Newform search results

Results (34 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
167.1.b.a	$167$	$1$	167.b	167.b	$2$	$5$	$5$	$0.083$	\(\Q(\zeta_{22})^+\)	$D_{11}$	\(\Q(\sqrt{-167}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+\beta _{4}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
1169.1.f.a	$1169$	$1$	1169.f	1169.f	$6$	$2$	$1$	$0.583$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(-2\)	\(1\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+3\zeta_{6}^{2}q^{4}-2q^{6}+\cdots\)
1169.1.f.c	$1169$	$1$	1169.f	1169.f	$6$	$20$	$10$	$0.583$	\(\Q(\zeta_{33})\)	$D_{33}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(2\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+(\zeta_{66}^{16}+\zeta_{66}^{28})q^{2}+(-\zeta_{66}^{9}-\zeta_{66}^{13}+\cdots)q^{3}+\cdots\)
1336.1.e.a	$1336$	$1$	1336.e	1336.e	$2$	$1$	$1$	$0.667$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-334}) \)	\(\Q(\sqrt{2}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)	$1$		\(q-q^{2}+q^{4}+2q^{7}-q^{8}+q^{9}-2q^{14}+\cdots\)
1336.1.e.e	$1336$	$1$	1336.e	1336.e	$2$	$10$	$10$	$0.667$	\(\Q(\zeta_{22})\)	$D_{22}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{22}^{6}q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{9})q^{3}-\zeta_{22}q^{4}+\cdots\)
1503.1.d.a	$1503$	$1$	1503.d	167.b	$2$	$5$	$5$	$0.750$	\(\Q(\zeta_{22})^+\)	$D_{11}$	\(\Q(\sqrt{-167}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
1503.1.f.a	$1503$	$1$	1503.f	1503.f	$6$	$2$	$1$	$0.750$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+\zeta_{6}q^{2}-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{6}+\zeta_{6}q^{7}+\cdots\)
1503.1.f.b	$1503$	$1$	1503.f	1503.f	$6$	$20$	$10$	$0.750$	\(\Q(\zeta_{33})\)	$D_{33}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+(-\zeta_{66}^{9}-\zeta_{66}^{13})q^{2}+\zeta_{66}^{14}q^{3}+\cdots\)
1837.1.f.a	$1837$	$1$	1837.f	1837.f	$10$	$4$	$1$	$0.917$	\(\Q(\zeta_{10})\)	$D_{5}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(3\)	\(-2\)	\(0\)	\(3\)	$1$		\(q+(1-\zeta_{10}^{3})q^{2}+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
1837.1.f.b	$1837$	$1$	1837.f	1837.f	$10$	$40$	$10$	$0.917$	\(\Q(\zeta_{55})\)	$D_{55}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(-3\)	\(2\)	\(0\)	\(-3\)	$1$		\(q+(-\zeta_{110}^{5}+\zeta_{110}^{6})q^{2}+(\zeta_{110}^{2}-\zeta_{110}^{31}+\cdots)q^{3}+\cdots\)
2004.1.g.a	$2004$	$1$	2004.g	2004.g	$2$	$1$	$1$	$1.000$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \)	\(\Q(\sqrt{3}) \)	✓	$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2004.1.g.b	$2004$	$1$	2004.g	2004.g	$2$	$1$	$1$	$1.000$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \)	\(\Q(\sqrt{3}) \)	✓	$4$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
2004.1.g.e	$2004$	$1$	2004.g	2004.g	$2$	$10$	$10$	$1.000$	\(\Q(\zeta_{22})\)	$D_{22}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{22}^{6}q^{2}+\zeta_{22}^{2}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{8}q^{6}+\cdots\)
2004.1.g.f	$2004$	$1$	2004.g	2004.g	$2$	$10$	$10$	$1.000$	\(\Q(\zeta_{22})\)	$D_{22}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{22}^{6}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{4}q^{6}+\cdots\)
2672.1.g.a	$2672$	$1$	2672.g	167.b	$2$	$5$	$5$	$1.334$	\(\Q(\zeta_{22})^+\)	$D_{11}$	\(\Q(\sqrt{-167}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}-\beta _{2}q^{7}+\cdots\)
2672.1.i.a	$2672$	$1$	2672.i	2672.i	$4$	$2$	$1$	$1.334$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+iq^{2}+(-1+i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots\)
2672.1.i.b	$2672$	$1$	2672.i	2672.i	$4$	$20$	$10$	$1.334$	\(\Q(\zeta_{44})\)	$D_{44}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{44}^{7}q^{2}+(\zeta_{44}^{5}+\zeta_{44}^{6})q^{3}+\zeta_{44}^{14}q^{4}+\cdots\)
