Newform search results

Results (36 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.2.c.a	$18$	$2$	18.c	9.c	$3$	$2$	$1$	$0.144$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-3\)	\(0\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
18.3.b.a	$18$	$3$	18.b	3.b	$2$	$2$	$2$	$0.490$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots\)
18.3.d.a	$18$	$3$	18.d	9.d	$6$	$4$	$2$	$0.490$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-18\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
18.4.a.a	$18$	$4$	18.a	1.a	$1$	$1$	$1$	$1.062$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-6\)	\(-16\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)
18.4.c.a	$18$	$4$	18.c	9.c	$3$	$2$	$1$	$1.062$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(9\)	\(31\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
18.4.c.b	$18$	$4$	18.c	9.c	$3$	$4$	$2$	$1.062$	\(\Q(\sqrt{-3}, \sqrt{-35})\)	None		$2$	$0$	\(4\)	\(3\)	\(9\)	\(-19\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots\)
18.5.d.a	$18$	$5$	18.d	9.d	$6$	$8$	$4$	$1.861$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(6\)	\(18\)	\(-26\)		$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(2+\beta _{1}-3\beta _{2}-\beta _{5})q^{3}+\cdots\)
18.6.a.a	$18$	$6$	18.a	1.a	$1$	$1$	$1$	$2.887$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(0\)	\(-96\)	\(-148\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-96q^{5}-148q^{7}+\cdots\)
18.6.a.b	$18$	$6$	18.a	1.a	$1$	$1$	$1$	$2.887$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(0\)	\(66\)	\(176\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+66q^{5}+176q^{7}+\cdots\)
18.6.a.c	$18$	$6$	18.a	1.a	$1$	$1$	$1$	$2.887$	\(\Q\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(96\)	\(-148\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+96q^{5}-148q^{7}+\cdots\)
18.6.c.a	$18$	$6$	18.c	9.c	$3$	$4$	$2$	$2.887$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(8\)	\(0\)	\(-54\)	\(74\)		$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\beta _{1}q^{2}+(-3+6\beta _{1}+\beta _{3})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots\)
18.6.c.b	$18$	$6$	18.c	9.c	$3$	$6$	$3$	$2.887$	6.0.\(\cdots\).3	None		$2$	$0$	\(-12\)	\(9\)	\(-54\)	\(-132\)		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-4\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
18.7.b.a	$18$	$7$	18.b	3.b	$2$	$2$	$2$	$4.141$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-968\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4\beta q^{2}-2^{5}q^{4}+123\beta q^{5}-22^{2}q^{7}+\cdots\)
18.7.d.a	$18$	$7$	18.d	9.d	$6$	$12$	$6$	$4.141$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-42\)	\(432\)	\(240\)		$2^{10}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(-6+4\beta _{1}+\beta _{2}-\beta _{3}+\beta _{7}+\cdots)q^{3}+\cdots\)
18.8.a.a	$18$	$8$	18.a	1.a	$1$	$1$	$1$	$5.623$	\(\Q\)	None	✓	$1$	$1$	\(-8\)	\(0\)	\(114\)	\(-1576\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+2^{6}q^{4}+114q^{5}-1576q^{7}+\cdots\)
18.8.a.b	$18$	$8$	18.a	1.a	$1$	$1$	$1$	$5.623$	\(\Q\)	None	✓	$1$	$0$	\(8\)	\(0\)	\(210\)	\(1016\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+2^{6}q^{4}+210q^{5}+1016q^{7}+\cdots\)
18.8.c.a	$18$	$8$	18.c	9.c	$3$	$6$	$3$	$5.623$	6.0.\(\cdots\).1	None		$2$	$0$	\(-24\)	\(-27\)	\(54\)	\(210\)		$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q-8\beta _{1}q^{2}+(-14+19\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
18.8.c.b	$18$	$8$	18.c	9.c	$3$	$8$	$4$	$5.623$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(32\)	\(-12\)	\(54\)	\(-44\)		$2^{4}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(8-8\beta _{1})q^{2}+(-7+11\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
18.9.b.a	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-7064\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+8\beta q^{2}-2^{7}q^{4}+165\beta q^{5}-3532q^{7}+\cdots\)
