Newform search results

Results (1-50 of 140 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
38.2.a.a	$38$	$2$	38.a	1.a	$1$	$1$	$1$	$0.303$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
38.2.a.b	$38$	$2$	38.a	1.a	$1$	$1$	$1$	$0.303$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(-4\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots\)
38.2.c.a	$38$	$2$	38.c	19.c	$3$	$2$	$1$	$0.303$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
38.2.c.b	$38$	$2$	38.c	19.c	$3$	$4$	$2$	$0.303$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
38.2.e.a	$38$	$2$	38.e	19.e	$9$	$6$	$1$	$0.303$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\zeta_{18}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{2}q^{4}+\cdots\)
38.3.b.a	$38$	$3$	38.b	19.b	$2$	$2$	$2$	$1.035$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+2\beta q^{3}-2q^{4}-q^{5}-4q^{6}+\cdots\)
38.3.d.a	$38$	$3$	38.d	19.d	$6$	$4$	$2$	$1.035$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(6\)	\(2\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
38.3.f.a	$38$	$3$	38.f	19.f	$18$	$24$	$4$	$1.035$		None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(-18\)			$\mathrm{SU}(2)[C_{18}]$
38.4.a.a	$38$	$4$	38.a	1.a	$1$	$1$	$1$	$2.242$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(-9\)	\(-31\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+4q^{4}-9q^{5}+4q^{6}+\cdots\)
38.4.a.b	$38$	$4$	38.a	1.a	$1$	$2$	$2$	$2.242$	\(\Q(\sqrt{177}) \)	None	✓	$1$	$0$	\(-4\)	\(1\)	\(10\)	\(57\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)
38.4.a.c	$38$	$4$	38.a	1.a	$1$	$2$	$2$	$2.242$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$0$	\(4\)	\(9\)	\(-9\)	\(-18\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(5-\beta )q^{3}+4q^{4}+(-6+3\beta )q^{5}+\cdots\)
38.4.c.a	$38$	$4$	38.c	19.c	$3$	$2$	$1$	$2.242$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(-5\)	\(-3\)	\(-64\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}+(-5+5\zeta_{6})q^{3}+\cdots\)
38.4.c.b	$38$	$4$	38.c	19.c	$3$	$2$	$1$	$2.242$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(5\)	\(12\)	\(16\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
38.4.c.c	$38$	$4$	38.c	19.c	$3$	$6$	$3$	$2.242$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(6\)	\(-5\)	\(-1\)	\(52\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\beta _{4})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{4}+\cdots)q^{3}+\cdots\)
38.4.e.a	$38$	$4$	38.e	19.e	$9$	$12$	$2$	$2.242$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-9\)	\(0\)	\(21\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-2\beta _{3}q^{2}+(-1+2\beta _{2}-\beta _{4}+2\beta _{6}+\cdots)q^{3}+\cdots\)
38.4.e.b	$38$	$4$	38.e	19.e	$9$	$18$	$3$	$2.242$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-33\)		$3^{2}$	$\mathrm{SU}(2)[C_{9}]$	\(q-2\beta _{8}q^{2}+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{9})q^{3}+\cdots\)
38.5.b.a	$38$	$5$	38.b	19.b	$2$	$8$	$8$	$3.928$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(18\)	\(-162\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-8q^{4}+(2-\beta _{6}+\cdots)q^{5}+\cdots\)
38.5.d.a	$38$	$5$	38.d	19.d	$6$	$16$	$8$	$3.928$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(-12\)	\(-18\)	\(72\)		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{5}+\beta _{9})q^{2}+(-1+\beta _{3})q^{3}+8\beta _{7}q^{4}+\cdots\)
