Newform search results

Results (1-50 of 151 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.3.c.a	$12$	$3$	12.c	3.b	$2$	$1$	$1$	$0.327$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(2\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots\)
12.3.d.a	$12$	$3$	12.d	4.b	$2$	$2$	$2$	$0.327$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
12.4.a.a	$12$	$4$	12.a	1.a	$1$	$1$	$1$	$0.708$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-18\)	\(8\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
12.4.b.a	$12$	$4$	12.b	12.b	$2$	$4$	$4$	$0.708$	\(\Q(\sqrt{3}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
12.5.c.a	$12$	$5$	12.c	3.b	$2$	$1$	$1$	$1.240$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(9\)	\(0\)	\(-94\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\)
12.5.d.a	$12$	$5$	12.d	4.b	$2$	$4$	$4$	$1.240$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(6\)	\(0\)	\(24\)	\(0\)		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots\)
12.6.b.a	$12$	$6$	12.b	12.b	$2$	$8$	$8$	$1.925$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{18}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(1-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
12.7.c.a	$12$	$7$	12.c	3.b	$2$	$2$	$2$	$2.761$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(484\)		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3+\beta )q^{3}+6\beta q^{5}+242q^{7}+(-711+\cdots)q^{9}+\cdots\)
12.7.d.a	$12$	$7$	12.d	4.b	$2$	$6$	$6$	$2.761$	6.0.50898483.1	None		$2$	$0$	\(-10\)	\(0\)	\(-44\)	\(0\)		$2^{12}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2-\beta _{1})q^{2}-\beta _{2}q^{3}+(3^{3}+2\beta _{1}+\cdots)q^{4}+\cdots\)
12.8.a.a	$12$	$8$	12.a	1.a	$1$	$1$	$1$	$3.749$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-27\)	\(-378\)	\(-832\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}-378q^{5}-832q^{7}+3^{6}q^{9}+\cdots\)
12.8.a.b	$12$	$8$	12.a	1.a	$1$	$1$	$1$	$3.749$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(27\)	\(270\)	\(1112\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}+270q^{5}+1112q^{7}+3^{6}q^{9}+\cdots\)
12.8.b.a	$12$	$8$	12.b	12.b	$2$	$4$	$4$	$3.749$	\(\Q(\sqrt{3}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-3\beta _{2}+3\beta _{3})q^{3}+(88+4\beta _{1}+\cdots)q^{4}+\cdots\)
12.8.b.b	$12$	$8$	12.b	12.b	$2$	$8$	$8$	$3.749$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{20}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-41+\beta _{2}+\cdots)q^{4}+\cdots\)
12.9.c.a	$12$	$9$	12.c	3.b	$2$	$1$	$1$	$4.889$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(81\)	\(0\)	\(4034\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{4}q^{3}+4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots\)
12.9.c.b	$12$	$9$	12.c	3.b	$2$	$2$	$2$	$4.889$	\(\Q(\sqrt{-110}) \)	None		$2$	$0$	\(0\)	\(-102\)	\(0\)	\(-6188\)		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-51+\beta )q^{3}-18\beta q^{5}-3094q^{7}+\cdots\)
12.9.d.a	$12$	$9$	12.d	4.b	$2$	$8$	$8$	$4.889$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(6\)	\(0\)	\(-336\)	\(0\)		$2^{22}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots\)
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		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{68}\cdot 3^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{4}q^{3}+(-21-\beta _{1})q^{4}+\cdots\)
12.11.c.a	$12$	$11$	12.c	3.b	$2$	$1$	$1$	$7.624$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-243\)	\(0\)	\(22082\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{5}q^{3}+22082q^{7}+3^{10}q^{9}+702218q^{13}+\cdots\)