18.9.b.b	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3304\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+8\beta q^{2}-2^{7}q^{4}-645\beta q^{5}+1652q^{7}+\cdots\)
18.9.d.a	$18$	$9$	18.d	9.d	$6$	$16$	$8$	$7.333$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(126\)	\(-882\)	\(-1846\)		$2^{28}\cdot 3^{22}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}+(7+2\beta _{1}+\beta _{3}+\beta _{4})q^{3}+\cdots\)
18.10.a.a	$18$	$10$	18.a	1.a	$1$	$1$	$1$	$9.271$	\(\Q\)	None	✓	$1$	$0$	\(-16\)	\(0\)	\(-870\)	\(-952\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+2^{8}q^{4}-870q^{5}-952q^{7}+\cdots\)
18.10.a.b	$18$	$10$	18.a	1.a	$1$	$1$	$1$	$9.271$	\(\Q\)	None	✓	$1$	$1$	\(-16\)	\(0\)	\(-384\)	\(5852\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+2^{8}q^{4}-384q^{5}+5852q^{7}+\cdots\)
18.10.a.c	$18$	$10$	18.a	1.a	$1$	$1$	$1$	$9.271$	\(\Q\)	None	✓	$1$	$1$	\(16\)	\(0\)	\(-2694\)	\(-3544\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+2^{8}q^{4}-2694q^{5}-3544q^{7}+\cdots\)
18.10.a.d	$18$	$10$	18.a	1.a	$1$	$1$	$1$	$9.271$	\(\Q\)	None	✓	$1$	$0$	\(16\)	\(0\)	\(384\)	\(5852\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+2^{8}q^{4}+384q^{5}+5852q^{7}+\cdots\)
18.10.c.a	$18$	$10$	18.c	9.c	$3$	$8$	$4$	$9.271$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(64\)	\(-81\)	\(171\)	\(7135\)		$2^{6}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{4}-2^{4}\beta _{1})q^{2}+(-21+22\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
18.10.c.b	$18$	$10$	18.c	9.c	$3$	$10$	$5$	$9.271$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(-80\)	\(156\)	\(171\)	\(-6451\)		$2^{8}\cdot 3^{16}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-2^{4}\beta _{1}q^{2}+(29-3^{3}\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
18.11.b.a	$18$	$11$	18.b	3.b	$2$	$2$	$2$	$11.436$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(41272\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{4}\beta q^{2}-2^{9}q^{4}-1443\beta q^{5}+20636q^{7}+\cdots\)
18.11.d.a	$18$	$11$	18.d	9.d	$6$	$20$	$10$	$11.436$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(-84\)	\(-9918\)	\(12238\)		$2^{46}\cdot 3^{37}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-2-4\beta _{1}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
18.12.a.a	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	\(\Q\)	None	✓	$1$	$1$	\(-32\)	\(0\)	\(-3630\)	\(32936\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{5}q^{2}+2^{10}q^{4}-3630q^{5}+32936q^{7}+\cdots\)
18.12.a.b	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	\(\Q\)	None	✓	$1$	$0$	\(-32\)	\(0\)	\(5280\)	\(-49036\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{5}q^{2}+2^{10}q^{4}+5280q^{5}-49036q^{7}+\cdots\)
18.12.a.c	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	\(\Q\)	None	✓	$1$	$0$	\(32\)	\(0\)	\(-5766\)	\(72464\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{5}q^{2}+2^{10}q^{4}-5766q^{5}+72464q^{7}+\cdots\)
18.12.a.d	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	\(\Q\)	None	✓	$1$	$1$	\(32\)	\(0\)	\(-5280\)	\(-49036\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{5}q^{2}+2^{10}q^{4}-5280q^{5}-49036q^{7}+\cdots\)
18.12.a.e	$18$	$12$	18.a	1.a	$1$	$1$	$1$	$13.830$	\(\Q\)	None	✓	$1$	$0$	\(32\)	\(0\)	\(11730\)	\(-50008\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{5}q^{2}+2^{10}q^{4}+11730q^{5}-50008q^{7}+\cdots\)
18.12.c.a	$18$	$12$	18.c	9.c	$3$	$10$	$5$	$13.830$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-160\)	\(-243\)	\(4104\)	\(44528\)		$2^{12}\cdot 3^{21}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+2^{5}\beta _{1}q^{2}+(-55-62\beta _{1}+\beta _{5})q^{3}+\cdots\)
18.12.c.b	$18$	$12$	18.c	9.c	$3$	$12$	$6$	$13.830$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(192\)	\(0\)	\(4104\)	\(-61554\)		$2^{14}\cdot 3^{25}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-2^{5}\beta _{1}q^{2}+(-39-77\beta _{1}-\beta _{3})q^{3}+\cdots\)