Newform search results

Results (1-50 of 1162 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.33.b.a	$11$	$33$	11.b	11.b	$2$	$1$	$1$	$71.353$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-85968833\)	\(-9728091649\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-85968833q^{3}+2^{32}q^{4}-9728091649q^{5}+\cdots\)
11.33.b.b	$11$	$33$	11.b	11.b	$2$	$30$	$30$	$71.353$		None		$2$	$0$	\(0\)	\(130139244\)	\(214212464192\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
11.33.d.a	$11$	$33$	11.d	11.d	$10$	$124$	$31$	$71.353$		None		$2$	$0$	\(-5\)	\(-44170416\)	\(-204484372548\)	\(-32\!\cdots\!30\)			$\mathrm{SU}(2)[C_{10}]$
11.34.a.a	$11$	$34$	11.a	1.a	$1$	$13$	$13$	$75.881$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-47235066\)	\(6852549396\)	\(-83\!\cdots\!60\)	$+$	$2^{60}\cdot 3^{18}\cdot 5^{6}\cdot 7\cdot 11^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-3633467-130\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
11.34.a.b	$11$	$34$	11.a	1.a	$1$	$15$	$15$	$75.881$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(65536\)	\(3552592\)	\(96792382414\)	\(-29\!\cdots\!00\)	$-$	$2^{61}\cdot 3^{18}\cdot 5^{4}\cdot 7^{4}\cdot 11^{8}$	$\mathrm{SU}(2)$	\(q+(4369+\beta _{1})q^{2}+(236832+115\beta _{1}+\cdots)q^{3}+\cdots\)
11.34.c.a	$11$	$34$	11.c	11.c	$5$	$128$	$32$	$75.881$		None		$2$	$0$	\(177819\)	\(-32157291\)	\(258478141185\)	\(14\!\cdots\!25\)			$\mathrm{SU}(2)[C_{5}]$
12.33.c.a	$12$	$33$	12.c	3.b	$2$	$1$	$1$	$77.840$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(43046721\)	\(0\)	\(-43\!\cdots\!86\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{16}q^{3}-43964556588286q^{7}+\cdots\)
12.33.c.b	$12$	$33$	12.c	3.b	$2$	$10$	$10$	$77.840$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-18867342\)	\(0\)	\(75\!\cdots\!52\)		$2^{82}\cdot 3^{68}\cdot 5^{6}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1886734+\beta _{1})q^{3}+(-41-205\beta _{1}+\cdots)q^{5}+\cdots\)
12.33.d.a	$12$	$33$	12.d	4.b	$2$	$32$	$32$	$77.840$		None		$2$	$0$	\(-83514\)	\(0\)	\(116749235904\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
11.35.b.a	$11$	$35$	11.b	11.b	$2$	$1$	$1$	$80.548$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(222600715\)	\(-15\!\cdots\!01\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+222600715q^{3}+2^{34}q^{4}-1512594730201q^{5}+\cdots\)
11.35.b.b	$11$	$35$	11.b	11.b	$2$	$32$	$32$	$80.548$		None		$2$	$0$	\(0\)	\(-421844802\)	\(764041734270\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
11.35.d.a	$11$	$35$	11.d	11.d	$10$	$132$	$33$	$80.548$		None		$2$	$0$	\(-5\)	\(199244082\)	\(748552995926\)	\(53\!\cdots\!60\)			$\mathrm{SU}(2)[C_{10}]$