12.11.c.b	$12$	$11$	12.c	3.b	$2$	$2$	$2$	$7.624$	\(\Q(\sqrt{-35}) \)	None		$2$	$0$	\(0\)	\(234\)	\(0\)	\(-20636\)		$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(117+\beta )q^{3}+6\beta q^{5}-10318q^{7}+\cdots\)
12.11.d.a	$12$	$11$	12.d	4.b	$2$	$10$	$10$	$7.624$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(22\)	\(0\)	\(3116\)	\(0\)		$2^{39}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\beta _{2})q^{2}+\beta _{1}q^{3}+(-65-2\beta _{1}+\cdots)q^{4}+\cdots\)
12.12.a.a	$12$	$12$	12.a	1.a	$1$	$1$	$1$	$9.220$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-243\)	\(9990\)	\(-86128\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{5}q^{3}+9990q^{5}-86128q^{7}+3^{10}q^{9}+\cdots\)
12.12.a.b	$12$	$12$	12.a	1.a	$1$	$1$	$1$	$9.220$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(243\)	\(2862\)	\(9128\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{5}q^{3}+2862q^{5}+9128q^{7}+3^{10}q^{9}+\cdots\)
12.12.b.a	$12$	$12$	12.b	12.b	$2$	$20$	$20$	$9.220$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{104}\cdot 3^{42}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(99+\beta _{2})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots\)
12.13.c.a	$12$	$13$	12.c	3.b	$2$	$4$	$4$	$10.968$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(300\)	\(0\)	\(15800\)		$2^{10}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(75+\beta _{1})q^{3}+(-3\beta _{1}+\beta _{2})q^{5}+(3950+\cdots)q^{7}+\cdots\)
12.13.d.a	$12$	$13$	12.d	4.b	$2$	$12$	$12$	$10.968$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-90\)	\(0\)	\(-10296\)	\(0\)		$2^{57}\cdot 3^{25}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-8+\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-386+\cdots)q^{4}+\cdots\)
12.14.a.a	$12$	$14$	12.a	1.a	$1$	$1$	$1$	$12.868$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-729\)	\(-14850\)	\(-62896\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{6}q^{3}-14850q^{5}-62896q^{7}+\cdots\)
12.14.a.b	$12$	$14$	12.a	1.a	$1$	$1$	$1$	$12.868$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(729\)	\(-24570\)	\(-173704\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{6}q^{3}-24570q^{5}-173704q^{7}+\cdots\)
12.14.b.a	$12$	$14$	12.b	12.b	$2$	$24$	$24$	$12.868$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
12.15.c.a	$12$	$15$	12.c	3.b	$2$	$1$	$1$	$14.919$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-2187\)	\(0\)	\(-1389022\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{7}q^{3}-1389022q^{7}+3^{14}q^{9}+\cdots\)
12.15.c.b	$12$	$15$	12.c	3.b	$2$	$4$	$4$	$14.919$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(2148\)	\(0\)	\(1709288\)		$2^{14}\cdot 3^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(537-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(427322+\cdots)q^{7}+\cdots\)
12.15.d.a	$12$	$15$	12.d	4.b	$2$	$14$	$14$	$14.919$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(182\)	\(0\)	\(-16124\)	\(0\)		$2^{81}\cdot 3^{41}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(13-\beta _{1})q^{2}+\beta _{2}q^{3}+(665-13\beta _{1}+\cdots)q^{4}+\cdots\)
12.16.a.a	$12$	$16$	12.a	1.a	$1$	$1$	$1$	$17.123$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2187\)	\(45702\)	\(1217888\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{7}q^{3}+45702q^{5}+1217888q^{7}+\cdots\)
12.16.a.b	$12$	$16$	12.a	1.a	$1$	$2$	$2$	$17.123$	\(\Q(\sqrt{8017}) \)	None	✓	$1$	$0$	\(0\)	\(4374\)	\(69660\)	\(2491504\)	$+$	$2^{7}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+3^{7}q^{3}+(34830-\beta )q^{5}+(1245752+\cdots)q^{7}+\cdots\)
12.16.b.a	$12$	$16$	12.b	12.b	$2$	$28$	$28$	$17.123$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
