Newform search results

Results (1-50 of 61 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
59.1.b.a	$59$	$1$	59.b	59.b	$2$	$1$	$1$	$0.029$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$1$		\(q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots\)
59.2.a.a	$59$	$2$	59.a	1.a	$1$	$5$	$5$	$0.471$	5.5.138136.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{4})q^{3}+\cdots\)
59.2.c.a	$59$	$2$	59.c	59.c	$29$	$112$	$4$	$0.471$		$_{}$	None	None		$2$	$0$	\(-26\)	\(-23\)	\(-25\)	\(-23\)			$\mathrm{SU}(2)[C_{29}]$
59.3.b.a	$59$	$3$	59.b	59.b	$2$	$3$	$3$	$1.608$	3.3.1593.1	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
59.3.b.b	$59$	$3$	59.b	59.b	$2$	$6$	$6$	$1.608$	6.0.7196038400.1	$_{}$	None	None		$2$	$0$	\(0\)	\(4\)	\(-8\)	\(6\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(-5-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
59.3.d.a	$59$	$3$	59.d	59.d	$58$	$252$	$9$	$1.608$		$_{}$	None	None		$2$	$0$	\(-29\)	\(-33\)	\(-21\)	\(-35\)			$\mathrm{SU}(2)[C_{58}]$
59.4.a.a	$59$	$4$	59.a	1.a	$1$	$2$	$2$	$3.481$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	$1$	$1$	\(-4\)	\(-2\)	\(6\)	\(-22\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta )q^{2}-q^{3}+(1+4\beta )q^{4}+(3+\cdots)q^{5}+\cdots\)
59.4.a.b	$59$	$4$	59.a	1.a	$1$	$2$	$2$	$3.481$	\(\Q(\sqrt{17}) \)	$_{}$	None	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-31\)	\(-8\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots\)
59.4.a.c	$59$	$4$	59.a	1.a	$1$	$10$	$10$	$3.481$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(3\)	\(3\)	\(15\)	\(40\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(6+\beta _{2})q^{4}+(2+\beta _{1}+\cdots)q^{5}+\cdots\)
59.4.c.a	$59$	$4$	59.c	59.c	$29$	$392$	$14$	$3.481$		$_{}$	None	None		$2$	$0$	\(-29\)	\(-29\)	\(-19\)	\(-39\)			$\mathrm{SU}(2)[C_{29}]$
59.5.b.a	$59$	$5$	59.b	59.b	$2$	$3$	$3$	$6.099$	3.3.1593.1	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(4\beta _{1}-3\beta _{2})q^{3}+2^{4}q^{4}+(5\beta _{1}-11\beta _{2})q^{5}+\cdots\)
59.5.b.b	$59$	$5$	59.b	59.b	$2$	$16$	$16$	$6.099$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-20\)	\(4\)	\(-82\)		$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(-12+\beta _{2}+\cdots)q^{4}+\cdots\)
59.5.d.a	$59$	$5$	59.d	59.d	$58$	$532$	$19$	$6.099$		$_{}$	None	None		$2$	$0$	\(-29\)	\(-9\)	\(-33\)	\(53\)			$\mathrm{SU}(2)[C_{58}]$
59.6.a.a	$59$	$6$	59.a	1.a	$1$	$9$	$9$	$9.463$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-9\)	\(0\)	\(-72\)	\(-208\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(7+\cdots)q^{4}+\cdots\)
59.6.a.b	$59$	$6$	59.a	1.a	$1$	$15$	$15$	$9.463$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(3\)	\(18\)	\(128\)	\(282\)	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{7})q^{3}+(20+\beta _{2})q^{4}+\cdots\)
59.6.c.a	$59$	$6$	59.c	59.c	$29$	$672$	$24$	$9.463$		$_{}$	None	None		$2$	$0$	\(-23\)	\(-47\)	\(-85\)	\(-103\)			$\mathrm{SU}(2)[C_{29}]$