12.34.a.a	$12$	$34$	12.a	1.a	$1$	$2$	$2$	$82.779$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(86093442\)	\(350946261900\)	\(-42\!\cdots\!72\)	$+$	$2^{7}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+3^{16}q^{3}+(175473130950-5\beta )q^{5}+\cdots\)
12.34.a.b	$12$	$34$	12.a	1.a	$1$	$3$	$3$	$82.779$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-129140163\)	\(-204182616870\)	\(23\!\cdots\!68\)	$-$	$2^{24}\cdot 3^{6}\cdot 5^{2}\cdot 11$	$\mathrm{SU}(2)$	\(q-3^{16}q^{3}+(-68060872290+\beta _{1}+\cdots)q^{5}+\cdots\)
12.34.b.a	$12$	$34$	12.b	12.b	$2$	$64$	$64$	$82.779$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
13.33.d.a	$13$	$33$	13.d	13.d	$4$	$74$	$37$	$84.327$		None		$2$	$0$	\(-2\)	\(-4\)	\(-58374617954\)	\(73\!\cdots\!28\)			$\mathrm{SU}(2)[C_{4}]$
13.33.f.a	$13$	$33$	13.f	13.f	$12$	$144$	$36$	$84.327$		None		$2$	$0$	\(-4\)	\(-2\)	\(58374617948\)	\(-80\!\cdots\!64\)			$\mathrm{SU}(2)[C_{12}]$
11.36.a.a	$11$	$36$	11.a	1.a	$1$	$13$	$13$	$85.355$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-376762713\)	\(-10\!\cdots\!65\)	\(-10\!\cdots\!62\)	$-$	$2^{60}\cdot 3^{23}\cdot 5^{5}\cdot 7^{4}\cdot 11^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-28981747-137\beta _{1}+\cdots)q^{3}+\cdots\)
11.36.a.b	$11$	$36$	11.a	1.a	$1$	$15$	$15$	$85.355$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(131072\)	\(210035680\)	\(58434409142\)	\(-41\!\cdots\!80\)	$+$	$2^{66}\cdot 3^{24}\cdot 5^{7}\cdot 7^{5}\cdot 11^{8}$	$\mathrm{SU}(2)$	\(q+(8738+\beta _{1})q^{2}+(14002358+152\beta _{1}+\cdots)q^{3}+\cdots\)
11.36.c.a	$11$	$36$	11.c	11.c	$5$	$136$	$34$	$85.355$		None		$2$	$0$	\(-410389\)	\(376477644\)	\(-786140657002\)	\(-15\!\cdots\!60\)			$\mathrm{SU}(2)[C_{5}]$
12.35.c.a	$12$	$35$	12.c	3.b	$2$	$1$	$1$	$87.871$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-129140163\)	\(0\)	\(30\!\cdots\!42\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{17}q^{3}+301392890307842q^{7}+\cdots\)
12.35.c.b	$12$	$35$	12.c	3.b	$2$	$10$	$10$	$87.871$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(88759314\)	\(0\)	\(-21\!\cdots\!16\)		$2^{91}\cdot 3^{71}\cdot 5^{7}\cdot 7^{2}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	\(q+(8875931-\beta _{1})q^{3}+(-253-632\beta _{1}+\cdots)q^{5}+\cdots\)
12.35.d.a	$12$	$35$	12.d	4.b	$2$	$34$	$34$	$87.871$		None		$2$	$0$	\(54742\)	\(0\)	\(42744511676\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
13.34.a.a	$13$	$34$	13.a	1.a	$1$	$16$	$16$	$89.678$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$1$	\(-9393\)	\(-124013323\)	\(-186717407289\)	\(-26\!\cdots\!49\)	$+$	$2^{66}\cdot 3^{18}\cdot 5^{4}\cdot 7^{2}\cdot 11^{4}\cdot 13^{8}$	$\mathrm{SU}(2)$	\(q+(-587-\beta _{1})q^{2}+(-7750829-63\beta _{1}+\cdots)q^{3}+\cdots\)