38.5.f.a	$38$	$5$	38.f	19.f	$18$	$36$	$6$	$3.928$		None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(90\)			$\mathrm{SU}(2)[C_{18}]$
38.6.a.a	$38$	$6$	38.a	1.a	$1$	$1$	$1$	$6.095$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(-6\)	\(31\)	\(-27\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-6q^{3}+2^{4}q^{4}+31q^{5}+24q^{6}+\cdots\)
38.6.a.b	$38$	$6$	38.a	1.a	$1$	$1$	$1$	$6.095$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(-14\)	\(-45\)	\(-121\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-14q^{3}+2^{4}q^{4}-45q^{5}-56q^{6}+\cdots\)
38.6.a.c	$38$	$6$	38.a	1.a	$1$	$2$	$2$	$6.095$	\(\Q(\sqrt{1441}) \)	None	✓	$1$	$0$	\(-8\)	\(3\)	\(-45\)	\(114\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+(2-\beta )q^{3}+2^{4}q^{4}+(-21+\cdots)q^{5}+\cdots\)
38.6.a.d	$38$	$6$	38.a	1.a	$1$	$3$	$3$	$6.095$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(12\)	\(13\)	\(81\)	\(228\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+(4+\beta _{1})q^{3}+2^{4}q^{4}+(3^{3}-\beta _{1}+\cdots)q^{5}+\cdots\)
38.6.c.a	$38$	$6$	38.c	19.c	$3$	$6$	$3$	$6.095$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(12\)	\(-15\)	\(14\)	\(-624\)		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\beta _{3})q^{2}+(-5+\beta _{1}+\beta _{2}+5\beta _{3}+\cdots)q^{3}+\cdots\)
38.6.c.b	$38$	$6$	38.c	19.c	$3$	$8$	$4$	$6.095$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(-16\)	\(-14\)	\(-36\)	\(76\)		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\beta _{2})q^{2}+(-3+3\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
38.6.e.a	$38$	$6$	38.e	19.e	$9$	$24$	$4$	$6.095$		None		$2$	$0$	\(0\)	\(18\)	\(0\)	\(438\)			$\mathrm{SU}(2)[C_{9}]$
38.6.e.b	$38$	$6$	38.e	19.e	$9$	$30$	$5$	$6.095$		None		$2$	$0$	\(0\)	\(15\)	\(0\)	\(-84\)			$\mathrm{SU}(2)[C_{9}]$
38.7.b.a	$38$	$7$	38.b	19.b	$2$	$10$	$10$	$8.742$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-112\)	\(-224\)		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(\beta _{5}+\beta _{6})q^{3}-2^{5}q^{4}+(-11+\cdots)q^{5}+\cdots\)
38.7.d.a	$38$	$7$	38.d	19.d	$6$	$20$	$10$	$8.742$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(-30\)	\(112\)	\(-208\)		$2^{20}\cdot 3^{4}\cdot 19^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{8}q^{2}+(-2+\beta _{2}+\beta _{6})q^{3}+(2^{5}+\cdots)q^{4}+\cdots\)
38.7.f.a	$38$	$7$	38.f	19.f	$18$	$60$	$10$	$8.742$		None		$2$	$0$	\(0\)	\(30\)	\(0\)	\(432\)			$\mathrm{SU}(2)[C_{18}]$
38.8.a.a	$38$	$8$	38.a	1.a	$1$	$1$	$1$	$11.871$	\(\Q\)	None	✓	$1$	$0$	\(-8\)	\(77\)	\(440\)	\(951\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+77q^{3}+2^{6}q^{4}+440q^{5}+\cdots\)
38.8.a.b	$38$	$8$	38.a	1.a	$1$	$2$	$2$	$11.871$	\(\Q(\sqrt{2737}) \)	None	✓	$1$	$0$	\(-16\)	\(-61\)	\(175\)	\(-2592\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+(-30-\beta )q^{3}+2^{6}q^{4}+(95+\cdots)q^{5}+\cdots\)
38.8.a.c	$38$	$8$	38.a	1.a	$1$	$2$	$2$	$11.871$	\(\Q(\sqrt{17953}) \)	None	✓	$1$	$1$	\(-16\)	\(-11\)	\(-69\)	\(-348\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+(-5-\beta )q^{3}+2^{6}q^{4}+(-6^{2}+\cdots)q^{5}+\cdots\)
38.8.a.d	$38$	$8$	38.a	1.a	$1$	$2$	$2$	$11.871$	\(\Q(\sqrt{633}) \)	None	✓	$1$	$1$	\(16\)	\(-69\)	\(155\)	\(-2238\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+(-33-3\beta )q^{3}+2^{6}q^{4}+(62+\cdots)q^{5}+\cdots\)
