Newform search results

Results (1-50 of 143 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
17.2.a.a	$17$	$2$	17.a	1.a	$1$	$1$	$1$	$0.136$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
17.2.d.a	$17$	$2$	17.d	17.d	$8$	$4$	$1$	$0.136$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(-4\)	\(-4\)	\(0\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
17.3.e.a	$17$	$3$	17.e	17.e	$16$	$8$	$1$	$0.463$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(-8\)	\(-8\)	\(16\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
17.3.e.b	$17$	$3$	17.e	17.e	$16$	$8$	$1$	$0.463$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(-24\)	\(-16\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
17.4.a.a	$17$	$4$	17.a	1.a	$1$	$1$	$1$	$1.003$	\(\Q\)	None	✓	$1$	$1$	\(-3\)	\(-8\)	\(6\)	\(-28\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots\)
17.4.a.b	$17$	$4$	17.a	1.a	$1$	$3$	$3$	$1.003$	3.3.2636.1	None	✓	$1$	$0$	\(1\)	\(4\)	\(-8\)	\(22\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
17.4.b.a	$17$	$4$	17.b	17.b	$2$	$4$	$4$	$1.003$	4.0.4669632.2	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots\)
17.4.c.a	$17$	$4$	17.c	17.c	$4$	$8$	$4$	$1.003$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(2\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{4}q^{3}+(-5-\beta _{2}+\cdots)q^{4}+\cdots\)
17.4.d.a	$17$	$4$	17.d	17.d	$8$	$12$	$3$	$1.003$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-4\)	\(-4\)	\(-20\)	\(-4\)		$2$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\beta _{3}-\beta _{10})q^{2}+\beta _{8}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
17.5.e.a	$17$	$5$	17.e	17.e	$16$	$40$	$5$	$1.757$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
17.6.a.a	$17$	$6$	17.a	1.a	$1$	$1$	$1$	$2.727$	\(\Q\)	None	✓	$1$	$1$	\(-6\)	\(10\)	\(-72\)	\(-196\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{2}+10q^{3}+4q^{4}-72q^{5}-60q^{6}+\cdots\)
17.6.a.b	$17$	$6$	17.a	1.a	$1$	$1$	$1$	$2.727$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-18\)	\(-16\)	\(28\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-18q^{3}-31q^{4}-2^{4}q^{5}-18q^{6}+\cdots\)
17.6.a.c	$17$	$6$	17.a	1.a	$1$	$4$	$4$	$2.727$	4.4.5416116.1	None	✓	$1$	$0$	\(3\)	\(28\)	\(80\)	\(284\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(7+\beta _{1}-\beta _{3})q^{3}+(18+\cdots)q^{4}+\cdots\)
17.6.b.a	$17$	$6$	17.b	17.b	$2$	$6$	$6$	$2.727$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{1}q^{3}+(14+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
17.6.c.a	$17$	$6$	17.c	17.c	$4$	$12$	$6$	$2.727$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-24\)	\(-40\)	\(-120\)		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{3}-\beta _{8})q^{3}+\cdots\)
17.6.d.a	$17$	$6$	17.d	17.d	$8$	$28$	$7$	$2.727$		None		$2$	$0$	\(-4\)	\(-4\)	\(40\)	\(-4\)			$\mathrm{SU}(2)[C_{8}]$
17.7.e.a	$17$	$7$	17.e	17.e	$16$	$64$	$8$	$3.911$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
17.8.a.a	$17$	$8$	17.a	1.a	$1$	$1$	$1$	$5.311$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(18\)	\(-10\)	\(-902\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+18q^{3}-124q^{4}-10q^{5}+\cdots\)
17.8.a.b	$17$	$8$	17.a	1.a	$1$	$3$	$3$	$5.311$	3.3.694349.1	None	✓	$1$	$1$	\(1\)	\(-86\)	\(-198\)	\(-1558\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(-28-\beta _{1}-2\beta _{2})q^{3}+(78+\cdots)q^{4}+\cdots\)
17.8.a.c	$17$	$8$	17.a	1.a	$1$	$6$	$6$	$5.311$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(15\)	\(40\)	\(-184\)	\(2064\)	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+(2+\beta _{1})q^{2}+(6+\beta _{1}+\beta _{4})q^{3}+(78+\cdots)q^{4}+\cdots\)
17.8.b.a	$17$	$8$	17.b	17.b	$2$	$10$	$10$	$5.311$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(-18\)	\(0\)	\(0\)	\(0\)		$2^{13}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\beta _{2})q^{2}+\beta _{1}q^{3}+(69-2\beta _{2}+\cdots)q^{4}+\cdots\)
17.8.c.a	$17$	$8$	17.c	17.c	$4$	$20$	$10$	$5.311$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(24\)	\(384\)	\(392\)		$2^{21}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(1-\beta _{6}+\beta _{8})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots\)
17.8.d.a	$17$	$8$	17.d	17.d	$8$	$36$	$9$	$5.311$		None		$2$	$0$	\(-4\)	\(-4\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{8}]$
17.9.e.a	$17$	$9$	17.e	17.e	$16$	$88$	$11$	$6.925$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
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	✓	$1$	$0$	\(-1\)	\(88\)	\(1362\)	\(9388\)	$-$	$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(12+2\beta _{1}-\beta _{4})q^{3}+(341+\cdots)q^{4}+\cdots\)
