Newform search results

Results (1-50 of 141 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
51.2.a.a	$51$	$2$	51.a	1.a	$1$	$1$	$1$	$0.407$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}-4q^{7}+q^{9}-3q^{11}+\cdots\)
51.2.a.b	$51$	$2$	51.a	1.a	$1$	$2$	$2$	$0.407$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(3\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
51.2.d.a	$51$	$2$	51.d	17.b	$2$	$2$	$2$	$0.407$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{2}+iq^{3}+2q^{4}+3iq^{5}-2iq^{6}+\cdots\)
51.2.d.b	$51$	$2$	51.d	17.b	$2$	$2$	$2$	$0.407$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+iq^{3}-q^{4}+iq^{6}-4iq^{7}+\cdots\)
51.2.e.a	$51$	$2$	51.e	17.c	$4$	$8$	$4$	$0.407$	8.0.836829184.2	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
51.2.h.a	$51$	$2$	51.h	17.d	$8$	$8$	$2$	$0.407$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}+\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots\)
51.2.i.a	$51$	$2$	51.i	51.i	$16$	$32$	$4$	$0.407$		None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-16\)			$\mathrm{SU}(2)[C_{16}]$
51.3.b.a	$51$	$3$	51.b	3.b	$2$	$10$	$10$	$1.390$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-4\)		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-2+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
51.3.c.a	$51$	$3$	51.c	51.c	$2$	$1$	$1$	$1.390$	\(\Q\)	\(\Q(\sqrt{-51}) \)	✓	$2$	$0$	\(0\)	\(-3\)	\(7\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+4q^{4}+7q^{5}+9q^{9}-5q^{11}+\cdots\)
51.3.c.b	$51$	$3$	51.c	51.c	$2$	$1$	$1$	$1.390$	\(\Q\)	\(\Q(\sqrt{-51}) \)	✓	$2$	$0$	\(0\)	\(3\)	\(-7\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}+4q^{4}-7q^{5}+9q^{9}+5q^{11}+\cdots\)
51.3.c.c	$51$	$3$	51.c	51.c	$2$	$8$	$8$	$1.390$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(-\beta _{1}+\beta _{7})q^{3}+(-4-\beta _{2}+\cdots)q^{4}+\cdots\)
51.3.f.a	$51$	$3$	51.f	51.f	$4$	$20$	$10$	$1.390$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(-4\)		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}-\beta _{11}q^{3}+(1-\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
51.3.g.a	$51$	$3$	51.g	51.g	$8$	$4$	$1$	$1.390$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(-4\)	\(12\)	\(8\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1-\zeta_{8}-\zeta_{8}^{2})q^{2}+3q^{3}+(2\zeta_{8}+\cdots)q^{4}+\cdots\)
51.3.g.b	$51$	$3$	51.g	51.g	$8$	$4$	$1$	$1.390$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(4\)	\(0\)	\(-8\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1+\zeta_{8}+\zeta_{8}^{2})q^{2}+3\zeta_{8}q^{3}+(2\zeta_{8}+\cdots)q^{4}+\cdots\)
51.3.g.c	$51$	$3$	51.g	51.g	$8$	$32$	$8$	$1.390$		None		$4$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{8}]$
51.3.j.a	$51$	$3$	51.j	17.e	$16$	$48$	$6$	$1.390$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
51.4.a.a	$51$	$4$	51.a	1.a	$1$	$1$	$1$	$3.009$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-3\)	\(16\)	\(34\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}-7q^{4}+2^{4}q^{5}+3q^{6}+\cdots\)
51.4.a.b	$51$	$4$	51.a	1.a	$1$	$1$	$1$	$3.009$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(3\)	\(-20\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-7q^{4}-20q^{5}-3q^{6}+\cdots\)
51.4.a.c	$51$	$4$	51.a	1.a	$1$	$1$	$1$	$3.009$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-3\)	\(-10\)	\(-8\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}-7q^{4}-10q^{5}-3q^{6}+\cdots\)
51.4.a.d	$51$	$4$	51.a	1.a	$1$	$2$	$2$	$3.009$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-6\)	\(6\)	\(-8\)	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-3q^{3}+10q^{4}+(3+4\beta )q^{5}+\cdots\)
51.4.a.e	$51$	$4$	51.a	1.a	$1$	$3$	$3$	$3.009$	3.3.5912.1	None	✓	$1$	$0$	\(5\)	\(9\)	\(8\)	\(-8\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{2}+3q^{3}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
51.4.d.a	$51$	$4$	51.d	17.b	$2$	$8$	$8$	$3.009$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}-\beta _{4}q^{3}+(5-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
51.4.e.a	$51$	$4$	51.e	17.c	$4$	$16$	$8$	$3.009$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-32\)	\(-8\)		$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{4}q^{3}+(-4-\beta _{7}+\cdots)q^{4}+\cdots\)
51.4.h.a	$51$	$4$	51.h	17.d	$8$	$40$	$10$	$3.009$		None		$2$	$0$	\(0\)	\(0\)	\(32\)	\(0\)			$\mathrm{SU}(2)[C_{8}]$
