Newform search results

Results (1-50 of 193 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.2.a.a	$27$	$2$	27.a	1.a	$1$	$1$	$1$	$0.216$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)
27.2.e.a	$27$	$2$	27.e	27.e	$9$	$12$	$2$	$0.216$	12.0.\(\cdots\).1	None		$2$	$0$	\(-6\)	\(-6\)	\(-3\)	\(-6\)		$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\)
27.3.b.a	$27$	$3$	27.b	3.b	$2$	$1$	$1$	$0.736$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-13\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}-13q^{7}-q^{13}+2^{4}q^{16}+11q^{19}+\cdots\)
27.3.b.b	$27$	$3$	27.b	3.b	$2$	$2$	$2$	$0.736$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-5q^{4}-iq^{5}+5q^{7}-iq^{8}+\cdots\)
27.3.d.a	$27$	$3$	27.d	9.d	$6$	$2$	$1$	$0.736$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(0\)	\(-6\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+2\zeta_{6})q^{5}+\cdots\)
27.3.f.a	$27$	$3$	27.f	27.f	$18$	$30$	$5$	$0.736$		None		$2$	$0$	\(-6\)	\(-6\)	\(-15\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
27.4.a.a	$27$	$4$	27.a	1.a	$1$	$1$	$1$	$1.593$	\(\Q\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-15\)	\(-25\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+q^{4}-15q^{5}-5^{2}q^{7}+21q^{8}+\cdots\)
27.4.a.b	$27$	$4$	27.a	1.a	$1$	$1$	$1$	$1.593$	\(\Q\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(15\)	\(-25\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+q^{4}+15q^{5}-5^{2}q^{7}-21q^{8}+\cdots\)
27.4.a.c	$27$	$4$	27.a	1.a	$1$	$2$	$2$	$1.593$	\(\Q(\sqrt{2}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(22\)	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+10q^{4}-4\beta q^{5}+11q^{7}+2\beta q^{8}+\cdots\)
27.4.c.a	$27$	$4$	27.c	9.c	$3$	$4$	$2$	$1.593$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(3\)	\(0\)	\(15\)	\(-7\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(-4+\beta _{1}-3\beta _{2}+3\beta _{3})q^{4}+\cdots\)
27.4.e.a	$27$	$4$	27.e	27.e	$9$	$48$	$8$	$1.593$		None		$2$	$0$	\(-6\)	\(-6\)	\(6\)	\(-6\)			$\mathrm{SU}(2)[C_{9}]$
27.5.b.a	$27$	$5$	27.b	3.b	$2$	$1$	$1$	$2.791$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(71\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{4}+71q^{7}-337q^{13}+2^{8}q^{16}+\cdots\)
27.5.b.b	$27$	$5$	27.b	3.b	$2$	$2$	$2$	$2.791$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(34\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-38q^{4}+2\beta q^{5}+17q^{7}-22\beta q^{8}+\cdots\)
27.5.b.c	$27$	$5$	27.b	3.b	$2$	$2$	$2$	$2.791$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-38\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+7q^{4}+11iq^{5}-19q^{7}+23iq^{8}+\cdots\)
27.5.d.a	$27$	$5$	27.d	9.d	$6$	$6$	$3$	$2.791$	6.0.39400128.1	None		$2$	$0$	\(3\)	\(0\)	\(12\)	\(12\)		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(4\beta _{1}+2\beta _{2}-\beta _{3}-3\beta _{4}+\cdots)q^{4}+\cdots\)
27.5.f.a	$27$	$5$	27.f	27.f	$18$	$66$	$11$	$2.791$		None		$2$	$0$	\(-6\)	\(-6\)	\(3\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
27.6.a.a	$27$	$6$	27.a	1.a	$1$	$1$	$1$	$4.330$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-211\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2^{5}q^{4}-211q^{7}-775q^{13}+2^{10}q^{16}+\cdots\)
27.6.a.b	$27$	$6$	27.a	1.a	$1$	$2$	$2$	$4.330$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-9\)	\(0\)	\(-72\)	\(-8\)	$+$	$3$	$\mathrm{SU}(2)$	\(q+(-4-\beta )q^{2}+(22+9\beta )q^{4}+(-41+\cdots)q^{5}+\cdots\)
