$	$0.838$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-1\)	\(-4\)	\(-8\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)
105.2.b.d	$105$	$2$	105.b	21.c	$2$	$4$	$4$	$0.838$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(1\)	\(4\)	\(-8\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{1}q^{3}+(-1+\cdots)q^{4}+\cdots\)
105.2.d.a	$105$	$2$	105.d	5.b	$2$	$2$	$2$	$0.838$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}+(1-2i)q^{5}-q^{6}+\cdots\)
105.2.d.b	$105$	$2$	105.d	5.b	$2$	$6$	$6$	$0.838$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots\)
105.2.g.a	$105$	$2$	105.g	105.g	$2$	$4$	$4$	$0.838$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
105.2.g.b	$105$	$2$	105.g	105.g	$2$	$4$	$4$	$0.838$	\(\Q(\sqrt{-5}, \sqrt{7})\)	\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{3}-2q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
105.2.g.c	$105$	$2$	105.g	105.g	$2$	$4$	$4$	$0.838$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
105.2.i.a	$105$	$2$	105.i	7.c	$3$	$2$	$1$	$0.838$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(1\)	\(5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
105.2.i.b	$105$	$2$	105.i	7.c	$3$	$2$	$1$	$0.838$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(-1\)	\(-1\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
105.2.i.c	$105$	$2$	105.i	7.c	$3$	$4$	$2$	$0.838$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{5}-\beta _{3}q^{6}+\cdots\)
105.2.i.d	$105$	$2$	105.i	7.c	$3$	$4$	$2$	$0.838$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(2\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
105.2.j.a	$105$	$2$	105.j	15.e	$4$	$24$	$12$	$0.838$		None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
105.2.m.a	$105$	$2$	105.m	35.f	$4$	$16$	$8$	$0.838$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+\beta _{10}q^{3}+(-\beta _{2}+\beta _{9}-\beta _{11}+\cdots)q^{4}+\cdots\)
105.2.p.a	$105$	$2$	105.p	105.p	$6$	$24$	$12$	$0.838$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
105.2.q.a	$105$	$2$	105.q	35.j	$6$	$16$	$8$	$0.838$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{5}+\beta _{6}-\beta _{15})q^{2}+\beta _{3}q^{3}+(1+\cdots)q^{4}+\cdots\)
105.2.s.a	$105$	$2$	105.s	21.g	$6$	$2$	$1$	$0.838$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-3\)	\(-1\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
105.2.s.b	$105$	$2$	105.s	21.g	$6$	$2$	$1$	$0.838$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(0\)	\(1\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
105.2.s.c	$105$	$2$	105.s	21.g	$6$	$8$	$4$	$0.838$	8.0.856615824.2	None		$2$	$0$	\(-3\)	\(1\)	\(4\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(1-\beta _{1}+\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
105.2.s.d	$105$	$2$	105.s	21.g	$6$	$8$	$4$	$0.838$	8.0.856615824.2	None		$2$	$0$	\(3\)	\(2\)	\(-4\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(1+\beta _{3}+\beta _{6})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
105.2.u.a	$105$	$2$	105.u	35.k	$12$	$32$	$8$	$0.838$		None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(8\)			$\mathrm{SU}(2)[C_{12}]$
105.2.x.a	$105$	$2$	105.x	105.x	$12$	$48$	$12$	$0.838$		None		$8$	$0$	\(0\)	\(-2\)	\(0\)	\(-12\)			$\mathrm{SU}(2)[C_{12}]$
105.3.c.a	$105$	$3$	105.c	3.b	$2$	$16$	$16$	$2.861$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(-2+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots\)
105.3.e.a	$105$	$3$	105.e	35.c	$2$	$16$	$16$	$2.861$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{4})q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots\)
105.3.f.a	$105$	$3$	105.f	15.d	$2$	$24$	$24$	$2.861$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
