Newform search results

Results (1-50 of 95 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.2.a.a	$37$	$2$	37.a	1.a	$1$	$1$	$1$	$0.295$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-3\)	\(-2\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+2q^{4}-2q^{5}+6q^{6}+\cdots\)
37.2.a.b	$37$	$2$	37.a	1.a	$1$	$1$	$1$	$0.295$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{7}-2q^{9}+3q^{11}+\cdots\)
37.2.b.a	$37$	$2$	37.b	37.b	$2$	$2$	$2$	$0.295$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-q^{3}-2q^{4}-2iq^{5}-2iq^{6}+\cdots\)
37.2.c.a	$37$	$2$	37.c	37.c	$3$	$2$	$1$	$0.295$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)
37.2.e.a	$37$	$2$	37.e	37.e	$6$	$4$	$2$	$0.295$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(2\)	\(-6\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
37.2.f.a	$37$	$2$	37.f	37.f	$9$	$6$	$1$	$0.295$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(-6\)	\(3\)	\(-6\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1+\zeta_{18}^{5})q^{2}+(\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
37.2.f.b	$37$	$2$	37.f	37.f	$9$	$6$	$1$	$0.295$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(3\)	\(-6\)	\(6\)	\(-12\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
37.2.h.a	$37$	$2$	37.h	37.h	$18$	$18$	$3$	$0.295$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(-9\)	\(-9\)	\(-3\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(\beta _{4}-\beta _{11})q^{2}+(-1-\beta _{12}+\beta _{16}+\cdots)q^{3}+\cdots\)
37.3.d.a	$37$	$3$	37.d	37.d	$4$	$12$	$6$	$1.008$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-6\)	\(0\)	\(-6\)	\(-4\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{1}+\beta _{6})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
37.3.g.a	$37$	$3$	37.g	37.g	$12$	$24$	$6$	$1.008$		None		$2$	$0$	\(0\)	\(-6\)	\(-18\)	\(-2\)			$\mathrm{SU}(2)[C_{12}]$
37.3.i.a	$37$	$3$	37.i	37.i	$36$	$60$	$5$	$1.008$		None		$2$	$0$	\(-12\)	\(-12\)	\(6\)	\(-12\)			$\mathrm{SU}(2)[C_{36}]$
37.4.a.a	$37$	$4$	37.a	1.a	$1$	$4$	$4$	$2.183$	4.4.21208.1	None	✓	$1$	$1$	\(-6\)	\(-11\)	\(-29\)	\(-32\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{2}-\beta _{3})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
37.4.a.b	$37$	$4$	37.a	1.a	$1$	$5$	$5$	$2.183$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(13\)	\(11\)	\(24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(3-\beta _{2})q^{3}+(3-\beta _{1}+\cdots)q^{4}+\cdots\)
37.4.b.a	$37$	$4$	37.b	37.b	$2$	$8$	$8$	$2.183$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(4\)		$2^{4}\cdot 3^{5}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-1-\beta _{3})q^{3}+(-4+\beta _{5}+\cdots)q^{4}+\cdots\)