51.4.i.a	$51$	$4$	51.i	51.i	$16$	$128$	$16$	$3.009$		None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-16\)			$\mathrm{SU}(2)[C_{16}]$
51.5.b.a	$51$	$5$	51.b	3.b	$2$	$22$	$22$	$5.272$		None		$2$	$0$	\(0\)	\(-10\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{2}]$
51.5.c.a	$51$	$5$	51.c	51.c	$2$	$1$	$1$	$5.272$	\(\Q\)	\(\Q(\sqrt{-51}) \)	✓	$2$	$0$	\(0\)	\(-9\)	\(1\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-9q^{3}+2^{4}q^{4}+q^{5}+3^{4}q^{9}+217q^{11}+\cdots\)
51.5.c.b	$51$	$5$	51.c	51.c	$2$	$1$	$1$	$5.272$	\(\Q\)	\(\Q(\sqrt{-51}) \)	✓	$2$	$0$	\(0\)	\(9\)	\(-1\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{3}+2^{4}q^{4}-q^{5}+3^{4}q^{9}-217q^{11}+\cdots\)
51.5.c.c	$51$	$5$	51.c	51.c	$2$	$20$	$20$	$5.272$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-8-\beta _{4})q^{4}-\beta _{14}q^{5}+\cdots\)
51.5.f.a	$51$	$5$	51.f	51.f	$4$	$44$	$22$	$5.272$		None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
51.5.g.a	$51$	$5$	51.g	51.g	$8$	$88$	$22$	$5.272$		None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)			$\mathrm{SU}(2)[C_{8}]$
51.5.j.a	$51$	$5$	51.j	17.e	$16$	$96$	$12$	$5.272$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
51.6.a.a	$51$	$6$	51.a	1.a	$1$	$2$	$2$	$8.180$	\(\Q(\sqrt{145}) \)	None	✓	$1$	$1$	\(-7\)	\(18\)	\(-113\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-3-\beta )q^{2}+9q^{3}+(13+7\beta )q^{4}+\cdots\)
51.6.a.b	$51$	$6$	51.a	1.a	$1$	$3$	$3$	$8.180$	3.3.76361.1	None	✓	$1$	$1$	\(5\)	\(-27\)	\(-37\)	\(-176\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{2}-9q^{3}+(12+\beta _{1}+2\beta _{2})q^{4}+\cdots\)
51.6.a.c	$51$	$6$	51.a	1.a	$1$	$4$	$4$	$8.180$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(5\)	\(36\)	\(146\)	\(60\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+9q^{3}+(3^{3}+4\beta _{2}+\beta _{3})q^{4}+\cdots\)
51.6.a.d	$51$	$6$	51.a	1.a	$1$	$5$	$5$	$8.180$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(-45\)	\(4\)	\(-40\)	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-9q^{3}+(24+\beta _{1}+2\beta _{2}+\beta _{4})q^{4}+\cdots\)
51.6.d.a	$51$	$6$	51.d	17.b	$2$	$16$	$16$	$8.180$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$2^{15}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{9}q^{3}+(2^{4}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
51.6.e.a	$51$	$6$	51.e	17.c	$4$	$32$	$16$	$8.180$		None		$2$	$0$	\(0\)	\(0\)	\(76\)	\(236\)			$\mathrm{SU}(2)[C_{4}]$
51.6.h.a	$51$	$6$	51.h	17.d	$8$	$56$	$14$	$8.180$		None		$2$	$0$	\(0\)	\(0\)	\(-88\)	\(0\)			$\mathrm{SU}(2)[C_{8}]$
51.6.i.a	$51$	$6$	51.i	51.i	$16$	$224$	$28$	$8.180$		None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(-16\)			$\mathrm{SU}(2)[C_{16}]$
51.7.b.a	$51$	$7$	51.b	3.b	$2$	$32$	$32$	$11.733$		None		$2$	$0$	\(0\)	\(32\)	\(0\)	\(568\)			$\mathrm{SU}(2)[C_{2}]$
51.7.c.a	$51$	$7$	51.c	51.c	$2$	$1$	$1$	$11.733$	\(\Q\)	\(\Q(\sqrt{-51}) \)	✓	$2$	$0$	\(0\)	\(-27\)	\(-182\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{3}q^{3}+2^{6}q^{4}-182q^{5}+3^{6}q^{9}+\cdots\)
51.7.c.b	$51$	$7$	51.c	51.c	$2$	$1$	$1$	$11.733$	\(\Q\)	\(\Q(\sqrt{-51}) \)	✓	$2$	$0$	\(0\)	\(27\)	\(182\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{3}q^{3}+2^{6}q^{4}+182q^{5}+3^{6}q^{9}+\cdots\)
51.7.c.c	$51$	$7$	51.c	51.c	$2$	$32$	$32$	$11.733$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
51.7.f.a	$51$	$7$	51.f	51.f	$4$	$68$	$34$	$11.733$		None		$4$	$0$	\(0\)	\(18\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
51.7.g.a	$51$	$7$	51.g	51.g	$8$	$136$	$34$	$11.733$		None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)			$\mathrm{SU}(2)[C_{8}]$
51.7.j.a	$51$	$7$	51.j	17.e	$16$	$144$	$18$	$11.733$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
51.8.a.a	$51$	$8$	51.a	1.a	$1$	$2$	$2$	$15.932$	\(\Q(\sqrt{1177}) \)	None	✓	$1$	$0$	\(7\)	\(54\)	\(320\)	\(-1500\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(4-\beta )q^{2}+3^{3}q^{3}+(182-7\beta )q^{4}+\cdots\)
51.8.a.b	$51$	$8$	51.a	1.a	$1$	$3$	$3$	$15.932$	3.3.1514860.1	None	✓	$1$	$1$	\(-7\)	\(-81\)	\(-440\)	\(808\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{2}-3^{3}q^{3}+(78-2\beta _{1}+\cdots)q^{4}+\cdots\)
51.8.a.c	$51$	$8$	51.a	1.a	$1$	$4$	$4$	$15.932$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(-15\)	\(108\)	\(-310\)	\(-1036\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-4+\beta _{1})q^{2}+3^{3}q^{3}+(39-7\beta _{1}+\cdots)q^{4}+\cdots\)