Newform search results

Results (1-50 of 162 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
22.2.c.a	$22$	$2$	22.c	11.c	$5$	$4$	$1$	$0.176$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-1\)	\(-4\)	\(-6\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
22.3.b.a	$22$	$3$	22.b	11.b	$2$	$2$	$2$	$0.599$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots\)
22.3.d.a	$22$	$3$	22.d	11.d	$10$	$8$	$2$	$0.599$	8.0.64000000.1	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(-30\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-2\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots\)
22.4.a.a	$22$	$4$	22.a	1.a	$1$	$1$	$1$	$1.298$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-7\)	\(-19\)	\(14\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-7q^{3}+4q^{4}-19q^{5}+14q^{6}+\cdots\)
22.4.a.b	$22$	$4$	22.a	1.a	$1$	$1$	$1$	$1.298$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(4\)	\(14\)	\(-8\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{3}+4q^{4}+14q^{5}-8q^{6}+\cdots\)
22.4.a.c	$22$	$4$	22.a	1.a	$1$	$1$	$1$	$1.298$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(1\)	\(-3\)	\(-10\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+4q^{4}-3q^{5}+2q^{6}+\cdots\)
22.4.c.a	$22$	$4$	22.c	11.c	$5$	$4$	$1$	$1.298$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-2\)	\(-1\)	\(3\)	\(25\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-2\zeta_{10}q^{2}+(-3+3\zeta_{10}+8\zeta_{10}^{3})q^{3}+\cdots\)
22.4.c.b	$22$	$4$	22.c	11.c	$5$	$8$	$2$	$1.298$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(4\)	\(3\)	\(5\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-2\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
22.5.b.a	$22$	$5$	22.b	11.b	$2$	$4$	$4$	$2.274$	\(\Q(\sqrt{-2}, \sqrt{553})\)	None		$2$	$0$	\(0\)	\(2\)	\(-30\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}-8q^{4}+(-8-\beta _{1}+\cdots)q^{5}+\cdots\)
22.5.d.a	$22$	$5$	22.d	11.d	$10$	$16$	$4$	$2.274$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(30\)	\(150\)		$2^{8}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{4}q^{2}+(1+\beta _{2}+3\beta _{3}-\beta _{10}-\beta _{13}+\cdots)q^{3}+\cdots\)
22.6.a.a	$22$	$6$	22.a	1.a	$1$	$1$	$1$	$3.528$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(-21\)	\(81\)	\(98\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-21q^{3}+2^{4}q^{4}+3^{4}q^{5}+84q^{6}+\cdots\)
22.6.a.b	$22$	$6$	22.a	1.a	$1$	$1$	$1$	$3.528$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(1\)	\(-51\)	\(-166\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+q^{3}+2^{4}q^{4}-51q^{5}-4q^{6}+\cdots\)
22.6.a.c	$22$	$6$	22.a	1.a	$1$	$1$	$1$	$3.528$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(-29\)	\(-31\)	\(-230\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-29q^{3}+2^{4}q^{4}-31q^{5}-116q^{6}+\cdots\)
22.6.a.d	$22$	$6$	22.a	1.a	$1$	$2$	$2$	$3.528$	\(\Q(\sqrt{793}) \)	None	✓	$1$	$0$	\(8\)	\(29\)	\(-13\)	\(-14\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+(15-\beta )q^{3}+2^{4}q^{4}+(-9+\cdots)q^{5}+\cdots\)
22.6.c.a	$22$	$6$	22.c	11.c	$5$	$8$	$2$	$3.528$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(8\)	\(20\)	\(-30\)	\(48\)		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q-4\beta _{3}q^{2}+(3+3\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
22.6.c.b	$22$	$6$	22.c	11.c	$5$	$12$	$3$	$3.528$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-12\)	\(0\)	\(44\)	\(-326\)		$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-4+4\beta _{1}+4\beta _{2}-4\beta _{3})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots\)