13.34.a.b	$13$	$34$	13.a	1.a	$1$	$17$	$17$	$89.678$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(187215\)	\(48173561\)	\(883458081723\)	\(27\!\cdots\!07\)	$-$	$2^{66}\cdot 3^{19}\cdot 5^{6}\cdot 7^{3}\cdot 11^{5}\cdot 13^{9}$	$\mathrm{SU}(2)$	\(q+(11013-\beta _{1})q^{2}+(2833728+31\beta _{1}+\cdots)q^{3}+\cdots\)
13.34.b.a	$13$	$34$	13.b	13.b	$2$	$38$	$38$	$89.678$		None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
13.34.c.a	$13$	$34$	13.c	13.c	$3$	$74$	$37$	$89.678$		None		$2$	$0$	\(65535\)	\(86093441\)	\(-334617601440\)	\(19\!\cdots\!61\)			$\mathrm{SU}(2)[C_{3}]$
13.34.e.a	$13$	$34$	13.e	13.e	$6$	$76$	$38$	$89.678$		None		$2$	$0$	\(-3\)	\(-86093443\)	\(0\)	\(-10\!\cdots\!77\)			$\mathrm{SU}(2)[C_{6}]$
11.37.b.a	$11$	$37$	11.b	11.b	$2$	$1$	$1$	$90.300$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-339284078\)	\(17\!\cdots\!26\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-339284078q^{3}+2^{36}q^{4}+1755797021426q^{5}+\cdots\)
11.37.b.b	$11$	$37$	11.b	11.b	$2$	$34$	$34$	$90.300$		None		$2$	$0$	\(0\)	\(458720916\)	\(-615535265668\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
11.37.d.a	$11$	$37$	11.d	11.d	$10$	$140$	$35$	$90.300$		None		$2$	$0$	\(-5\)	\(-119436843\)	\(-11\!\cdots\!63\)	\(-10\!\cdots\!05\)			$\mathrm{SU}(2)[C_{10}]$
14.33.b.a	$14$	$33$	14.b	7.b	$2$	$20$	$20$	$90.813$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(38\!\cdots\!84\)		$2^{195}\cdot 3^{24}\cdot 5^{4}\cdot 7^{40}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+2^{31}q^{4}+(551\beta _{1}+\cdots)q^{5}+\cdots\)
14.33.d.a	$14$	$33$	14.d	7.d	$6$	$44$	$22$	$90.813$		None		$2$	$0$	\(0\)	\(86093442\)	\(337551521994\)	\(-18\!\cdots\!28\)			$\mathrm{SU}(2)[C_{6}]$
12.36.a.a	$12$	$36$	12.a	1.a	$1$	$3$	$3$	$93.114$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-387420489\)	\(-846903258990\)	\(-27\!\cdots\!84\)	$-$	$2^{22}\cdot 3^{7}\cdot 5^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q-3^{17}q^{3}+(-282301086330-\beta _{2})q^{5}+\cdots\)
12.36.a.b	$12$	$36$	12.a	1.a	$1$	$3$	$3$	$93.114$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(387420489\)	\(10\!\cdots\!02\)	\(43\!\cdots\!84\)	$+$	$2^{24}\cdot 3^{7}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+3^{17}q^{3}+(338261617134+\beta _{1}+\cdots)q^{5}+\cdots\)
12.36.b.a	$12$	$36$	12.b	12.b	$2$	$68$	$68$	$93.114$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
13.35.d.a	$13$	$35$	13.d	13.d	$4$	$76$	$38$	$95.193$		None		$2$	$0$	\(-131074\)	\(-4\)	\(-106861279192\)	\(61\!\cdots\!48\)			$\mathrm{SU}(2)[C_{4}]$
13.35.f.a	$13$	$35$	13.f	13.f	$12$	$156$	$39$	$95.193$		None		$2$	$0$	\(131068\)	\(-2\)	\(106861279186\)	\(-56\!\cdots\!84\)			$\mathrm{SU}(2)[C_{12}]$
11.38.a.a	$11$	$38$	11.a	1.a	$1$	$15$	$15$	$95.385$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-262144\)	\(630107040\)	\(-17\!\cdots\!34\)	\(-92\!\cdots\!60\)	$+$	$2^{80}\cdot 3^{29}\cdot 5^{8}\cdot 7\cdot 11^{8}$	$\mathrm{SU}(2)$	\(q+(-17476-\beta _{1})q^{2}+(42007168+\cdots)q^{3}+\cdots\)
