Newform search results

Results (1-50 of 21484 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.6.a.a	$3$	$6$	3.a	1.a	$1$	$1$	$1$	$0.481$	\(\Q\)	None	✓	$1$	$0$	\(-6\)	\(9\)	\(6\)	\(-40\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\)
5.5.c.a	$5$	$5$	5.c	5.c	$4$	$2$	$1$	$0.517$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(-12\)	\(40\)	\(-52\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{2}+(-6+6i)q^{3}-14iq^{4}+\cdots\)
6.5.b.a	$6$	$5$	6.b	3.b	$2$	$2$	$2$	$0.620$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(52\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-3-3\beta )q^{3}-8q^{4}+6\beta q^{5}+\cdots\)
2.8.a.a	$2$	$8$	2.a	1.a	$1$	$1$	$1$	$0.625$	\(\Q\)	None	✓	$1$	$0$	\(-8\)	\(12\)	\(-210\)	\(1016\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+12q^{3}+2^{6}q^{4}-210q^{5}+\cdots\)
4.6.a.a	$4$	$6$	4.a	1.a	$1$	$1$	$1$	$0.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-12\)	\(54\)	\(-88\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)
7.5.d.a	$7$	$5$	7.d	7.d	$6$	$4$	$2$	$0.724$	\(\Q(\sqrt{-3}, \sqrt{22})\)	None		$2$	$0$	\(-4\)	\(6\)	\(-30\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{1}-2\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
5.6.a.a	$5$	$6$	5.a	1.a	$1$	$1$	$1$	$0.802$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-4\)	\(25\)	\(192\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
5.6.b.a	$5$	$6$	5.b	5.b	$2$	$2$	$2$	$0.802$	\(\Q(\sqrt{-11}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-90\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+3\beta q^{3}-12q^{4}+(-45-5\beta )q^{5}+\cdots\)
8.5.d.b	$8$	$5$	8.d	8.d	$2$	$2$	$2$	$0.827$	\(\Q(\sqrt{-15}) \)	None		$2$	$0$	\(-2\)	\(12\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots\)
4.7.b.a	$4$	$7$	4.b	4.b	$2$	$2$	$2$	$0.920$	\(\Q(\sqrt{-15}) \)	None		$2$	$0$	\(4\)	\(0\)	\(20\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots\)
9.5.b.a	$9$	$5$	9.b	3.b	$2$	$2$	$2$	$0.930$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-56\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)
9.5.d.a	$9$	$5$	9.d	9.d	$6$	$6$	$3$	$0.930$	6.0.39400128.1	None		$2$	$0$	\(-3\)	\(-3\)	\(-12\)	\(12\)		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots\)
3.8.a.a	$3$	$8$	3.a	1.a	$1$	$1$	$1$	$0.937$	\(\Q\)	None	✓	$1$	$0$	\(6\)	\(-27\)	\(390\)	\(-64\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots\)
6.6.a.a	$6$	$6$	6.a	1.a	$1$	$1$	$1$	$0.962$	\(\Q\)	None	✓	$1$	$0$	\(4\)	\(-9\)	\(-66\)	\(176\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-9q^{3}+2^{4}q^{4}-66q^{5}-6^{2}q^{6}+\cdots\)
10.5.c.a	$10$	$5$	10.c	5.c	$4$	$2$	$1$	$1.034$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-4\)	\(18\)	\(-30\)	\(58\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2-2i)q^{2}+(9-9i)q^{3}+8iq^{4}+\cdots\)
10.5.c.b	$10$	$5$	10.c	5.c	$4$	$2$	$1$	$1.034$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(4\)	\(2\)	\(-30\)	\(-38\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2+2i)q^{2}+(1-i)q^{3}+8iq^{4}+(-15+\cdots)q^{5}+\cdots\)
7.6.a.a	$7$	$6$	7.a	1.a	$1$	$1$	$1$	$1.123$	\(\Q\)	None	✓	$1$	$1$	\(-10\)	\(-14\)	\(-56\)	\(-49\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-10q^{2}-14q^{3}+68q^{4}-56q^{5}+\cdots\)
7.6.a.b	$7$	$6$	7.a	1.a	$1$	$2$	$2$	$1.123$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$0$	\(9\)	\(-6\)	\(-18\)	\(98\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(5-\beta )q^{2}+(-6+6\beta )q^{3}+(7-9\beta )q^{4}+\cdots\)
7.6.c.a	$7$	$6$	7.c	7.c	$3$	$4$	$2$	$1.123$	\(\Q(\sqrt{-3}, \sqrt{37})\)	None		$2$	$0$	\(-2\)	\(8\)	\(38\)	\(-168\)		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
11.5.b.b	$11$	$5$	11.b	11.b	$2$	$2$	$2$	$1.137$	\(\Q(\sqrt{-30}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(62\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-3q^{3}-14q^{4}+31q^{5}-3\beta q^{6}+\cdots\)
11.5.d.a	$11$	$5$	11.d	11.d	$10$	$12$	$3$	$1.137$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-5\)	\(-6\)	\(-18\)	\(-80\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1-\beta _{2}-2\beta _{3}-\beta _{4}+\beta _{7})q^{2}+\cdots\)
5.7.c.a	$5$	$7$	5.c	5.c	$4$	$4$	$2$	$1.150$	\(\Q(i, \sqrt{201})\)	None		$2$	$0$	\(-10\)	\(30\)	\(-70\)	\(550\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
12.5.d.a	$12$	$5$	12.d	4.b	$2$	$4$	$4$	$1.240$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(6\)	\(0\)	\(24\)	\(0\)		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots\)
8.6.a.a	$8$	$6$	8.a	1.a	$1$	$1$	$1$	$1.283$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(20\)	\(-74\)	\(-24\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)
8.6.b.a	$8$	$6$	8.b	8.b	$2$	$4$	$4$	$1.283$	4.0.218489.1	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(96\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)
