Newform search results

Results (1-50 of 229 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
16.2.e.a	$16$	$2$	16.e	16.e	$4$	$2$	$1$	$0.128$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
16.3.c.a	$16$	$3$	16.c	4.b	$2$	$1$	$1$	$0.436$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots\)
16.3.f.a	$16$	$3$	16.f	16.f	$4$	$6$	$3$	$0.436$	6.0.399424.1	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
16.4.a.a	$16$	$4$	16.a	1.a	$1$	$1$	$1$	$0.944$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(-24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)
16.4.e.a	$16$	$4$	16.e	16.e	$4$	$10$	$5$	$0.944$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
16.5.c.a	$16$	$5$	16.c	4.b	$2$	$2$	$2$	$1.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(36\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}+18q^{5}+2\zeta_{6}q^{7}-111q^{9}+\cdots\)
16.5.f.a	$16$	$5$	16.f	16.f	$4$	$14$	$7$	$1.654$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)		$2^{21}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+2\beta _{3}-\beta _{11}+\cdots)q^{4}+\cdots\)
16.6.a.a	$16$	$6$	16.a	1.a	$1$	$1$	$1$	$2.566$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-20\)	\(-74\)	\(24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-20q^{3}-74q^{5}+24q^{7}+157q^{9}+\cdots\)
16.6.a.b	$16$	$6$	16.a	1.a	$1$	$1$	$1$	$2.566$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(12\)	\(54\)	\(88\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+12q^{3}+54q^{5}+88q^{7}-99q^{9}+\cdots\)
16.6.e.a	$16$	$6$	16.e	16.e	$4$	$18$	$9$	$2.566$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$2^{36}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{2}-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{9}+\cdots)q^{4}+\cdots\)
16.7.c.a	$16$	$7$	16.c	4.b	$2$	$1$	$1$	$3.681$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(234\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+234q^{5}+3^{6}q^{9}-4070q^{13}-990q^{17}+\cdots\)
16.7.c.b	$16$	$7$	16.c	4.b	$2$	$2$	$2$	$3.681$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-300\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-150q^{5}-22\zeta_{6}q^{7}-39q^{9}+\cdots\)
16.7.f.a	$16$	$7$	16.f	16.f	$4$	$22$	$11$	$3.681$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
16.8.a.a	$16$	$8$	16.a	1.a	$1$	$1$	$1$	$4.998$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-44\)	\(430\)	\(1224\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-44q^{3}+430q^{5}+1224q^{7}-251q^{9}+\cdots\)
16.8.a.b	$16$	$8$	16.a	1.a	$1$	$1$	$1$	$4.998$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-12\)	\(-210\)	\(-1016\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-12q^{3}-210q^{5}-1016q^{7}-2043q^{9}+\cdots\)
16.8.a.c	$16$	$8$	16.a	1.a	$1$	$1$	$1$	$4.998$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(84\)	\(-82\)	\(456\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+84q^{3}-82q^{5}+456q^{7}+4869q^{9}+\cdots\)
16.8.e.a	$16$	$8$	16.e	16.e	$4$	$26$	$13$	$4.998$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
16.9.c.a	$16$	$9$	16.c	4.b	$2$	$2$	$2$	$6.518$	\(\Q(\sqrt{-35}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1020\)	\(0\)		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-510q^{5}+18\beta q^{7}-13599q^{9}+\cdots\)
16.9.c.b	$16$	$9$	16.c	4.b	$2$	$2$	$2$	$6.518$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(516\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}+258q^{5}-238\zeta_{6}q^{7}+6369q^{9}+\cdots\)
16.9.f.a	$16$	$9$	16.f	16.f	$4$	$30$	$15$	$6.518$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
16.10.a.a	$16$	$10$	16.a	1.a	$1$	$1$	$1$	$8.241$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-228\)	\(-666\)	\(6328\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-228q^{3}-666q^{5}+6328q^{7}+32301q^{9}+\cdots\)
16.10.a.b	$16$	$10$	16.a	1.a	$1$	$1$	$1$	$8.241$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-68\)	\(1510\)	\(-10248\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-68q^{3}+1510q^{5}-10248q^{7}-15059q^{9}+\cdots\)
16.10.a.c	$16$	$10$	16.a	1.a	$1$	$1$	$1$	$8.241$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(60\)	\(-2074\)	\(4344\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+60q^{3}-2074q^{5}+4344q^{7}-16083q^{9}+\cdots\)
16.10.a.d	$16$	$10$	16.a	1.a	$1$	$1$	$1$	$8.241$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(156\)	\(870\)	\(952\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+156q^{3}+870q^{5}+952q^{7}+4653q^{9}+\cdots\)
16.10.e.a	$16$	$10$	16.e	16.e	$4$	$34$	$17$	$8.241$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
16.11.c.a	$16$	$11$	16.c	4.b	$2$	$1$	$1$	$10.166$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(474\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+474q^{5}+3^{10}q^{9}+683050q^{13}+\cdots\)