12.17.c.a	$12$	$17$	12.c	3.b	$2$	$1$	$1$	$19.479$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(6561\)	\(0\)	\(4743554\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{8}q^{3}+4743554q^{7}+3^{16}q^{9}+\cdots\)
12.17.c.b	$12$	$17$	12.c	3.b	$2$	$4$	$4$	$19.479$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(-12420\)	\(0\)	\(-1050280\)		$2^{9}\cdot 3^{11}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3105-\beta _{1})q^{3}+(-8\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
12.17.d.a	$12$	$17$	12.d	4.b	$2$	$16$	$16$	$19.479$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-186\)	\(0\)	\(354144\)	\(0\)		$2^{106}\cdot 3^{51}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-12-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(8542+\cdots)q^{4}+\cdots\)
12.18.a.a	$12$	$18$	12.a	1.a	$1$	$1$	$1$	$21.987$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-6561\)	\(-1608930\)	\(-9417184\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{8}q^{3}-1608930q^{5}-9417184q^{7}+\cdots\)
12.18.a.b	$12$	$18$	12.a	1.a	$1$	$1$	$1$	$21.987$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(6561\)	\(130950\)	\(-14846776\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{8}q^{3}+130950q^{5}-14846776q^{7}+\cdots\)
12.18.b.a	$12$	$18$	12.b	12.b	$2$	$32$	$32$	$21.987$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
12.19.c.a	$12$	$19$	12.c	3.b	$2$	$6$	$6$	$24.646$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(23934\)	\(0\)	\(11024364\)		$2^{32}\cdot 3^{19}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3989-\beta _{1})q^{3}+(-4\beta _{1}+\beta _{2})q^{5}+\cdots\)
12.19.d.a	$12$	$19$	12.d	4.b	$2$	$18$	$18$	$24.646$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-170\)	\(0\)	\(-1721764\)	\(0\)		$2^{139}\cdot 3^{67}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-9-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-24281+\cdots)q^{4}+\cdots\)
12.20.a.a	$12$	$20$	12.a	1.a	$1$	$2$	$2$	$27.458$	\(\Q(\sqrt{193153}) \)	None	✓	$1$	$1$	\(0\)	\(-39366\)	\(624780\)	\(4667104\)	$-$	$2^{7}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q-3^{9}q^{3}+(312390-\beta )q^{5}+(2333552+\cdots)q^{7}+\cdots\)
12.20.a.b	$12$	$20$	12.a	1.a	$1$	$2$	$2$	$27.458$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(39366\)	\(-3267108\)	\(-27023984\)	$+$	$2^{8}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+3^{9}q^{3}+(-1633554-\beta )q^{5}+(-13511992+\cdots)q^{7}+\cdots\)
12.20.b.a	$12$	$20$	12.b	12.b	$2$	$36$	$36$	$27.458$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
12.21.c.a	$12$	$21$	12.c	3.b	$2$	$1$	$1$	$30.422$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(59049\)	\(0\)	\(-77335774\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{10}q^{3}-77335774q^{7}+3^{20}q^{9}+\cdots\)
12.21.c.b	$12$	$21$	12.c	3.b	$2$	$6$	$6$	$30.422$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(-84378\)	\(0\)	\(-145040532\)		$2^{26}\cdot 3^{22}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-14063+\beta _{1})q^{3}+(3^{3}\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
12.21.d.a	$12$	$21$	12.d	4.b	$2$	$20$	$20$	$30.422$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(1254\)	\(0\)	\(1476984\)	\(0\)		$2^{174}\cdot 3^{82}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(63-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
12.22.a.a	$12$	$22$	12.a	1.a	$1$	$1$	$1$	$33.537$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(59049\)	\(-11268090\)	\(281914136\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{10}q^{3}-11268090q^{5}+281914136q^{7}+\cdots\)