Newform search results

Results (29 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.2.a.a	$11$	$2$	11.a	1.a	$1$	$1$	$1$	$0.088$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(-1\)	\(1\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
11.3.b.a	$11$	$3$	11.b	11.b	$2$	$1$	$1$	$0.300$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-5\)	\(-1\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots\)
11.3.d.a	$11$	$3$	11.d	11.d	$10$	$4$	$1$	$0.300$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-5\)	\(0\)	\(-4\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)
11.4.a.a	$11$	$4$	11.a	1.a	$1$	$2$	$2$	$0.649$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(-2\)	\(2\)	\(20\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots\)
11.4.c.a	$11$	$4$	11.c	11.c	$5$	$8$	$2$	$0.649$	8.0.\(\cdots\).1	None		$2$	$0$	\(-7\)	\(-3\)	\(-7\)	\(-35\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
11.5.b.a	$11$	$5$	11.b	11.b	$2$	$1$	$1$	$1.137$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(7\)	\(-49\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+7q^{3}+2^{4}q^{4}-7^{2}q^{5}-2^{5}q^{9}+11^{2}q^{11}+\cdots\)
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		$2$	$0$	\(-5\)	\(-6\)	\(-18\)	\(-80\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1-\beta _{2}-2\beta _{3}-\beta _{4}+\beta _{7})q^{2}+\cdots\)
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	✓	$1$	$0$	\(0\)	\(34\)	\(24\)	\(84\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)
11.6.c.a	$11$	$6$	11.c	11.c	$5$	$16$	$4$	$1.764$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-1\)	\(-24\)	\(-10\)	\(196\)		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{7})q^{2}+\cdots\)
11.7.b.a	$11$	$7$	11.b	11.b	$2$	$1$	$1$	$2.531$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(10\)	\(74\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+10q^{3}+2^{6}q^{4}+74q^{5}-629q^{9}+\cdots\)
11.7.b.b	$11$	$7$	11.b	11.b	$2$	$4$	$4$	$2.531$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(24\)	\(-260\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(6-\beta _{2})q^{3}+(-71+\beta _{2}+\cdots)q^{4}+\cdots\)
11.7.d.a	$11$	$7$	11.d	11.d	$10$	$20$	$5$	$2.531$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-5\)	\(-39\)	\(181\)	\(-365\)		$2^{4}\cdot 5\cdot 11^{2}$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\beta _{4}+\beta _{6}-\beta _{9})q^{2}+(3\beta _{4}+2\beta _{5}+\cdots)q^{3}+\cdots\)
11.8.a.a	$11$	$8$	11.a	1.a	$1$	$2$	$2$	$3.436$	\(\Q(\sqrt{15}) \)	None	✓	$1$	$1$	\(-8\)	\(-6\)	\(-470\)	\(-1228\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-4+\beta )q^{2}+(-3-6\beta )q^{3}+(-52+\cdots)q^{4}+\cdots\)
11.8.a.b	$11$	$8$	11.a	1.a	$1$	$4$	$4$	$3.436$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-35\)	\(537\)	\(170\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(-9-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
11.8.c.a	$11$	$8$	11.c	11.c	$5$	$24$	$6$	$3.436$		None		$2$	$0$	\(3\)	\(36\)	\(-72\)	\(68\)			$\mathrm{SU}(2)[C_{5}]$
11.9.b.a	$11$	$9$	11.b	11.b	$2$	$1$	$1$	$4.481$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-113\)	\(1151\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-113q^{3}+2^{8}q^{4}+1151q^{5}+6208q^{9}+\cdots\)
11.9.b.b	$11$	$9$	11.b	11.b	$2$	$6$	$6$	$4.481$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(-36\)	\(-448\)	\(0\)		$2^{7}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-6-\beta _{4})q^{3}+(-203+3\beta _{3}+\cdots)q^{4}+\cdots\)
11.9.d.a	$11$	$9$	11.d	11.d	$10$	$28$	$7$	$4.481$		None		$2$	$0$	\(-5\)	\(144\)	\(-708\)	\(5470\)			$\mathrm{SU}(2)[C_{10}]$
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		$2$	$0$	\(-21\)	\(69\)	\(225\)	\(-10675\)			$\mathrm{SU}(2)[C_{5}]$
11.11.b.a	$11$	$11$	11.b	11.b	$2$	$1$	$1$	$6.989$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(475\)	\(-3001\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+475q^{3}+2^{10}q^{4}-3001q^{5}+166576q^{9}+\cdots\)
11.11.b.b	$11$	$11$	11.b	11.b	$2$	$8$	$8$	$6.989$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-402\)	\(2430\)	\(0\)		$2^{8}\cdot 3^{3}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-50+\beta _{2})q^{3}+(-22^{2}+\cdots)q^{4}+\cdots\)
11.11.d.a	$11$	$11$	11.d	11.d	$10$	$36$	$9$	$6.989$		None		$2$	$0$	\(-5\)	\(-78\)	\(566\)	\(-9740\)			$\mathrm{SU}(2)[C_{10}]$
11.12.a.a	$11$	$12$	11.a	1.a	$1$	$3$	$3$	$8.452$	3.3.202533.1	None	✓	$1$	$1$	\(0\)	\(-393\)	\(-7305\)	\(-5082\)	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-131-2\beta _{1}-4\beta _{2})q^{3}+\cdots\)
11.12.a.b	$11$	$12$	11.a	1.a	$1$	$5$	$5$	$8.452$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(32\)	\(160\)	\(-8398\)	\(79040\)	$+$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots\)
11.12.c.a	$11$	$12$	11.c	11.c	$5$	$40$	$10$	$8.452$		None		$2$	$0$	\(11\)	\(-276\)	\(6038\)	\(55440\)			$\mathrm{SU}(2)[C_{5}]$