13.5.d.a	$13$	$5$	13.d	13.d	$4$	$6$	$3$	$1.344$	6.0.\(\cdots\).1	None		$2$	$0$	\(-2\)	\(-4\)	\(-14\)	\(48\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
13.5.f.a	$13$	$5$	13.f	13.f	$12$	$16$	$4$	$1.344$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-4\)	\(-2\)	\(8\)	\(56\)		$2^{4}\cdot 3^{2}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{12}q^{2}+(-1-\beta _{8}+\beta _{9}+\beta _{12}+\cdots)q^{3}+\cdots\)
6.7.b.a	$6$	$7$	6.b	3.b	$2$	$2$	$2$	$1.380$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(42\)	\(0\)	\(4\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(21+3\beta )q^{3}-2^{5}q^{4}-30\beta q^{5}+\cdots\)
9.6.a.a	$9$	$6$	9.a	1.a	$1$	$1$	$1$	$1.443$	\(\Q\)	None	✓	$1$	$0$	\(6\)	\(0\)	\(-6\)	\(-40\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots\)
9.6.c.a	$9$	$6$	9.c	9.c	$3$	$8$	$4$	$1.443$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(3\)	\(-12\)	\(78\)	\(28\)		$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)
14.5.b.a	$14$	$5$	14.b	7.b	$2$	$4$	$4$	$1.447$	4.0.1308672.3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-76\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
14.5.d.a	$14$	$5$	14.d	7.d	$6$	$4$	$2$	$1.447$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(-18\)	\(54\)	\(-28\)		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-6+2\beta _{1}-3\beta _{2}-2\beta _{3})q^{3}+\cdots\)
15.5.c.a	$15$	$5$	15.c	3.b	$2$	$6$	$6$	$1.551$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(76\)		$3\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
15.5.d.c	$15$	$5$	15.d	15.d	$2$	$4$	$4$	$1.551$	\(\Q(\sqrt{10}, \sqrt{-26})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)
15.5.f.a	$15$	$5$	15.f	5.c	$4$	$8$	$4$	$1.551$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-84\)	\(20\)		$3^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
5.8.a.a	$5$	$8$	5.a	1.a	$1$	$1$	$1$	$1.562$	\(\Q\)	None	✓	$1$	$1$	\(-14\)	\(-48\)	\(125\)	\(-1644\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots\)
5.8.a.b	$5$	$8$	5.a	1.a	$1$	$2$	$2$	$1.562$	\(\Q(\sqrt{19}) \)	None	✓	$1$	$0$	\(20\)	\(20\)	\(-250\)	\(-100\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots\)
5.8.b.a	$5$	$8$	5.b	5.b	$2$	$2$	$2$	$1.562$	\(\Q(\sqrt{-29}) \)	None		$2$	$0$	\(0\)	\(0\)	\(150\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots\)
10.6.a.a	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(-26\)	\(-25\)	\(-22\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-26q^{3}+2^{4}q^{4}-5^{2}q^{5}+104q^{6}+\cdots\)
10.6.a.b	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(24\)	\(25\)	\(-172\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+24q^{3}+2^{4}q^{4}+5^{2}q^{5}-96q^{6}+\cdots\)
10.6.a.c	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	\(\Q\)	None	✓	$1$	$0$	\(4\)	\(6\)	\(-25\)	\(-118\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+6q^{3}+2^{4}q^{4}-5^{2}q^{5}+24q^{6}+\cdots\)
10.6.b.a	$10$	$6$	10.b	5.b	$2$	$2$	$2$	$1.604$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(110\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+7iq^{3}-2^{4}q^{4}+(55+5i)q^{5}+\cdots\)
7.7.b.b	$7$	$7$	7.b	7.b	$2$	$2$	$2$	$1.610$	\(\Q(\sqrt{-510}) \)	None		$2$	$0$	\(-16\)	\(0\)	\(0\)	\(266\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-8q^{2}+\beta q^{3}-\beta q^{5}-8\beta q^{6}+(133+\cdots)q^{7}+\cdots\)
7.7.d.a	$7$	$7$	7.d	7.d	$6$	$2$	$1$	$1.610$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(12\)	\(-21\)	\(315\)	\(-686\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+12\zeta_{6}q^{2}+(-7-7\zeta_{6})q^{3}+(-80+\cdots)q^{4}+\cdots\)
7.7.d.b	$7$	$7$	7.d	7.d	$6$	$4$	$2$	$1.610$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(-8\)	\(18\)	\(-150\)	\(280\)		$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-4-4\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(6+3\beta _{1}+\cdots)q^{3}+\cdots\)
16.5.c.a	$16$	$5$	16.c	4.b	$2$	$2$	$2$	$1.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(36\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}+18q^{5}+2\zeta_{6}q^{7}-111q^{9}+\cdots\)
16.5.f.a	$16$	$5$	16.f	16.f	$4$	$14$	$7$	$1.654$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)		$2^{21}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+2\beta _{3}-\beta _{11}+\cdots)q^{4}+\cdots\)
17.5.e.a	$17$	$5$	17.e	17.e	$16$	$40$	$5$	$1.757$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
11.6.a.a	$11$	$6$	11.a	1.a	$1$	$1$	$1$	$1.764$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(-15\)	\(-19\)	\(10\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-15q^{3}-2^{4}q^{4}-19q^{5}+60q^{6}+\cdots\)
11.6.a.b	$11$	$6$	11.a	1.a	$1$	$3$	$3$	$1.764$	3.3.54492.1	None	✓	$1$	$0$	\(0\)	\(34\)	\(24\)	\(84\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)