Newform search results

Results (1-50 of 3473 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2.10.a.a	$2$	$10$	2.a	1.a	$1$	$1$	$1$	$1.030$	\(\Q\)	None	✓	$1$	$0$	\(16\)	\(-156\)	\(870\)	\(-952\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots\)
3.10.a.a	$3$	$10$	3.a	1.a	$1$	$1$	$1$	$1.545$	\(\Q\)	None	✓	$1$	$1$	\(-36\)	\(-81\)	\(-1314\)	\(-4480\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-6^{2}q^{2}-3^{4}q^{3}+28^{2}q^{4}-1314q^{5}+\cdots\)
3.10.a.b	$3$	$10$	3.a	1.a	$1$	$1$	$1$	$1.545$	\(\Q\)	None	✓	$1$	$0$	\(18\)	\(81\)	\(-1530\)	\(9128\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots\)
4.10.a.a	$4$	$10$	4.a	1.a	$1$	$1$	$1$	$2.060$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(228\)	\(-666\)	\(-6328\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots\)
5.10.a.a	$5$	$10$	5.a	1.a	$1$	$1$	$1$	$2.575$	\(\Q\)	None	✓	$1$	$1$	\(-8\)	\(-114\)	\(-625\)	\(4242\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots\)
5.10.a.b	$5$	$10$	5.a	1.a	$1$	$2$	$2$	$2.575$	\(\Q(\sqrt{1009}) \)	None	✓	$1$	$0$	\(-10\)	\(260\)	\(1250\)	\(1700\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)
5.10.b.a	$5$	$10$	5.b	5.b	$2$	$4$	$4$	$2.575$	4.0.49740556.1	None		$2$	$0$	\(0\)	\(0\)	\(1140\)	\(0\)		$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-342+\cdots)q^{4}+\cdots\)
6.10.a.a	$6$	$10$	6.a	1.a	$1$	$1$	$1$	$3.090$	\(\Q\)	None	✓	$1$	$0$	\(-16\)	\(81\)	\(2694\)	\(-3544\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+2694q^{5}+\cdots\)
7.10.a.a	$7$	$10$	7.a	1.a	$1$	$2$	$2$	$3.605$	\(\Q(\sqrt{193}) \)	None	✓	$1$	$1$	\(-6\)	\(-86\)	\(-2238\)	\(-4802\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-3-\beta )q^{2}+(-43+11\beta )q^{3}+(-310+\cdots)q^{4}+\cdots\)
7.10.a.b	$7$	$10$	7.a	1.a	$1$	$3$	$3$	$3.605$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(21\)	\(84\)	\(1554\)	\(7203\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(7-\beta _{2})q^{2}+(28-\beta _{1}-\beta _{2})q^{3}+(519+\cdots)q^{4}+\cdots\)
7.10.c.a	$7$	$10$	7.c	7.c	$3$	$10$	$5$	$3.605$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-18\)	\(161\)	\(1533\)	\(-1036\)		$2^{12}\cdot 3^{3}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots\)
8.10.a.a	$8$	$10$	8.a	1.a	$1$	$1$	$1$	$4.120$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-60\)	\(-2074\)	\(-4344\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots\)
8.10.a.b	$8$	$10$	8.a	1.a	$1$	$1$	$1$	$4.120$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(68\)	\(1510\)	\(10248\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots\)
8.10.b.a	$8$	$10$	8.b	8.b	$2$	$8$	$8$	$4.120$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(-18\)	\(0\)	\(0\)	\(4800\)		$2^{28}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots\)
9.10.a.a	$9$	$10$	9.a	1.a	$1$	$1$	$1$	$4.635$	\(\Q\)	None	✓	$1$	$0$	\(-18\)	\(0\)	\(1530\)	\(9128\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-18q^{2}-188q^{4}+1530q^{5}+9128q^{7}+\cdots\)
9.10.a.b	$9$	$10$	9.a	1.a	$1$	$1$	$1$	$4.635$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-12580\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2^{9}q^{4}-12580q^{7}+118370q^{13}+\cdots\)
9.10.a.c	$9$	$10$	9.a	1.a	$1$	$1$	$1$	$4.635$	\(\Q\)	None	✓	$1$	$0$	\(36\)	\(0\)	\(1314\)	\(-4480\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+6^{2}q^{2}+28^{2}q^{4}+1314q^{5}-4480q^{7}+\cdots\)
9.10.c.a	$9$	$10$	9.c	9.c	$3$	$16$	$8$	$4.635$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(15\)	\(-3\)	\(453\)	\(-343\)		$2^{14}\cdot 3^{28}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+\beta _{2}-2\beta _{3})q^{2}+(9-18\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