37.4.c.a	$37$	$4$	37.c	37.c	$3$	$18$	$9$	$2.183$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(2\)	\(1\)	\(3\)	\(-25\)		$2^{14}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{6}-\beta _{11})q^{3}+(-4+\beta _{1}+\cdots)q^{4}+\cdots\)
37.4.e.a	$37$	$4$	37.e	37.e	$6$	$16$	$8$	$2.183$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-6\)	\(-3\)	\(18\)	\(23\)		$2^{12}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}-\beta _{6}q^{3}+(2-\beta _{3}-2\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
37.4.f.a	$37$	$4$	37.f	37.f	$9$	$54$	$9$	$2.183$		None		$2$	$0$	\(-9\)	\(-12\)	\(6\)	\(96\)			$\mathrm{SU}(2)[C_{9}]$
37.4.h.a	$37$	$4$	37.h	37.h	$18$	$48$	$8$	$2.183$		None		$2$	$0$	\(-3\)	\(0\)	\(-27\)	\(-108\)			$\mathrm{SU}(2)[C_{18}]$
37.5.d.a	$37$	$5$	37.d	37.d	$4$	$22$	$11$	$3.825$		None		$2$	$0$	\(4\)	\(0\)	\(4\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
37.5.g.a	$37$	$5$	37.g	37.g	$12$	$44$	$11$	$3.825$		None		$2$	$0$	\(-10\)	\(-6\)	\(98\)	\(-2\)			$\mathrm{SU}(2)[C_{12}]$
37.5.i.a	$37$	$5$	37.i	37.i	$36$	$144$	$12$	$3.825$		None		$2$	$0$	\(-12\)	\(-12\)	\(-120\)	\(-12\)			$\mathrm{SU}(2)[C_{36}]$
37.6.a.a	$37$	$6$	37.a	1.a	$1$	$7$	$7$	$5.934$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-8\)	\(-47\)	\(-64\)	\(-293\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+\cdots\)
37.6.a.b	$37$	$6$	37.a	1.a	$1$	$8$	$8$	$5.934$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(12\)	\(25\)	\(136\)	\(99\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{2}+(3-\beta _{5})q^{3}+(20-2\beta _{1}+\cdots)q^{4}+\cdots\)
37.6.b.a	$37$	$6$	37.b	37.b	$2$	$16$	$16$	$5.934$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(-18\)	\(0\)	\(190\)		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-17+\beta _{2}+\cdots)q^{4}+\cdots\)
37.6.c.a	$37$	$6$	37.c	37.c	$3$	$30$	$15$	$5.934$		None		$2$	$0$	\(-4\)	\(16\)	\(-51\)	\(50\)			$\mathrm{SU}(2)[C_{3}]$
37.6.e.a	$37$	$6$	37.e	37.e	$6$	$32$	$16$	$5.934$		None		$2$	$0$	\(-6\)	\(18\)	\(144\)	\(-52\)			$\mathrm{SU}(2)[C_{6}]$
37.6.f.a	$37$	$6$	37.f	37.f	$9$	$84$	$14$	$5.934$		None		$2$	$0$	\(-9\)	\(-3\)	\(-30\)	\(-213\)			$\mathrm{SU}(2)[C_{9}]$
37.6.h.a	$37$	$6$	37.h	37.h	$18$	$90$	$15$	$5.934$		None		$2$	$0$	\(-3\)	\(-9\)	\(-153\)	\(201\)			$\mathrm{SU}(2)[C_{18}]$
37.7.d.a	$37$	$7$	37.d	37.d	$4$	$36$	$18$	$8.512$		None		$2$	$0$	\(-4\)	\(0\)	\(-256\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
37.7.g.a	$37$	$7$	37.g	37.g	$12$	$72$	$18$	$8.512$		None		$2$	$0$	\(-2\)	\(-6\)	\(52\)	\(-2\)			$\mathrm{SU}(2)[C_{12}]$
37.7.i.a	$37$	$7$	37.i	37.i	$36$	$216$	$18$	$8.512$		None		$2$	$0$	\(-12\)	\(-12\)	\(186\)	\(-12\)			$\mathrm{SU}(2)[C_{36}]$
37.8.a.a	$37$	$8$	37.a	1.a	$1$	$10$	$10$	$11.558$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-24\)	\(-95\)	\(-624\)	\(-501\)	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{2}+(-10+\beta _{1}-\beta _{7}+\cdots)q^{3}+\cdots\)