38.8.a.e	$38$	$8$	38.a	1.a	$1$	$4$	$4$	$11.871$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(32\)	\(12\)	\(-279\)	\(2485\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+8q^{2}+(3-\beta _{1})q^{3}+2^{6}q^{4}+(-70+\cdots)q^{5}+\cdots\)
38.8.c.a	$38$	$8$	38.c	19.c	$3$	$12$	$6$	$11.871$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-48\)	\(12\)	\(124\)	\(-1036\)		$2^{6}\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+8\beta _{2}q^{2}+(\beta _{1}-2\beta _{2})q^{3}+(-2^{6}-2^{6}\beta _{2}+\cdots)q^{4}+\cdots\)
38.8.c.b	$38$	$8$	38.c	19.c	$3$	$14$	$7$	$11.871$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(56\)	\(55\)	\(-126\)	\(1928\)		$2^{8}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+8\beta _{3}q^{2}+(\beta _{1}+\beta _{2}+8\beta _{3})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots\)
38.8.e.a	$38$	$8$	38.e	19.e	$9$	$30$	$5$	$11.871$		None		$2$	$0$	\(0\)	\(45\)	\(0\)	\(1806\)			$\mathrm{SU}(2)[C_{9}]$
38.8.e.b	$38$	$8$	38.e	19.e	$9$	$36$	$6$	$11.871$		None		$2$	$0$	\(0\)	\(-84\)	\(0\)	\(-2988\)			$\mathrm{SU}(2)[C_{9}]$
38.9.b.a	$38$	$9$	38.b	19.b	$2$	$12$	$12$	$15.480$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(558\)	\(-5422\)		$2^{21}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(\beta _{6}-\beta _{7})q^{3}-2^{7}q^{4}+(47+\cdots)q^{5}+\cdots\)
38.9.d.a	$38$	$9$	38.d	19.d	$6$	$24$	$12$	$15.480$		None		$2$	$0$	\(0\)	\(168\)	\(-558\)	\(11992\)			$\mathrm{SU}(2)[C_{6}]$
38.9.f.a	$38$	$9$	38.f	19.f	$18$	$84$	$14$	$15.480$		None		$2$	$0$	\(0\)	\(-168\)	\(0\)	\(-6570\)			$\mathrm{SU}(2)[C_{18}]$
38.10.a.a	$38$	$10$	38.a	1.a	$1$	$1$	$1$	$19.571$	\(\Q\)	None	✓	$1$	$1$	\(16\)	\(-119\)	\(-684\)	\(9149\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}-119q^{3}+2^{8}q^{4}-684q^{5}+\cdots\)
38.10.a.b	$38$	$10$	38.a	1.a	$1$	$1$	$1$	$19.571$	\(\Q\)	None	✓	$1$	$1$	\(16\)	\(102\)	\(-1581\)	\(-4865\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+102q^{3}+2^{8}q^{4}-1581q^{5}+\cdots\)
38.10.a.c	$38$	$10$	38.a	1.a	$1$	$3$	$3$	$19.571$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-48\)	\(3\)	\(486\)	\(-13317\)	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+(1+\beta _{1})q^{3}+2^{8}q^{4}+(162+\cdots)q^{5}+\cdots\)
38.10.a.d	$38$	$10$	38.a	1.a	$1$	$4$	$4$	$19.571$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-64\)	\(84\)	\(-1395\)	\(12307\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+(21+\beta _{1})q^{3}+2^{8}q^{4}+(-350+\cdots)q^{5}+\cdots\)
38.10.a.e	$38$	$10$	38.a	1.a	$1$	$4$	$4$	$19.571$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(64\)	\(226\)	\(866\)	\(2670\)	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+(57+\beta _{2})q^{3}+2^{8}q^{4}+(218+\cdots)q^{5}+\cdots\)
38.10.c.a	$38$	$10$	38.c	19.c	$3$	$14$	$7$	$19.571$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(112\)	\(165\)	\(909\)	\(3692\)		$2^{10}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{4}-2^{4}\beta _{2})q^{2}+(24-\beta _{1}-24\beta _{2}+\cdots)q^{3}+\cdots\)
38.10.c.b	$38$	$10$	38.c	19.c	$3$	$16$	$8$	$19.571$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-128\)	\(70\)	\(-341\)	\(3704\)		$2^{12}\cdot 3^{5}\cdot 19^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2^{4}+2^{4}\beta _{2})q^{2}+(9-\beta _{1}-9\beta _{2}+\cdots)q^{3}+\cdots\)
38.10.e.a	$38$	$10$	38.e	19.e	$9$	$42$	$7$	$19.571$		None		$2$	$0$	\(0\)	\(-252\)	\(0\)	\(14373\)			$\mathrm{SU}(2)[C_{9}]$