27.6.a.c	$27$	$6$	27.a	1.a	$1$	$2$	$2$	$4.330$	\(\Q(\sqrt{6}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(334\)	$-$	$3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+22q^{4}+8\beta q^{5}+167q^{7}+\cdots\)
27.6.a.d	$27$	$6$	27.a	1.a	$1$	$2$	$2$	$4.330$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(9\)	\(0\)	\(72\)	\(-8\)	$-$	$3$	$\mathrm{SU}(2)$	\(q+(4+\beta )q^{2}+(22+9\beta )q^{4}+(41-10\beta )q^{5}+\cdots\)
27.6.c.a	$27$	$6$	27.c	9.c	$3$	$8$	$4$	$4.330$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(-3\)	\(0\)	\(-78\)	\(28\)		$2^{2}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(-13\beta _{1}+\cdots)q^{4}+\cdots\)
27.6.e.a	$27$	$6$	27.e	27.e	$9$	$84$	$14$	$4.330$		None		$2$	$0$	\(-6\)	\(-6\)	\(-93\)	\(-6\)			$\mathrm{SU}(2)[C_{9}]$
27.7.b.a	$27$	$7$	27.b	3.b	$2$	$2$	$2$	$6.211$	\(\Q(\sqrt{-10}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-806\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-26q^{4}+14\beta q^{5}-403q^{7}+\cdots\)
27.7.b.b	$27$	$7$	27.b	3.b	$2$	$2$	$2$	$6.211$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(598\)		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+28q^{4}-40iq^{5}+299q^{7}+\cdots\)
27.7.b.c	$27$	$7$	27.b	3.b	$2$	$4$	$4$	$6.211$	\(\Q(i, \sqrt{41})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-676\)		$3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-7^{2}+\beta _{3})q^{4}+(7\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
27.7.d.a	$27$	$7$	27.d	9.d	$6$	$10$	$5$	$6.211$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(3\)	\(0\)	\(219\)	\(-121\)		$2^{2}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-5^{2}\beta _{4}+\beta _{5})q^{4}+\cdots\)
27.7.f.a	$27$	$7$	27.f	27.f	$18$	$102$	$17$	$6.211$		None		$2$	$0$	\(-6\)	\(-6\)	\(210\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
27.8.a.a	$27$	$8$	27.a	1.a	$1$	$1$	$1$	$8.434$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1763\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2^{7}q^{4}+1763q^{7}+12605q^{13}+\cdots\)
27.8.a.b	$27$	$8$	27.a	1.a	$1$	$2$	$2$	$8.434$	\(\Q(\sqrt{65}) \)	None	✓	$1$	$1$	\(-9\)	\(0\)	\(-180\)	\(700\)	$-$	$3$	$\mathrm{SU}(2)$	\(q+(-5-\beta )q^{2}+(43+9\beta )q^{4}+(-91+\cdots)q^{5}+\cdots\)
27.8.a.c	$27$	$8$	27.a	1.a	$1$	$2$	$2$	$8.434$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-1118\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-20q^{4}-34\beta q^{5}-559q^{7}+\cdots\)
27.8.a.d	$27$	$8$	27.a	1.a	$1$	$2$	$2$	$8.434$	\(\Q(\sqrt{42}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2522\)	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+250q^{4}+20\beta q^{5}-1261q^{7}+\cdots\)
27.8.a.e	$27$	$8$	27.a	1.a	$1$	$2$	$2$	$8.434$	\(\Q(\sqrt{65}) \)	None	✓	$1$	$0$	\(9\)	\(0\)	\(180\)	\(700\)	$+$	$3$	$\mathrm{SU}(2)$	\(q+(5+\beta )q^{2}+(43+9\beta )q^{4}+(91+2\beta )q^{5}+\cdots\)
27.8.c.a	$27$	$8$	27.c	9.c	$3$	$12$	$6$	$8.434$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(9\)	\(0\)	\(180\)	\(-84\)		$2^{8}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{6}+\beta _{7})q^{2}+(-52+3\beta _{6}+\cdots)q^{4}+\cdots\)
27.8.e.a	$27$	$8$	27.e	27.e	$9$	$120$	$20$	$8.434$		None		$2$	$0$	\(-6\)	\(-6\)	\(-219\)	\(-6\)			$\mathrm{SU}(2)[C_{9}]$
27.9.b.a	$27$	$9$	27.b	3.b	$2$	$1$	$1$	$10.999$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(239\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{8}q^{4}+239q^{7}+56447q^{13}+2^{16}q^{16}+\cdots\)