3173.1.f.a	$3173$	$1$	3173.f	3173.f	$6$	$2$	$1$	$1.584$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(1\)	\(-2\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{6}q^{2}-\zeta_{6}q^{3}-2\zeta_{6}^{2}q^{6}-q^{7}+\cdots\)
3173.1.f.b	$3173$	$1$	3173.f	3173.f	$6$	$20$	$10$	$1.584$	\(\Q(\zeta_{33})\)	$D_{33}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(-1\)	\(2\)	\(0\)	\(2\)	$1$		\(q+(-\zeta_{66}^{9}-\zeta_{66}^{13})q^{2}+(\zeta_{66}^{8}+\zeta_{66}^{14}+\cdots)q^{3}+\cdots\)
3173.1.j.a	$3173$	$1$	3173.j	3173.j	$18$	$6$	$1$	$1.584$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(1-\zeta_{18}^{7})q^{2}+\zeta_{18}^{5}q^{3}+(1-\zeta_{18}^{5}+\cdots)q^{4}+\cdots\)
3173.1.j.b	$3173$	$1$	3173.j	3173.j	$18$	$60$	$10$	$1.584$	\(\Q(\zeta_{99})\)	$D_{99}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{198}^{45}+\zeta_{198}^{76})q^{2}+(-\zeta_{198}^{29}+\cdots)q^{3}+\cdots\)
3507.1.b.a	$3507$	$1$	3507.b	3507.b	$2$	$1$	$1$	$1.750$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-3507}) \)	\(\Q(\sqrt{21}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-q^{3}+q^{4}-q^{7}+q^{9}-q^{12}+q^{16}+\cdots\)
3507.1.b.b	$3507$	$1$	3507.b	3507.b	$2$	$1$	$1$	$1.750$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-3507}) \)	\(\Q(\sqrt{21}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+q^{3}+q^{4}-q^{7}+q^{9}+q^{12}+q^{16}+\cdots\)
3507.1.b.c	$3507$	$1$	3507.b	3507.b	$2$	$10$	$10$	$1.750$	\(\Q(\zeta_{22})\)	$D_{22}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+(-\zeta_{22}^{4}-\zeta_{22}^{7})q^{2}+\zeta_{22}^{6}q^{3}+\cdots\)
3507.1.b.d	$3507$	$1$	3507.b	3507.b	$2$	$10$	$10$	$1.750$	\(\Q(\zeta_{22})\)	$D_{22}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q+(-\zeta_{22}^{4}-\zeta_{22}^{7})q^{2}-\zeta_{22}^{6}q^{3}+\cdots\)
3507.1.p.a	$3507$	$1$	3507.p	3507.p	$6$	$2$	$1$	$1.750$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
3507.1.p.b	$3507$	$1$	3507.p	3507.p	$6$	$2$	$1$	$1.750$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(1\)	$1$		\(q+q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+q^{9}+(1-\zeta_{6}^{2}+\cdots)q^{11}+\cdots\)
3507.1.p.c	$3507$	$1$	3507.p	3507.p	$6$	$20$	$10$	$1.750$	\(\Q(\zeta_{33})\)	$D_{66}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-1\)	$1$		\(q+(-\zeta_{66}^{4}-\zeta_{66}^{7})q^{2}+\zeta_{66}^{6}q^{3}+\cdots\)
3507.1.p.d	$3507$	$1$	3507.p	3507.p	$6$	$20$	$10$	$1.750$	\(\Q(\zeta_{33})\)	$D_{66}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+(\zeta_{66}^{23}+\zeta_{66}^{32})q^{2}+\zeta_{66}^{29}q^{3}+\cdots\)
501.2.c.a	$501$	$2$	501.c	501.c	$2$	$22$	$22$	$4.001$		$_{}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{2}]$
167.3.b.a	$167$	$3$	167.b	167.b	$2$	$11$	$11$	$4.550$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	$_{}$	\(\Q(\sqrt{-167}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{3}-\beta _{8})q^{3}+(4+\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots\)
668.2.b.a	$668$	$2$	668.b	668.b	$2$	$22$	$22$	$5.334$		$_{}$	\(\Q(\sqrt{-167}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{2}]$
167.5.b.a	$167$	$5$	167.b	167.b	$2$	$11$	$11$	$17.263$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	$_{}$	\(\Q(\sqrt{-167}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{4}+\beta _{7})q^{2}+(-3\beta _{5}+2\beta _{6})q^{3}+\cdots\)
167.7.b.a	$167$	$7$	167.b	167.b	$2$	$11$	$11$	$38.419$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	$_{}$	\(\Q(\sqrt{-167}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{5}$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{3}-\beta _{4})q^{2}+(-5\beta _{6}-2\beta _{8})q^{3}+\cdots\)