10.10.a.a	$10$	$10$	10.a	1.a	$1$	$1$	$1$	$5.150$	\(\Q\)	None	✓	$1$	$0$	\(-16\)	\(-204\)	\(625\)	\(5432\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}-204q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
10.10.a.b	$10$	$10$	10.a	1.a	$1$	$1$	$1$	$5.150$	\(\Q\)	None	✓	$1$	$1$	\(-16\)	\(46\)	\(-625\)	\(-10318\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+46q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
10.10.a.c	$10$	$10$	10.a	1.a	$1$	$1$	$1$	$5.150$	\(\Q\)	None	✓	$1$	$0$	\(16\)	\(174\)	\(-625\)	\(4658\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+174q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
10.10.b.a	$10$	$10$	10.b	5.b	$2$	$4$	$4$	$5.150$	\(\Q(i, \sqrt{319})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2580\)	\(0\)		$2^{10}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-5\beta _{1}-\beta _{3})q^{3}-2^{8}q^{4}+\cdots\)
11.10.a.a	$11$	$10$	11.a	1.a	$1$	$3$	$3$	$5.665$	3.3.2659452.1	None	✓	$1$	$1$	\(0\)	\(-186\)	\(-1824\)	\(-7260\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-62+4\beta _{1}-\beta _{2})q^{3}+(304+\cdots)q^{4}+\cdots\)
11.10.a.b	$11$	$10$	11.a	1.a	$1$	$5$	$5$	$5.665$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(16\)	\(112\)	\(1594\)	\(8400\)	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{2}+(22+3\beta _{1}+\beta _{4})q^{3}+\cdots\)
11.10.c.a	$11$	$10$	11.c	11.c	$5$	$32$	$8$	$5.665$		None		$2$	$0$	\(-21\)	\(69\)	\(225\)	\(-10675\)			$\mathrm{SU}(2)[C_{5}]$
12.10.a.a	$12$	$10$	12.a	1.a	$1$	$1$	$1$	$6.180$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-81\)	\(990\)	\(8576\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{4}q^{3}+990q^{5}+8576q^{7}+3^{8}q^{9}+\cdots\)
12.10.b.a	$12$	$10$	12.b	12.b	$2$	$16$	$16$	$6.180$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{68}\cdot 3^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{4}q^{3}+(-21-\beta _{1})q^{4}+\cdots\)
13.10.a.a	$13$	$10$	13.a	1.a	$1$	$4$	$4$	$6.695$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(-33\)	\(-163\)	\(471\)	\(-11241\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-8-\beta _{1})q^{2}+(-41+2\beta _{1}-\beta _{3})q^{3}+\cdots\)
13.10.a.b	$13$	$10$	13.a	1.a	$1$	$5$	$5$	$6.695$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(15\)	\(161\)	\(1803\)	\(10099\)	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{2}+(2^{5}+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
13.10.b.a	$13$	$10$	13.b	13.b	$2$	$10$	$10$	$6.695$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$2^{7}\cdot 3^{4}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{8}+\beta _{2})q^{4}+\cdots\)
13.10.c.a	$13$	$10$	13.c	13.c	$3$	$18$	$9$	$6.695$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(15\)	\(161\)	\(-2280\)	\(-1939\)		$2^{16}\cdot 3^{3}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2\beta _{2}-\beta _{3})q^{2}+(-18\beta _{2}-\beta _{6}+\cdots)q^{3}+\cdots\)
13.10.e.a	$13$	$10$	13.e	13.e	$6$	$20$	$10$	$6.695$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-3\)	\(-163\)	\(0\)	\(1023\)		$2^{22}\cdot 3^{10}\cdot 13^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(2^{4}\beta _{5}-\beta _{6})q^{3}+(2^{8}+\cdots)q^{4}+\cdots\)
14.10.a.a	$14$	$10$	14.a	1.a	$1$	$1$	$1$	$7.211$	\(\Q\)	None	✓	$1$	$1$	\(-16\)	\(-6\)	\(560\)	\(-2401\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}-6q^{3}+2^{8}q^{4}+560q^{5}+\cdots\)
14.10.a.b	$14$	$10$	14.a	1.a	$1$	$1$	$1$	$7.211$	\(\Q\)	None	✓	$1$	$0$	\(16\)	\(170\)	\(544\)	\(-2401\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+170q^{3}+2^{8}q^{4}+544q^{5}+\cdots\)