27.9.b.b	$27$	$9$	27.b	3.b	$2$	$2$	$2$	$10.999$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3934\)		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-608q^{4}-28\beta q^{5}+1967q^{7}+\cdots\)
27.9.b.c	$27$	$9$	27.b	3.b	$2$	$2$	$2$	$10.999$	\(\Q(\sqrt{-30}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1358\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-14q^{4}+26\beta q^{5}-679q^{7}+\cdots\)
27.9.b.d	$27$	$9$	27.b	3.b	$2$	$6$	$6$	$10.999$	6.0.6171673600.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1698\)		$2^{3}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-131+\beta _{2})q^{4}+(20\beta _{1}+\cdots)q^{5}+\cdots\)
27.9.d.a	$27$	$9$	27.d	9.d	$6$	$14$	$7$	$10.999$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(3\)	\(0\)	\(-438\)	\(922\)		$2^{6}\cdot 3^{30}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-2\beta _{1}-2\beta _{2}+110\beta _{3}+\cdots)q^{4}+\cdots\)
27.9.f.a	$27$	$9$	27.f	27.f	$18$	$138$	$23$	$10.999$		None		$2$	$0$	\(-6\)	\(-6\)	\(-447\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
27.10.a.a	$27$	$10$	27.a	1.a	$1$	$2$	$2$	$13.906$	\(\Q(\sqrt{14}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-1526\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-8q^{4}-22\beta q^{5}-763q^{7}+\cdots\)
27.10.a.b	$27$	$10$	27.a	1.a	$1$	$3$	$3$	$13.906$	3.3.177113.1	None	✓	$1$	$0$	\(-3\)	\(0\)	\(1983\)	\(-3693\)	$-$	$2\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(199-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
27.10.a.c	$27$	$10$	27.a	1.a	$1$	$3$	$3$	$13.906$	3.3.177113.1	None	✓	$1$	$1$	\(3\)	\(0\)	\(-1983\)	\(-3693\)	$+$	$2\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(199-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
27.10.a.d	$27$	$10$	27.a	1.a	$1$	$4$	$4$	$13.906$	4.4.203942560.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(11852\)	$-$	$2^{3}\cdot 3^{8}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(559+\beta _{3})q^{4}+(-10\beta _{1}+\cdots)q^{5}+\cdots\)
27.10.c.a	$27$	$10$	27.c	9.c	$3$	$16$	$8$	$13.906$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-15\)	\(0\)	\(-453\)	\(-343\)		$2^{14}\cdot 3^{40}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+\beta _{8}+2\beta _{9})q^{2}+(2\beta _{1}-2\beta _{8}+\cdots)q^{4}+\cdots\)
27.10.e.a	$27$	$10$	27.e	27.e	$9$	$156$	$26$	$13.906$		None		$2$	$0$	\(-6\)	\(-6\)	\(2382\)	\(-6\)			$\mathrm{SU}(2)[C_{9}]$
27.11.b.a	$27$	$11$	27.b	3.b	$2$	$1$	$1$	$17.155$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(10907\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{10}q^{4}+10907q^{7}-141961q^{13}+\cdots\)
27.11.b.b	$27$	$11$	27.b	3.b	$2$	$2$	$2$	$17.155$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-32186\)		$2^{2}\cdot 3\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}-1676q^{4}+2^{4}\zeta_{6}q^{5}-16093q^{7}+\cdots\)
27.11.b.c	$27$	$11$	27.b	3.b	$2$	$4$	$4$	$17.155$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(20516\)		$2^{2}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-137-\beta _{3})q^{4}+(-43\beta _{1}+\cdots)q^{5}+\cdots\)
27.11.b.d	$27$	$11$	27.b	3.b	$2$	$6$	$6$	$17.155$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4638\)		$2^{5}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-443+\beta _{2})q^{4}+(-26\beta _{1}+\cdots)q^{5}+\cdots\)