105.3.h.a	$105$	$3$	105.h	7.b	$2$	$12$	$12$	$2.861$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(-8\)		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-\beta _{3}q^{3}+(4-\beta _{1})q^{4}+\beta _{8}q^{5}+\cdots\)
105.3.k.a	$105$	$3$	105.k	105.k	$4$	$4$	$2$	$2.861$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-28\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(-2-\zeta_{8}+2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots\)
105.3.k.b	$105$	$3$	105.k	105.k	$4$	$4$	$2$	$2.861$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(2+\zeta_{8}-2\zeta_{8}^{2})q^{3}-3\zeta_{8}^{2}q^{4}+\cdots\)
105.3.k.c	$105$	$3$	105.k	105.k	$4$	$16$	$8$	$2.861$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(32\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+(\beta _{7}+\beta _{10}-\beta _{13}+\beta _{15})q^{3}+\cdots\)
105.3.k.d	$105$	$3$	105.k	105.k	$4$	$32$	$16$	$2.861$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
105.3.l.a	$105$	$3$	105.l	5.c	$4$	$24$	$12$	$2.861$		None		$2$	$0$	\(8\)	\(0\)	\(16\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
105.3.n.a	$105$	$3$	105.n	7.d	$6$	$8$	$4$	$2.861$	8.0.\(\cdots\).16	None		$2$	$0$	\(2\)	\(-12\)	\(0\)	\(-16\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
105.3.n.b	$105$	$3$	105.n	7.d	$6$	$12$	$6$	$2.861$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(2\)	\(18\)	\(0\)	\(22\)		$2^{2}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}-\beta _{10})q^{2}+(2+\beta _{3})q^{3}+(4\beta _{3}+\cdots)q^{4}+\cdots\)
105.3.o.a	$105$	$3$	105.o	105.o	$6$	$16$	$8$	$2.861$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{9}+\beta _{13})q^{3}+(-1+\cdots)q^{4}+\cdots\)
105.3.o.b	$105$	$3$	105.o	105.o	$6$	$40$	$20$	$2.861$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
105.3.r.a	$105$	$3$	105.r	35.i	$6$	$32$	$16$	$2.861$		None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
105.3.t.a	$105$	$3$	105.t	21.h	$6$	$8$	$4$	$2.861$	8.0.3317760000.8	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(56\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}-\beta _{4}-\beta _{5})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
105.3.t.b	$105$	$3$	105.t	21.h	$6$	$36$	$18$	$2.861$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-58\)			$\mathrm{SU}(2)[C_{6}]$
105.3.v.a	$105$	$3$	105.v	35.l	$12$	$64$	$16$	$2.861$		None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)			$\mathrm{SU}(2)[C_{12}]$
105.3.w.a	$105$	$3$	105.w	105.w	$12$	$112$	$28$	$2.861$		None		$8$	$0$	\(0\)	\(-6\)	\(0\)	\(-16\)			$\mathrm{SU}(2)[C_{12}]$
105.4.a.a	$105$	$4$	105.a	1.a	$1$	$1$	$1$	$6.195$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-8q^{4}+5q^{5}+7q^{7}+9q^{9}+\cdots\)
105.4.a.b	$105$	$4$	105.a	1.a	$1$	$1$	$1$	$6.195$	\(\Q\)	None	✓	$1$	$0$	\(5\)	\(-3\)	\(5\)	\(7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{2}-3q^{3}+17q^{4}+5q^{5}-15q^{6}+\cdots\)
105.4.a.c	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-7\)	\(-6\)	\(-10\)	\(-14\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-3-\beta )q^{2}-3q^{3}+(5+7\beta )q^{4}+\cdots\)
105.4.a.d	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-4\)	\(6\)	\(-10\)	\(-14\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots\)
105.4.a.e	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(-6\)	\(10\)	\(-14\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots\)
105.4.a.f	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{65}) \)	None	✓	$1$	$0$	\(1\)	\(6\)	\(10\)	\(-14\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+3q^{3}+(8+\beta )q^{4}+5q^{5}+3\beta q^{6}+\cdots\)
105.4.a.g	$105$	$4$	105.a	1.a	$1$	$2$	$2$	$6.195$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(3\)	\(6\)	\(-10\)	\(14\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3q^{3}+(3+3\beta )q^{4}-5q^{5}+\cdots\)