22.7.b.a	$22$	$7$	22.b	11.b	$2$	$6$	$6$	$5.061$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(-52\)	\(368\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-9+\beta _{1})q^{3}-2^{5}q^{4}+(61+\cdots)q^{5}+\cdots\)
22.7.d.a	$22$	$7$	22.d	11.d	$10$	$24$	$6$	$5.061$		None		$2$	$0$	\(0\)	\(52\)	\(-368\)	\(720\)			$\mathrm{SU}(2)[C_{10}]$
22.8.a.a	$22$	$8$	22.a	1.a	$1$	$1$	$1$	$6.872$	\(\Q\)	None	✓	$1$	$1$	\(-8\)	\(-19\)	\(317\)	\(-1030\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}-19q^{3}+2^{6}q^{4}+317q^{5}+\cdots\)
22.8.a.b	$22$	$8$	22.a	1.a	$1$	$1$	$1$	$6.872$	\(\Q\)	None	✓	$1$	$0$	\(-8\)	\(91\)	\(185\)	\(-722\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+91q^{3}+2^{6}q^{4}+185q^{5}+\cdots\)
22.8.a.c	$22$	$8$	22.a	1.a	$1$	$1$	$1$	$6.872$	\(\Q\)	None	✓	$1$	$1$	\(8\)	\(-21\)	\(-551\)	\(62\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}-21q^{3}+2^{6}q^{4}-551q^{5}+\cdots\)
22.8.a.d	$22$	$8$	22.a	1.a	$1$	$2$	$2$	$6.872$	\(\Q(\sqrt{14881}) \)	None	✓	$1$	$0$	\(16\)	\(-23\)	\(331\)	\(1794\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+(-11-\beta )q^{3}+2^{6}q^{4}+(165+\cdots)q^{5}+\cdots\)
22.8.c.a	$22$	$8$	22.c	11.c	$5$	$12$	$3$	$6.872$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-24\)	\(44\)	\(220\)	\(534\)		$2^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-8+8\beta _{1}+8\beta _{2}+8\beta _{3})q^{2}+(5\beta _{1}+\cdots)q^{3}+\cdots\)
22.8.c.b	$22$	$8$	22.c	11.c	$5$	$16$	$4$	$6.872$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(32\)	\(-96\)	\(-82\)	\(-700\)		$2^{8}\cdot 5\cdot 11^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q-8\beta _{2}q^{2}+(-10-10\beta _{2}+3\beta _{3}+3\beta _{5}+\cdots)q^{3}+\cdots\)
22.9.b.a	$22$	$9$	22.b	11.b	$2$	$8$	$8$	$8.962$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(182\)	\(-1410\)	\(0\)		$2^{16}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(23+\beta _{1})q^{3}-2^{7}q^{4}+(-176+\cdots)q^{5}+\cdots\)
22.9.d.a	$22$	$9$	22.d	11.d	$10$	$32$	$8$	$8.962$		None		$2$	$0$	\(0\)	\(-182\)	\(1410\)	\(-10950\)			$\mathrm{SU}(2)[C_{10}]$
22.10.a.a	$22$	$10$	22.a	1.a	$1$	$1$	$1$	$11.331$	\(\Q\)	None	✓	$1$	$1$	\(16\)	\(-41\)	\(-1039\)	\(-3482\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}-41q^{3}+2^{8}q^{4}-1039q^{5}+\cdots\)
22.10.a.b	$22$	$10$	22.a	1.a	$1$	$1$	$1$	$11.331$	\(\Q\)	None	✓	$1$	$0$	\(16\)	\(137\)	\(-595\)	\(11354\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+137q^{3}+2^{8}q^{4}-595q^{5}+\cdots\)
22.10.a.c	$22$	$10$	22.a	1.a	$1$	$1$	$1$	$11.331$	\(\Q\)	None	✓	$1$	$0$	\(16\)	\(201\)	\(2349\)	\(-8806\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+201q^{3}+2^{8}q^{4}+2349q^{5}+\cdots\)
22.10.a.d	$22$	$10$	22.a	1.a	$1$	$2$	$2$	$11.331$	\(\Q(\sqrt{889}) \)	None	✓	$1$	$0$	\(-32\)	\(-21\)	\(-521\)	\(-7490\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+(-6-9\beta )q^{3}+2^{8}q^{4}+(-212+\cdots)q^{5}+\cdots\)
22.10.a.e	$22$	$10$	22.a	1.a	$1$	$2$	$2$	$11.331$	\(\Q(\sqrt{463}) \)	None	✓	$1$	$1$	\(-32\)	\(34\)	\(-1478\)	\(8196\)	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+(17+\beta )q^{3}+2^{8}q^{4}+(-739+\cdots)q^{5}+\cdots\)
22.10.c.a	$22$	$10$	22.c	11.c	$5$	$16$	$4$	$11.331$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(64\)	\(-13\)	\(1999\)	\(3779\)		$2^{12}\cdot 3^{4}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(2^{4}+2^{4}\beta _{1}+2^{4}\beta _{2}-2^{4}\beta _{3})q^{2}+\cdots\)
22.10.c.b	$22$	$10$	22.c	11.c	$5$	$20$	$5$	$11.331$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-80\)	\(15\)	\(-2455\)	\(17413\)		$2^{16}\cdot 3^{4}\cdot 5\cdot 11^{7}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2^{4}+2^{4}\beta _{3}-2^{4}\beta _{4}-2^{4}\beta _{5})q^{2}+\cdots\)