37.8.a.b	$37$	$8$	37.a	1.a	$1$	$11$	$11$	$11.558$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(16\)	\(121\)	\(376\)	\(2243\)	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(11+\beta _{2})q^{3}+(71+2\beta _{1}+\cdots)q^{4}+\cdots\)
37.8.b.a	$37$	$8$	37.b	37.b	$2$	$20$	$20$	$11.558$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(78\)	\(0\)	\(-1746\)		$2^{19}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(4+\beta _{4})q^{3}+(-42+\beta _{2}+\cdots)q^{4}+\cdots\)
37.8.c.a	$37$	$8$	37.c	37.c	$3$	$42$	$21$	$11.558$		None		$2$	$0$	\(-16\)	\(-68\)	\(-337\)	\(-158\)			$\mathrm{SU}(2)[C_{3}]$
37.8.e.a	$37$	$8$	37.e	37.e	$6$	$40$	$20$	$11.558$		None		$2$	$0$	\(18\)	\(-42\)	\(-672\)	\(156\)			$\mathrm{SU}(2)[C_{6}]$
37.8.f.a	$37$	$8$	37.f	37.f	$9$	$132$	$22$	$11.558$		None		$2$	$0$	\(15\)	\(33\)	\(576\)	\(-597\)			$\mathrm{SU}(2)[C_{9}]$
37.8.h.a	$37$	$8$	37.h	37.h	$18$	$126$	$21$	$11.558$		None		$2$	$0$	\(-27\)	\(-45\)	\(663\)	\(585\)			$\mathrm{SU}(2)[C_{18}]$
37.9.d.a	$37$	$9$	37.d	37.d	$4$	$50$	$25$	$15.073$		None		$2$	$0$	\(4\)	\(0\)	\(124\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
37.9.g.a	$37$	$9$	37.g	37.g	$12$	$100$	$25$	$15.073$		None		$2$	$0$	\(-10\)	\(-6\)	\(-1642\)	\(-2\)			$\mathrm{SU}(2)[C_{12}]$
37.9.i.a	$37$	$9$	37.i	37.i	$36$	$288$	$24$	$15.073$		None		$2$	$0$	\(-12\)	\(-12\)	\(1500\)	\(-12\)			$\mathrm{SU}(2)[C_{36}]$
37.10.a.a	$37$	$10$	37.a	1.a	$1$	$13$	$13$	$19.056$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(-32\)	\(-251\)	\(-2159\)	\(-12576\)	$+$	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{2}+(-20+\beta _{1}-\beta _{5}+\cdots)q^{3}+\cdots\)
37.10.a.b	$37$	$10$	37.a	1.a	$1$	$14$	$14$	$19.056$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(48\)	\(397\)	\(2841\)	\(6632\)	$-$	$2^{9}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{2}+(28+\beta _{3})q^{3}+(248+5\beta _{1}+\cdots)q^{4}+\cdots\)
37.10.b.a	$37$	$10$	37.b	37.b	$2$	$28$	$28$	$19.056$		None		$2$	$0$	\(0\)	\(-150\)	\(0\)	\(5940\)			$\mathrm{SU}(2)[C_{2}]$
37.10.c.a	$37$	$10$	37.c	37.c	$3$	$54$	$27$	$19.056$		None		$2$	$0$	\(32\)	\(73\)	\(2729\)	\(4231\)			$\mathrm{SU}(2)[C_{3}]$
37.10.e.a	$37$	$10$	37.e	37.e	$6$	$56$	$28$	$19.056$		None		$2$	$0$	\(-54\)	\(-75\)	\(-186\)	\(-4233\)			$\mathrm{SU}(2)[C_{6}]$
37.10.f.a	$37$	$10$	37.f	37.f	$9$	$162$	$27$	$19.056$		None		$2$	$0$	\(-57\)	\(-228\)	\(-3420\)	\(5808\)			$\mathrm{SU}(2)[C_{9}]$
37.10.h.a	$37$	$10$	37.h	37.h	$18$	$168$	$28$	$19.056$		None		$2$	$0$	\(45\)	\(216\)	\(177\)	\(-5820\)			$\mathrm{SU}(2)[C_{18}]$
37.11.d.a	$37$	$11$	37.d	37.d	$4$	$60$	$30$	$23.508$		None		$2$	$0$	\(-12\)	\(0\)	\(11094\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
37.11.g.a	$37$	$11$	37.g	37.g	$12$	$120$	$30$	$23.508$		None		$2$	$0$	\(6\)	\(-6\)	\(2922\)	\(-2\)			$\mathrm{SU}(2)[C_{12}]$