59.7.b.a	$59$	$7$	59.b	59.b	$2$	$1$	$1$	$13.573$	\(\Q\)	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(-5\)	\(191\)	\(155\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-5q^{3}+2^{6}q^{4}+191q^{5}+155q^{7}+\cdots\)
59.7.b.b	$59$	$7$	59.b	59.b	$2$	$2$	$2$	$13.573$	\(\Q(\sqrt{177}) \)	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(5\)	\(-191\)	\(-155\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+7\beta )q^{3}+2^{6}q^{4}+(-85-21\beta )q^{5}+\cdots\)
59.7.b.c	$59$	$7$	59.b	59.b	$2$	$26$	$26$	$13.573$		$_{}$	None	None		$2$	$0$	\(0\)	\(10\)	\(142\)	\(406\)			$\mathrm{SU}(2)[C_{2}]$
59.7.d.a	$59$	$7$	59.d	59.d	$58$	$812$	$29$	$13.573$		$_{}$	None	None		$2$	$0$	\(-29\)	\(-39\)	\(-171\)	\(-435\)			$\mathrm{SU}(2)[C_{58}]$
59.8.a.a	$59$	$8$	59.a	1.a	$1$	$14$	$14$	$18.431$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-9\)	\(-54\)	\(-430\)	\(-2390\)	$-$	$2^{9}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-4+\beta _{3})q^{3}+(41+\cdots)q^{4}+\cdots\)
59.8.a.b	$59$	$8$	59.a	1.a	$1$	$20$	$20$	$18.431$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(15\)	\(0\)	\(570\)	\(1040\)	$+$	$2^{11}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(77-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
59.8.c.a	$59$	$8$	59.c	59.c	$29$	$952$	$34$	$18.431$		$_{}$	None	None		$2$	$0$	\(-35\)	\(25\)	\(-169\)	\(1321\)			$\mathrm{SU}(2)[C_{29}]$
59.9.b.a	$59$	$9$	59.b	59.b	$2$	$3$	$3$	$24.035$	3.3.1593.1	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-41\beta _{1}+22\beta _{2})q^{3}+2^{8}q^{4}+(-316\beta _{1}+\cdots)q^{5}+\cdots\)
59.9.b.b	$59$	$9$	59.b	59.b	$2$	$36$	$36$	$24.035$		$_{}$	None	None		$2$	$0$	\(0\)	\(40\)	\(-296\)	\(-162\)			$\mathrm{SU}(2)[C_{2}]$
59.9.d.a	$59$	$9$	59.d	59.d	$58$	$1092$	$39$	$24.035$		$_{}$	None	None		$2$	$0$	\(-29\)	\(-69\)	\(267\)	\(133\)			$\mathrm{SU}(2)[C_{58}]$
59.10.a.a	$59$	$10$	59.a	1.a	$1$	$19$	$19$	$30.387$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-33\)	\(-81\)	\(-3297\)	\(-7128\)	$+$	$2^{15}\cdot 3^{5}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(-4-\beta _{4})q^{3}+(189+\cdots)q^{4}+\cdots\)
59.10.a.b	$59$	$10$	59.a	1.a	$1$	$25$	$25$	$30.387$		$_{}$	None	None	✓	$1$	$0$	\(15\)	\(81\)	\(1703\)	\(16882\)	$-$		$\mathrm{SU}(2)$
59.10.c.a	$59$	$10$	59.c	59.c	$29$	$1232$	$44$	$30.387$		$_{}$	None	None		$2$	$0$	\(-11\)	\(-29\)	\(1565\)	\(-9783\)			$\mathrm{SU}(2)[C_{29}]$
59.11.b.a	$59$	$11$	59.b	59.b	$2$	$3$	$3$	$37.486$	3.3.1593.1	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-101\beta _{1}-66\beta _{2})q^{3}+2^{10}q^{4}+\cdots\)
59.11.b.b	$59$	$11$	59.b	59.b	$2$	$46$	$46$	$37.486$		$_{}$	None	None		$2$	$0$	\(0\)	\(16\)	\(-3308\)	\(-18394\)			$\mathrm{SU}(2)[C_{2}]$
59.11.d.a	$59$	$11$	59.d	59.d	$58$	$1372$	$49$	$37.486$		$_{}$	None	None		$2$	$0$	\(-29\)	\(-45\)	\(3279\)	\(18365\)			$\mathrm{SU}(2)[C_{58}]$
59.12.a.a	$59$	$12$	59.a	1.a	$1$	$23$	$23$	$45.332$		$_{}$	None	None	✓	$1$	$1$	\(-9\)	\(-486\)	\(-18310\)	\(-83046\)	$-$		$\mathrm{SU}(2)$
