Newform search results

Results (1-50 of 91 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
230.2.a.a	$230$	$2$	230.a	1.a	$1$	$2$	$2$	$1.837$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$0$	\(-2\)	\(-1\)	\(-2\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
230.2.a.b	$230$	$2$	230.a	1.a	$1$	$2$	$2$	$1.837$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-2\)	\(3\)	\(2\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
230.2.a.c	$230$	$2$	230.a	1.a	$1$	$2$	$2$	$1.837$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(2\)	\(1\)	\(2\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
230.2.a.d	$230$	$2$	230.a	1.a	$1$	$3$	$3$	$1.837$	3.3.1101.1	None	✓	$1$	$0$	\(3\)	\(1\)	\(-3\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
230.2.b.a	$230$	$2$	230.b	5.b	$2$	$4$	$4$	$1.837$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+(1+2\beta _{2})q^{5}+\cdots\)
230.2.b.b	$230$	$2$	230.b	5.b	$2$	$8$	$8$	$1.837$	8.0.\(\cdots\).3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{5})q^{3}-q^{4}+(\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)
230.2.e.a	$230$	$2$	230.e	115.e	$4$	$8$	$4$	$1.837$	8.0.110166016.2	None		$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.b	$230$	$2$	230.e	115.e	$4$	$8$	$4$	$1.837$	8.0.110166016.2	None		$2$	$0$	\(0\)	\(-4\)	\(4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.c	$230$	$2$	230.e	115.e	$4$	$8$	$4$	$1.837$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(16\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{16}^{6}q^{2}+(2+2\zeta_{16}^{4})q^{3}-\zeta_{16}^{4}q^{4}+\cdots\)
230.2.g.a	$230$	$2$	230.g	23.c	$11$	$10$	$1$	$1.837$	\(\Q(\zeta_{22})\)	None		$2$	$0$	\(-1\)	\(3\)	\(-1\)	\(-15\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\zeta_{22}^{4}q^{2}+(1-\zeta_{22}+\zeta_{22}^{2}+\zeta_{22}^{4}+\cdots)q^{3}+\cdots\)
230.2.g.b	$230$	$2$	230.g	23.c	$11$	$20$	$2$	$1.837$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(2\)	\(-3\)	\(-2\)	\(19\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{6}q^{2}+(\beta _{1}-\beta _{2}+\beta _{5}-\beta _{13}+\beta _{18}+\cdots)q^{3}+\cdots\)
230.2.g.c	$230$	$2$	230.g	23.c	$11$	$20$	$2$	$1.837$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(2\)	\(1\)	\(2\)	\(-12\)		$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{3}q^{2}+(\beta _{5}+\beta _{18})q^{3}+\beta _{12}q^{4}+\cdots\)
230.2.g.d	$230$	$2$	230.g	23.c	$11$	$30$	$3$	$1.837$		None		$2$	$0$	\(-3\)	\(-1\)	\(3\)	\(8\)			$\mathrm{SU}(2)[C_{11}]$
230.2.j.a	$230$	$2$	230.j	115.j	$22$	$120$	$12$	$1.837$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
230.2.l.a	$230$	$2$	230.l	115.l	$44$	$240$	$12$	$1.837$		None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{44}]$
230.3.c.a	$230$	$3$	230.c	115.c	$2$	$24$	$24$	$6.267$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
230.3.d.a	$230$	$3$	230.d	23.b	$2$	$16$	$16$	$6.267$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}-\beta _{5}q^{3}+2q^{4}+\beta _{2}q^{5}-\beta _{10}q^{6}+\cdots\)
230.3.f.a	$230$	$3$	230.f	5.c	$4$	$20$	$10$	$6.267$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-20\)	\(0\)	\(4\)	\(8\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{8})q^{2}+\beta _{1}q^{3}+2\beta _{8}q^{4}+\cdots\)
230.3.f.b	$230$	$3$	230.f	5.c	$4$	$24$	$12$	$6.267$		None		$2$	$0$	\(24\)	\(0\)	\(4\)	\(8\)			$\mathrm{SU}(2)[C_{4}]$
230.3.h.a	$230$	$3$	230.h	23.d	$22$	$160$	$16$	$6.267$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
230.3.i.a	$230$	$3$	230.i	115.i	$22$	$240$	$24$	$6.267$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
230.3.k.a	$230$	$3$	230.k	115.k	$44$	$240$	$12$	$6.267$		None		$4$	$0$	\(-24\)	\(0\)	\(-4\)	\(-74\)			$\mathrm{SU}(2)[C_{44}]$
230.3.k.b	$230$	$3$	230.k	115.k	$44$	$240$	$12$	$6.267$		None		$4$	$0$	\(24\)	\(8\)	\(-4\)	\(50\)			$\mathrm{SU}(2)[C_{44}]$
230.4.a.a	$230$	$4$	230.a	1.a	$1$	$1$	$1$	$13.570$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-5\)	\(-5\)	\(12\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-5q^{3}+4q^{4}-5q^{5}+10q^{6}+\cdots\)
230.4.a.b	$230$	$4$	230.a	1.a	$1$	$1$	$1$	$13.570$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(4\)	\(-5\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
