Newform search results

Results (29 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1003.1.b.a	$1003$	$1$	1003.b	1003.b	$2$	$1$	$1$	$0.501$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1003}) \)	\(\Q(\sqrt{17}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots\)
1003.1.b.b	$1003$	$1$	1003.b	1003.b	$2$	$2$	$2$	$0.501$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
1003.1.f.a	$1003$	$1$	1003.f	1003.f	$4$	$2$	$1$	$0.501$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$1$		\(q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots\)
1003.1.f.b	$1003$	$1$	1003.f	1003.f	$4$	$4$	$2$	$0.501$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$2$		\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
1003.1.h.a	$1003$	$1$	1003.h	1003.h	$8$	$4$	$1$	$0.501$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
1003.1.h.b	$1003$	$1$	1003.h	1003.h	$8$	$8$	$2$	$0.501$	\(\Q(\zeta_{24})\)	$D_{24}$	\(\Q(\sqrt{-59}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2$		\(q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
1003.2.a.a	$1003$	$2$	1003.a	1.a	$1$	$1$	$1$	$8.009$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(-1\)	\(3\)	\(1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-q^{4}+q^{5}-3q^{6}+q^{7}+\cdots\)
1003.2.a.b	$1003$	$2$	1003.a	1.a	$1$	$1$	$1$	$8.009$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{4}-2q^{5}+2q^{7}+q^{9}+\cdots\)
1003.2.a.c	$1003$	$2$	1003.a	1.a	$1$	$1$	$1$	$8.009$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(1\)	\(1\)	\(1\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
1003.2.a.d	$1003$	$2$	1003.a	1.a	$1$	$1$	$1$	$8.009$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2q^{5}-2q^{7}-3q^{9}+\cdots\)
1003.2.a.e	$1003$	$2$	1003.a	1.a	$1$	$3$	$3$	$8.009$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	\(-3\)	\(2\)	\(-4\)	\(-2\)	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta _{2})q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1003.2.a.f	$1003$	$2$	1003.a	1.a	$1$	$4$	$4$	$8.009$	4.4.2225.1	$_{}$	None	None	✓	$1$	$1$	\(-3\)	\(-2\)	\(1\)	\(8\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1003.2.a.g	$1003$	$2$	1003.a	1.a	$1$	$10$	$10$	$8.009$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-1\)	\(-7\)	\(-12\)	\(-9\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{8}q^{2}+(-1+\beta _{1})q^{3}+(2-\beta _{5})q^{4}+\cdots\)
1003.2.a.h	$1003$	$2$	1003.a	1.a	$1$	$16$	$16$	$8.009$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-6\)	\(-7\)	\(-21\)	\(-11\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1003.2.a.i	$1003$	$2$	1003.a	1.a	$1$	$18$	$18$	$8.009$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(5\)	\(1\)	\(21\)	\(-1\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
1003.2.a.j	$1003$	$2$	1003.a	1.a	$1$	$22$	$22$	$8.009$		$_{}$	None	None	✓	$1$	$0$	\(5\)	\(7\)	\(19\)	\(3\)	$-$		$\mathrm{SU}(2)$
1003.2.d.a	$1003$	$2$	1003.d	17.b	$2$	$2$	$2$	$8.009$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-q^{4}-3q^{8}+3q^{9}-\beta q^{11}+\cdots\)
1003.2.d.b	$1003$	$2$	1003.d	17.b	$2$	$4$	$4$	$8.009$	\(\Q(i, \sqrt{5})\)	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
1003.2.d.c	$1003$	$2$	1003.d	17.b	$2$	$38$	$38$	$8.009$		$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
1003.2.d.d	$1003$	$2$	1003.d	17.b	$2$	$44$	$44$	$8.009$		$_{}$	None	None		$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
1003.4.a.a	$1003$	$4$	1003.a	1.a	$1$	$3$	$3$	$59.179$	3.3.75845.1	$_{}$	None	None	✓	$1$	$1$	\(-3\)	\(-5\)	\(17\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-2-\beta _{2})q^{3}-7q^{4}+(6+\beta _{2})q^{5}+\cdots\)
1003.4.a.b	$1003$	$4$	1003.a	1.a	$1$	$52$	$52$	$59.179$		$_{}$	None	None	✓	$1$	$1$	\(-8\)	\(-19\)	\(-95\)	\(-50\)	$-$		$\mathrm{SU}(2)$
1003.4.a.c	$1003$	$4$	1003.a	1.a	$1$	$57$	$57$	$59.179$		$_{}$	None	None	✓	$1$	$1$	\(-11\)	\(-18\)	\(-132\)	\(-52\)	$-$		$\mathrm{SU}(2)$
1003.4.a.d	$1003$	$4$	1003.a	1.a	$1$	$59$	$59$	$59.179$		$_{}$	None	None	✓	$1$	$0$	\(13\)	\(12\)	\(102\)	\(-24\)	$+$		$\mathrm{SU}(2)$
1003.4.a.e	$1003$	$4$	1003.a	1.a	$1$	$61$	$61$	$59.179$		$_{}$	None	None	✓	$1$	$0$	\(13\)	\(30\)	\(128\)	\(116\)	$+$		$\mathrm{SU}(2)$
1003.6.a.a	$1003$	$6$	1003.a	1.a	$1$	$94$	$94$	$160.865$		$_{}$	None	None	✓	$1$	$1$	\(-23\)	\(-99\)	\(-759\)	\(-929\)	$+$		$\mathrm{SU}(2)$
1003.6.a.b	$1003$	$6$	1003.a	1.a	$1$	$96$	$96$	$160.865$		$_{}$	None	None	✓	$1$	$1$	\(-23\)	\(-45\)	\(-391\)	\(51\)	$+$		$\mathrm{SU}(2)$
1003.6.a.c	$1003$	$6$	1003.a	1.a	$1$	$98$	$98$	$160.865$		$_{}$	None	None	✓	$1$	$0$	\(25\)	\(45\)	\(541\)	\(247\)	$-$		$\mathrm{SU}(2)$
1003.6.a.d	$1003$	$6$	1003.a	1.a	$1$	$100$	$100$	$160.865$		$_{}$	None	None	✓	$1$	$0$	\(25\)	\(63\)	\(509\)	\(247\)	$-$		$\mathrm{SU}(2)$