17.10.b.a	$17$	$10$	17.b	17.b	$2$	$12$	$12$	$8.756$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(30\)	\(0\)	\(0\)	\(0\)		$2^{17}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta _{2})q^{2}+\beta _{1}q^{3}+(154+4\beta _{2}+\cdots)q^{4}+\cdots\)
17.10.c.a	$17$	$10$	17.c	17.c	$4$	$24$	$12$	$8.756$		None		$2$	$0$	\(0\)	\(144\)	\(-1710\)	\(3810\)			$\mathrm{SU}(2)[C_{4}]$
17.10.d.a	$17$	$10$	17.d	17.d	$8$	$52$	$13$	$8.756$		None		$2$	$0$	\(-4\)	\(-4\)	\(-1140\)	\(-4\)			$\mathrm{SU}(2)[C_{8}]$
17.11.e.a	$17$	$11$	17.e	17.e	$16$	$112$	$14$	$10.801$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
17.12.a.a	$17$	$12$	17.a	1.a	$1$	$6$	$6$	$13.062$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-9\)	\(-476\)	\(-12884\)	\(-23436\)	$-$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(-79+\beta _{2})q^{3}+(767+\cdots)q^{4}+\cdots\)
17.12.a.b	$17$	$12$	17.a	1.a	$1$	$8$	$8$	$13.062$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(55\)	\(496\)	\(8592\)	\(95288\)	$+$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	\(q+(7-\beta _{1})q^{2}+(62-\beta _{1}+\beta _{3})q^{3}+(1344+\cdots)q^{4}+\cdots\)
17.12.b.a	$17$	$12$	17.b	17.b	$2$	$16$	$16$	$13.062$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2^{29}\cdot 3^{4}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1271+\beta _{3})q^{4}+\cdots\)
17.12.c.a	$17$	$12$	17.c	17.c	$4$	$32$	$16$	$13.062$		None		$2$	$0$	\(0\)	\(-528\)	\(-15496\)	\(-38368\)			$\mathrm{SU}(2)[C_{4}]$
17.12.d.a	$17$	$12$	17.d	17.d	$8$	$60$	$15$	$13.062$		None		$2$	$0$	\(-4\)	\(-4\)	\(10120\)	\(-4\)			$\mathrm{SU}(2)[C_{8}]$
17.13.e.a	$17$	$13$	17.e	17.e	$16$	$136$	$17$	$15.538$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
17.14.a.a	$17$	$14$	17.a	1.a	$1$	$8$	$8$	$18.229$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-65\)	\(-1328\)	\(15312\)	\(-699576\)	$+$	$2^{11}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(-8-\beta _{1})q^{2}+(-167+5\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
17.14.a.b	$17$	$14$	17.a	1.a	$1$	$10$	$10$	$18.229$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(63\)	\(1588\)	\(-25820\)	\(694532\)	$-$	$2^{18}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(6+\beta _{1})q^{2}+(158+3\beta _{1}-\beta _{3})q^{3}+\cdots\)
17.14.b.a	$17$	$14$	17.b	17.b	$2$	$18$	$18$	$18.229$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$2^{38}\cdot 3^{6}\cdot 17^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(2710+\beta _{3})q^{4}+\cdots\)
17.14.c.a	$17$	$14$	17.c	17.c	$4$	$36$	$18$	$18.229$		None		$2$	$0$	\(0\)	\(-264\)	\(73220\)	\(5040\)			$\mathrm{SU}(2)[C_{4}]$
17.14.d.a	$17$	$14$	17.d	17.d	$8$	$76$	$19$	$18.229$		None		$2$	$0$	\(-4\)	\(-4\)	\(-62720\)	\(-4\)			$\mathrm{SU}(2)[C_{8}]$
17.15.e.a	$17$	$15$	17.e	17.e	$16$	$160$	$20$	$21.136$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
17.16.a.a	$17$	$16$	17.a	1.a	$1$	$9$	$9$	$24.258$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-217\)	\(-3656\)	\(-222858\)	\(-8750084\)	$-$	$2^{21}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-24-\beta _{1})q^{2}+(-406-4\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
17.16.a.b	$17$	$16$	17.a	1.a	$1$	$11$	$11$	$24.258$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(39\)	\(5092\)	\(59416\)	\(1250446\)	$+$	$2^{20}\cdot 3^{7}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(4-\beta _{1})q^{2}+(462+3\beta _{1}-\beta _{2})q^{3}+\cdots\)
17.16.b.a	$17$	$16$	17.b	17.b	$2$	$22$	$22$	$24.258$		None		$2$	$0$	\(-258\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
17.16.c.a	$17$	$16$	17.c	17.c	$4$	$44$	$22$	$24.258$		None		$2$	$0$	\(0\)	\(5256\)	\(-252126\)	\(1854722\)			$\mathrm{SU}(2)[C_{4}]$
17.16.d.a	$17$	$16$	17.d	17.d	$8$	$84$	$21$	$24.258$		None		$2$	$0$	\(-4\)	\(-4\)	\(311340\)	\(-4\)			$\mathrm{SU}(2)[C_{8}]$
17.17.e.a	$17$	$17$	17.e	17.e	$16$	$184$	$23$	$27.595$		None		$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)			$\mathrm{SU}(2)[C_{16}]$
17.18.a.a	$17$	$18$	17.a	1.a	$1$	$10$	$10$	$31.148$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(15\)	\(-4760\)	\(61880\)	\(-19310368\)	$+$	$2^{19}\cdot 3^{9}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{2}+(-475-\beta _{1}+\beta _{3})q^{3}+\cdots\)
17.18.a.b	$17$	$18$	17.a	1.a	$1$	$12$	$12$	$31.148$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(527\)	\(21484\)	\(1770512\)	\(22379060\)	$-$	$2^{34}\cdot 3^{8}$	$\mathrm{SU}(2)$	\(q+(44-\beta _{1})q^{2}+(1790+2\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)