230.4.a.c	$230$	$4$	230.a	1.a	$1$	$1$	$1$	$13.570$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(7\)	\(5\)	\(20\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+7q^{3}+4q^{4}+5q^{5}-14q^{6}+\cdots\)
230.4.a.d	$230$	$4$	230.a	1.a	$1$	$1$	$1$	$13.570$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(-1\)	\(5\)	\(-32\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+4q^{4}+5q^{5}-2q^{6}+\cdots\)
230.4.a.e	$230$	$4$	230.a	1.a	$1$	$1$	$1$	$13.570$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(1\)	\(-5\)	\(-18\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+4q^{4}-5q^{5}+2q^{6}+\cdots\)
230.4.a.f	$230$	$4$	230.a	1.a	$1$	$2$	$2$	$13.570$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$1$	\(-4\)	\(-3\)	\(10\)	\(-17\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1-\beta )q^{3}+4q^{4}+5q^{5}+\cdots\)
230.4.a.g	$230$	$4$	230.a	1.a	$1$	$3$	$3$	$13.570$	3.3.318165.1	None	✓	$1$	$0$	\(-6\)	\(-1\)	\(15\)	\(7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+5q^{5}+2\beta _{1}q^{6}+\cdots\)
230.4.a.h	$230$	$4$	230.a	1.a	$1$	$4$	$4$	$13.570$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-8\)	\(-4\)	\(-20\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.i	$230$	$4$	230.a	1.a	$1$	$4$	$4$	$13.570$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(8\)	\(4\)	\(-20\)	\(26\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.j	$230$	$4$	230.a	1.a	$1$	$4$	$4$	$13.570$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(8\)	\(14\)	\(20\)	\(8\)	$+$	$3$	$\mathrm{SU}(2)$	\(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
230.4.b.a	$230$	$4$	230.b	5.b	$2$	$14$	$14$	$13.570$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{8}q^{2}+(\beta _{1}-\beta _{8})q^{3}-4q^{4}+(-\beta _{7}+\cdots)q^{5}+\cdots\)
230.4.b.b	$230$	$4$	230.b	5.b	$2$	$18$	$18$	$13.570$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{5}q^{2}+\beta _{1}q^{3}-4q^{4}+(-\beta _{5}-\beta _{12}+\cdots)q^{5}+\cdots\)
230.4.e.a	$230$	$4$	230.e	115.e	$4$	$72$	$36$	$13.570$		None		$4$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
230.4.g.a	$230$	$4$	230.g	23.c	$11$	$50$	$5$	$13.570$		None		$2$	$0$	\(-10\)	\(-5\)	\(25\)	\(-19\)			$\mathrm{SU}(2)[C_{11}]$
230.4.g.b	$230$	$4$	230.g	23.c	$11$	$60$	$6$	$13.570$		None		$2$	$0$	\(12\)	\(-3\)	\(-30\)	\(100\)			$\mathrm{SU}(2)[C_{11}]$
230.4.g.c	$230$	$4$	230.g	23.c	$11$	$60$	$6$	$13.570$		None		$2$	$0$	\(12\)	\(5\)	\(30\)	\(-3\)			$\mathrm{SU}(2)[C_{11}]$
230.4.g.d	$230$	$4$	230.g	23.c	$11$	$70$	$7$	$13.570$		None		$2$	$0$	\(-14\)	\(3\)	\(-35\)	\(-78\)			$\mathrm{SU}(2)[C_{11}]$
230.4.j.a	$230$	$4$	230.j	115.j	$22$	$360$	$36$	$13.570$		None		$4$	$0$	\(0\)	\(0\)	\(32\)	\(0\)			$\mathrm{SU}(2)[C_{22}]$
230.4.l.a	$230$	$4$	230.l	115.l	$44$	$720$	$36$	$13.570$		None		$4$	$0$	\(0\)	\(16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{44}]$
230.5.c.a	$230$	$5$	230.c	115.c	$2$	$48$	$48$	$23.775$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
230.5.d.a	$230$	$5$	230.d	23.b	$2$	$32$	$32$	$23.775$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
230.5.f.a	$230$	$5$	230.f	5.c	$4$	$44$	$22$	$23.775$		None		$2$	$0$	\(-88\)	\(0\)	\(24\)	\(-80\)			$\mathrm{SU}(2)[C_{4}]$
230.5.f.b	$230$	$5$	230.f	5.c	$4$	$44$	$22$	$23.775$		None		$2$	$0$	\(88\)	\(0\)	\(24\)	\(-80\)			$\mathrm{SU}(2)[C_{4}]$
230.6.a.a	$230$	$6$	230.a	1.a	$1$	$1$	$1$	$36.888$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(8\)	\(-25\)	\(199\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+8q^{3}+2^{4}q^{4}-5^{2}q^{5}-2^{5}q^{6}+\cdots\)
230.6.a.b	$230$	$6$	230.a	1.a	$1$	$2$	$2$	$36.888$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-8\)	\(6\)	\(-50\)	\(-164\)	$+$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+(3+6\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
230.6.a.c	$230$	$6$	230.a	1.a	$1$	$3$	$3$	$36.888$	3.3.27980.1	None	✓	$1$	$1$	\(-12\)	\(-26\)	\(75\)	\(1\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-4q^{2}+(-9+\beta _{2})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
230.6.a.d	$230$	$6$	230.a	1.a	$1$	$3$	$3$	$36.888$	3.3.27980.1	None	✓	$1$	$1$	\(12\)	\(-34\)	\(75\)	\(-121\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+4q^{2}+(-11-\beta _{2})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)