11.38.a.b	$11$	$38$	11.a	1.a	$1$	$17$	$17$	$95.385$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(80109739\)	\(12\!\cdots\!09\)	\(97\!\cdots\!54\)	$-$	$2^{82}\cdot 3^{30}\cdot 5^{6}\cdot 7^{4}\cdot 11^{10}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(4712338+71\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
11.38.c.a	$11$	$38$	11.c	11.c	$5$	$144$	$36$	$95.385$		None		$2$	$0$	\(650939\)	\(-738199584\)	\(-61\!\cdots\!80\)	\(74\!\cdots\!96\)			$\mathrm{SU}(2)[C_{5}]$
14.34.a.a	$14$	$34$	14.a	1.a	$1$	$3$	$3$	$96.576$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(196608\)	\(21946356\)	\(-84870483150\)	\(99\!\cdots\!03\)	$+$	$2^{4}\cdot 3^{4}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+2^{16}q^{2}+(7315452-\beta _{1})q^{3}+2^{32}q^{4}+\cdots\)
14.34.a.b	$14$	$34$	14.a	1.a	$1$	$4$	$4$	$96.576$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(-262144\)	\(16609278\)	\(-476408821630\)	\(-13\!\cdots\!04\)	$+$	$2^{14}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q-2^{16}q^{2}+(4152319+\beta _{1})q^{3}+2^{32}q^{4}+\cdots\)
14.34.a.c	$14$	$34$	14.a	1.a	$1$	$4$	$4$	$96.576$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(262144\)	\(-14456386\)	\(201960095554\)	\(-13\!\cdots\!04\)	$-$	$2^{14}\cdot 3^{4}\cdot 5\cdot 7^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+2^{16}q^{2}+(-3614096-\beta _{1})q^{3}+\cdots\)
14.34.a.d	$14$	$34$	14.a	1.a	$1$	$5$	$5$	$96.576$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(-327680\)	\(139105462\)	\(-151655542920\)	\(16\!\cdots\!05\)	$-$	$2^{19}\cdot 3^{5}\cdot 5^{2}\cdot 7^{4}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q-2^{16}q^{2}+(27821092+\beta _{1})q^{3}+2^{32}q^{4}+\cdots\)
14.34.c.a	$14$	$34$	14.c	7.c	$3$	$22$	$11$	$96.576$		None		$2$	$0$	\(-720896\)	\(-73991969\)	\(-404551342333\)	\(15\!\cdots\!96\)			$\mathrm{SU}(2)[C_{3}]$
14.34.c.b	$14$	$34$	14.c	7.c	$3$	$22$	$11$	$96.576$		None		$2$	$0$	\(720896\)	\(-12101473\)	\(224766950275\)	\(20\!\cdots\!80\)			$\mathrm{SU}(2)[C_{3}]$
15.33.c.a	$15$	$33$	15.c	3.b	$2$	$42$	$42$	$97.300$		None		$2$	$0$	\(0\)	\(45566528\)	\(0\)	\(23\!\cdots\!16\)			$\mathrm{SU}(2)[C_{2}]$
15.33.d.a	$15$	$33$	15.d	15.d	$2$	$1$	$1$	$97.300$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-81343\)	\(43046721\)	\(152587890625\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-81343q^{2}+3^{16}q^{3}+2321716353q^{4}+\cdots\)
15.33.d.b	$15$	$33$	15.d	15.d	$2$	$1$	$1$	$97.300$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(81343\)	\(-43046721\)	\(-152587890625\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+81343q^{2}-3^{16}q^{3}+2321716353q^{4}+\cdots\)