22.11.b.a	$22$	$11$	22.b	11.b	$2$	$10$	$10$	$13.978$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(-106\)	\(1138\)	\(0\)		$2^{24}\cdot 3^{2}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-11-\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)
22.11.d.a	$22$	$11$	22.d	11.d	$10$	$40$	$10$	$13.978$		None		$2$	$0$	\(0\)	\(106\)	\(-1138\)	\(19470\)			$\mathrm{SU}(2)[C_{10}]$
22.12.a.a	$22$	$12$	22.a	1.a	$1$	$2$	$2$	$16.904$	\(\Q(\sqrt{331}) \)	None	✓	$1$	$1$	\(64\)	\(-426\)	\(2290\)	\(-86324\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+2^{5}q^{2}+(-213+3\beta )q^{3}+2^{10}q^{4}+\cdots\)
22.12.a.b	$22$	$12$	22.a	1.a	$1$	$3$	$3$	$16.904$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-96\)	\(-70\)	\(-5624\)	\(-30576\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2^{5}q^{2}+(-23+\beta _{2})q^{3}+2^{10}q^{4}+\cdots\)
22.12.a.c	$22$	$12$	22.a	1.a	$1$	$3$	$3$	$16.904$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(-96\)	\(106\)	\(17344\)	\(13204\)	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q-2^{5}q^{2}+(35+\beta _{1})q^{3}+2^{10}q^{4}+(5771+\cdots)q^{5}+\cdots\)
22.12.a.d	$22$	$12$	22.a	1.a	$1$	$3$	$3$	$16.904$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(96\)	\(370\)	\(-1928\)	\(58472\)	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{5}q^{2}+(123-\beta _{1})q^{3}+2^{10}q^{4}+\cdots\)
22.12.c.a	$22$	$12$	22.c	11.c	$5$	$20$	$5$	$16.904$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-160\)	\(56\)	\(-362\)	\(-167178\)		$2^{24}\cdot 3^{4}\cdot 5\cdot 11^{8}$	$\mathrm{SU}(2)[C_{5}]$	\(q+2^{5}\beta _{2}q^{2}+(7+\beta _{1}+7\beta _{2}+9\beta _{4}+\cdots)q^{3}+\cdots\)
22.12.c.b	$22$	$12$	22.c	11.c	$5$	$24$	$6$	$16.904$		None		$2$	$0$	\(192\)	\(-36\)	\(-11720\)	\(20572\)			$\mathrm{SU}(2)[C_{5}]$
22.13.b.a	$22$	$13$	22.b	11.b	$2$	$12$	$12$	$20.108$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-1240\)	\(-1440\)	\(0\)		$2^{38}\cdot 3^{2}\cdot 11^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-103-\beta _{1})q^{3}-2^{11}q^{4}+\cdots\)
22.13.d.a	$22$	$13$	22.d	11.d	$10$	$48$	$12$	$20.108$		None		$2$	$0$	\(0\)	\(1240\)	\(1440\)	\(439200\)			$\mathrm{SU}(2)[C_{10}]$
22.14.a.a	$22$	$14$	22.a	1.a	$1$	$2$	$2$	$23.591$	\(\Q(\sqrt{100039}) \)	None	✓	$1$	$1$	\(-128\)	\(-662\)	\(-48566\)	\(404508\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+(-331+\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.b	$22$	$14$	22.a	1.a	$1$	$2$	$2$	$23.591$	\(\Q(\sqrt{55441}) \)	None	✓	$1$	$0$	\(-128\)	\(1626\)	\(7666\)	\(637048\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+(813-3\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.c	$22$	$14$	22.a	1.a	$1$	$2$	$2$	$23.591$	\(\Q(\sqrt{45769}) \)	None	✓	$1$	$1$	\(128\)	\(-926\)	\(2914\)	\(-170560\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}+(-463-\beta )q^{3}+2^{12}q^{4}+\cdots\)
22.14.a.d	$22$	$14$	22.a	1.a	$1$	$3$	$3$	$23.591$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(192\)	\(-298\)	\(40432\)	\(40452\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}+(-10^{2}-\beta _{1}-\beta _{2})q^{3}+2^{12}q^{4}+\cdots\)
22.14.c.a	$22$	$14$	22.c	11.c	$5$	$24$	$6$	$23.591$		None		$2$	$0$	\(384\)	\(2708\)	\(32920\)	\(-509572\)			$\mathrm{SU}(2)[C_{5}]$
22.14.c.b	$22$	$14$	22.c	11.c	$5$	$28$	$7$	$23.591$		None		$2$	$0$	\(-448\)	\(-1248\)	\(71554\)	\(361734\)			$\mathrm{SU}(2)[C_{5}]$
22.15.b.a	$22$	$15$	22.b	11.b	$2$	$14$	$14$	$27.352$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(4394\)	\(69758\)	\(0\)		$2^{56}\cdot 3^{6}\cdot 11^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(314+\beta _{1})q^{3}-2^{13}q^{4}+\cdots\)