59.12.a.b	$59$	$12$	59.a	1.a	$1$	$29$	$29$	$45.332$		$_{}$	None	None	✓	$1$	$0$	\(87\)	\(0\)	\(6690\)	\(85024\)	$+$		$\mathrm{SU}(2)$
59.12.c.a	$59$	$12$	59.c	59.c	$29$	$1512$	$54$	$45.332$		$_{}$	None	None		$2$	$0$	\(-59\)	\(-47\)	\(1931\)	\(31481\)			$\mathrm{SU}(2)[C_{29}]$
59.13.b.a	$59$	$13$	59.b	59.b	$2$	$1$	$1$	$53.926$	\(\Q\)	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(-1433\)	\(5231\)	\(-211273\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-1433q^{3}+2^{12}q^{4}+5231q^{5}-211273q^{7}+\cdots\)
59.13.b.b	$59$	$13$	59.b	59.b	$2$	$2$	$2$	$53.926$	\(\Q(\sqrt{177}) \)	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(1433\)	\(-5231\)	\(211273\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(734-35\beta )q^{3}+2^{12}q^{4}+(-610+\cdots)q^{5}+\cdots\)
59.13.b.c	$59$	$13$	59.b	59.b	$2$	$56$	$56$	$53.926$		$_{}$	None	None		$2$	$0$	\(0\)	\(-602\)	\(10654\)	\(191758\)			$\mathrm{SU}(2)[C_{2}]$
59.14.a.a	$59$	$14$	59.a	1.a	$1$	$29$	$29$	$63.266$		$_{}$	None	None	✓	$1$	$1$	\(-129\)	\(0\)	\(-41622\)	\(-669728\)	$+$		$\mathrm{SU}(2)$
59.14.a.b	$59$	$14$	59.a	1.a	$1$	$35$	$35$	$63.266$		$_{}$	None	None	✓	$1$	$0$	\(63\)	\(1458\)	\(83378\)	\(506762\)	$-$		$\mathrm{SU}(2)$
59.15.b.a	$59$	$15$	59.b	59.b	$2$	$3$	$3$	$73.354$	3.3.1593.1	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$13$	$\mathrm{U}(1)[D_{2}]$	\(q+(250\beta _{1}+113\beta _{2})q^{3}+2^{14}q^{4}+(8659\beta _{1}+\cdots)q^{5}+\cdots\)
59.15.b.b	$59$	$15$	59.b	59.b	$2$	$66$	$66$	$73.354$		$_{}$	None	None		$2$	$0$	\(0\)	\(76\)	\(71992\)	\(-1016394\)			$\mathrm{SU}(2)[C_{2}]$
59.16.a.a	$59$	$16$	59.a	1.a	$1$	$33$	$33$	$84.189$		$_{}$	None	None	✓	$1$	$1$	\(-345\)	\(-2187\)	\(-361015\)	\(-5353406\)	$-$		$\mathrm{SU}(2)$
59.16.a.b	$59$	$16$	59.a	1.a	$1$	$39$	$39$	$84.189$		$_{}$	None	None	✓	$1$	$0$	\(39\)	\(2187\)	\(263985\)	\(2882024\)	$+$		$\mathrm{SU}(2)$
59.17.b.a	$59$	$17$	59.b	59.b	$2$	$3$	$3$	$95.771$	3.3.1593.1	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$17$	$\mathrm{U}(1)[D_{2}]$	\(q+(-413\beta _{1}-586\beta _{2})q^{3}+2^{16}q^{4}+\cdots\)
59.17.b.b	$59$	$17$	59.b	59.b	$2$	$76$	$76$	$95.771$		$_{}$	None	None		$2$	$0$	\(0\)	\(11716\)	\(-338396\)	\(767678\)			$\mathrm{SU}(2)[C_{2}]$
59.18.a.a	$59$	$18$	59.a	1.a	$1$	$38$	$38$	$108.101$		$_{}$	None	None	✓	$1$	$1$	\(15\)	\(0\)	\(-1062222\)	\(-43925040\)	$+$		$\mathrm{SU}(2)$
59.18.a.b	$59$	$18$	59.a	1.a	$1$	$44$	$44$	$108.101$		$_{}$	None	None	✓	$1$	$0$	\(783\)	\(13122\)	\(2062778\)	\(13722970\)	$-$		$\mathrm{SU}(2)$
59.19.b.a	$59$	$19$	59.b	59.b	$2$	$1$	$1$	$121.178$	\(\Q\)	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(10810\)	\(-1985254\)	\(-50982910\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+10810q^{3}+2^{18}q^{4}-1985254q^{5}+\cdots\)
59.19.b.b	$59$	$19$	59.b	59.b	$2$	$2$	$2$	$121.178$	\(\Q(\sqrt{177}) \)	$_{}$	\(\Q(\sqrt{-59}) \)	None	✓	$2$	$0$	\(0\)	\(-10810\)	\(1985254\)	\(50982910\)		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-5405-616\beta )q^{3}+2^{18}q^{4}+(992627+\cdots)q^{5}+\cdots\)