14.10.a.c	$14$	$10$	14.a	1.a	$1$	$2$	$2$	$7.211$	\(\Q(\sqrt{2305}) \)	None	✓	$1$	$0$	\(-32\)	\(-14\)	\(-2730\)	\(4802\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+(-7-5\beta )q^{3}+2^{8}q^{4}+(-1365+\cdots)q^{5}+\cdots\)
14.10.c.a	$14$	$10$	14.c	7.c	$3$	$6$	$3$	$7.211$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(-48\)	\(-233\)	\(-733\)	\(5012\)		$2^{6}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2^{4}-2^{4}\beta _{2})q^{2}+(78\beta _{2}-\beta _{3})q^{3}+\cdots\)
14.10.c.b	$14$	$10$	14.c	7.c	$3$	$6$	$3$	$7.211$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(48\)	\(71\)	\(-1085\)	\(-6796\)		$2^{6}\cdot 7$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{4}+2^{4}\beta _{1})q^{2}+(-24\beta _{1}-\beta _{3})q^{3}+\cdots\)
15.10.a.a	$15$	$10$	15.a	1.a	$1$	$1$	$1$	$7.726$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(81\)	\(625\)	\(-7680\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+3^{4}q^{3}-496q^{4}+5^{4}q^{5}+\cdots\)
15.10.a.b	$15$	$10$	15.a	1.a	$1$	$1$	$1$	$7.726$	\(\Q\)	None	✓	$1$	$1$	\(22\)	\(-81\)	\(-625\)	\(-5988\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+22q^{2}-3^{4}q^{3}-28q^{4}-5^{4}q^{5}+\cdots\)
15.10.a.c	$15$	$10$	15.a	1.a	$1$	$2$	$2$	$7.726$	\(\Q(\sqrt{4729}) \)	None	✓	$1$	$0$	\(19\)	\(162\)	\(-1250\)	\(-11872\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(10-\beta )q^{2}+3^{4}q^{3}+(770-19\beta )q^{4}+\cdots\)
15.10.a.d	$15$	$10$	15.a	1.a	$1$	$2$	$2$	$7.726$	\(\Q(\sqrt{241}) \)	None	✓	$1$	$0$	\(31\)	\(-162\)	\(1250\)	\(14112\)	$-$	$3$	$\mathrm{SU}(2)$	\(q+(15-\beta )q^{2}-3^{4}q^{3}+(255-31\beta )q^{4}+\cdots\)
15.10.b.a	$15$	$10$	15.b	5.b	$2$	$8$	$8$	$7.726$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-690\)	\(0\)		$2^{3}\cdot 3^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{4}q^{3}+(-149-\beta _{1})q^{4}+\cdots\)
15.10.e.a	$15$	$10$	15.e	15.e	$4$	$32$	$16$	$7.726$		None		$4$	$0$	\(0\)	\(-150\)	\(0\)	\(-9760\)			$\mathrm{SU}(2)[C_{4}]$
16.10.a.a	$16$	$10$	16.a	1.a	$1$	$1$	$1$	$8.241$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-228\)	\(-666\)	\(6328\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-228q^{3}-666q^{5}+6328q^{7}+32301q^{9}+\cdots\)
16.10.a.b	$16$	$10$	16.a	1.a	$1$	$1$	$1$	$8.241$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-68\)	\(1510\)	\(-10248\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-68q^{3}+1510q^{5}-10248q^{7}-15059q^{9}+\cdots\)
16.10.a.c	$16$	$10$	16.a	1.a	$1$	$1$	$1$	$8.241$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(60\)	\(-2074\)	\(4344\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+60q^{3}-2074q^{5}+4344q^{7}-16083q^{9}+\cdots\)
16.10.a.d	$16$	$10$	16.a	1.a	$1$	$1$	$1$	$8.241$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(156\)	\(870\)	\(952\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+156q^{3}+870q^{5}+952q^{7}+4653q^{9}+\cdots\)
16.10.e.a	$16$	$10$	16.e	16.e	$4$	$34$	$17$	$8.241$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
17.10.a.a	$17$	$10$	17.a	1.a	$1$	$5$	$5$	$8.756$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(-33\)	\(-236\)	\(1480\)	\(-13202\)	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-7+\beta _{1})q^{2}+(-48+2\beta _{1}+\beta _{4})q^{3}+\cdots\)
17.10.a.b	$17$	$10$	17.a	1.a	$1$	$7$	$7$	$8.756$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(88\)	\(1362\)	\(9388\)	$-$	$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(12+2\beta _{1}-\beta _{4})q^{3}+(341+\cdots)q^{4}+\cdots\)