16.11.c.b	$16$	$11$	16.c	4.b	$2$	$4$	$4$	$10.166$	\(\Q(\sqrt{-3}, \sqrt{505})\)	None		$2$	$0$	\(0\)	\(0\)	\(4200\)	\(0\)		$2^{25}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(1050+\beta _{2})q^{5}+(-12\beta _{1}+\cdots)q^{7}+\cdots\)
16.11.f.a	$16$	$11$	16.f	16.f	$4$	$38$	$19$	$10.166$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
16.12.a.a	$16$	$12$	16.a	1.a	$1$	$1$	$1$	$12.293$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-252\)	\(4830\)	\(16744\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-252q^{3}+4830q^{5}+16744q^{7}+\cdots\)
16.12.a.b	$16$	$12$	16.a	1.a	$1$	$1$	$1$	$12.293$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(36\)	\(-3490\)	\(55464\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\cdots\)
16.12.a.c	$16$	$12$	16.a	1.a	$1$	$1$	$1$	$12.293$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(516\)	\(-10530\)	\(-49304\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+516q^{3}-10530q^{5}-49304q^{7}+\cdots\)
16.12.a.d	$16$	$12$	16.a	1.a	$1$	$2$	$2$	$12.293$	\(\Q(\sqrt{109}) \)	None	✓	$1$	$0$	\(0\)	\(-56\)	\(7868\)	\(-91056\)	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(-28-\beta )q^{3}+(3934-12\beta )q^{5}+\cdots\)
16.12.e.a	$16$	$12$	16.e	16.e	$4$	$42$	$21$	$12.293$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
16.13.c.a	$16$	$13$	16.c	4.b	$2$	$2$	$2$	$14.624$	\(\Q(\sqrt{-1155}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-540\)	\(0\)		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-270q^{5}-222\beta q^{7}-133839q^{9}+\cdots\)
16.13.c.b	$16$	$13$	16.c	4.b	$2$	$4$	$4$	$14.624$	\(\Q(\sqrt{-3}, \sqrt{2521})\)	None		$2$	$0$	\(0\)	\(0\)	\(-14904\)	\(0\)		$2^{24}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-3726-\beta _{3})q^{5}+(-162\beta _{1}+\cdots)q^{7}+\cdots\)
16.13.f.a	$16$	$13$	16.f	16.f	$4$	$46$	$23$	$14.624$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
16.14.a.a	$16$	$14$	16.a	1.a	$1$	$1$	$1$	$17.157$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1236\)	\(-57450\)	\(-64232\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-1236q^{3}-57450q^{5}-64232q^{7}+\cdots\)
16.14.a.b	$16$	$14$	16.a	1.a	$1$	$1$	$1$	$17.157$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-468\)	\(56214\)	\(-333032\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-468q^{3}+56214q^{5}-333032q^{7}+\cdots\)
16.14.a.c	$16$	$14$	16.a	1.a	$1$	$1$	$1$	$17.157$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(12\)	\(-4330\)	\(139992\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+12q^{3}-4330q^{5}+139992q^{7}+\cdots\)
16.14.a.d	$16$	$14$	16.a	1.a	$1$	$1$	$1$	$17.157$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1836\)	\(3990\)	\(433432\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+1836q^{3}+3990q^{5}+433432q^{7}+\cdots\)
16.14.a.e	$16$	$14$	16.a	1.a	$1$	$2$	$2$	$17.157$	\(\Q(\sqrt{781}) \)	None	✓	$1$	$1$	\(0\)	\(-872\)	\(18476\)	\(-110928\)	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(-436-\beta )q^{3}+(9238+12\beta )q^{5}+\cdots\)
16.14.e.a	$16$	$14$	16.e	16.e	$4$	$50$	$25$	$17.157$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
16.15.c.a	$16$	$15$	16.c	4.b	$2$	$1$	$1$	$19.893$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-152886\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-152886q^{5}+3^{14}q^{9}-46322630q^{13}+\cdots\)
16.15.c.b	$16$	$15$	16.c	4.b	$2$	$2$	$2$	$19.893$	\(\Q(\sqrt{-3395}) \)	None		$2$	$0$	\(0\)	\(0\)	\(215700\)	\(0\)		$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+107850q^{5}+522\beta q^{7}-3039111q^{9}+\cdots\)
16.15.c.c	$16$	$15$	16.c	4.b	$2$	$4$	$4$	$19.893$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-87000\)	\(0\)		$2^{25}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-21750+\beta _{3})q^{5}+(245\beta _{1}+\cdots)q^{7}+\cdots\)
16.15.f.a	$16$	$15$	16.f	16.f	$4$	$54$	$27$	$19.893$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
16.16.a.a	$16$	$16$	16.a	1.a	$1$	$1$	$1$	$22.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-6252\)	\(90510\)	\(-56\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6252q^{3}+90510q^{5}-56q^{7}+24738597q^{9}+\cdots\)
16.16.a.b	$16$	$16$	16.a	1.a	$1$	$1$	$1$	$22.831$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2700\)	\(-251890\)	\(-1374072\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2700q^{3}-251890q^{5}-1374072q^{7}+\cdots\)
16.16.a.c	$16$	$16$	16.a	1.a	$1$	$1$	$1$	$22.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(276\)	\(-132210\)	\(3585736\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+276q^{3}-132210q^{5}+3585736q^{7}+\cdots\)
16.16.a.d	$16$	$16$	16.a	1.a	$1$	$1$	$1$	$22.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3348\)	\(52110\)	\(-2822456\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+3348q^{3}+52110q^{5}-2822456q^{7}+\cdots\)