Newform search results

Level	Weight	Analytic conductor	\(Nk^2\)	Dim.
Bad \(p\)	Char.	Primitive character	Character order	Coefficient field
Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank
Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 325 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.1.g.a	$144$	$1$	144.g	4.b	$2$	$1$	$1$	$0.072$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{3}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots\)
144.2.a.a	$144$	$2$	144.a	1.a	$1$	$1$	$1$	$1.150$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q+4q^{7}+2q^{13}-8q^{19}-5q^{25}+4q^{31}+\cdots\)
144.2.a.b	$144$	$2$	144.a	1.a	$1$	$1$	$1$	$1.150$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
144.2.c.a	$144$	$2$	144.c	12.b	$2$	$2$	$2$	$1.150$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}+4q^{13}-\beta q^{17}-13q^{25}+\cdots\)
144.2.i.a	$144$	$2$	144.i	9.c	$3$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
144.2.i.b	$144$	$2$	144.i	9.c	$3$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
144.2.i.c	$144$	$2$	144.i	9.c	$3$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
144.2.i.d	$144$	$2$	144.i	9.c	$3$	$4$	$2$	$1.150$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(1\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
144.2.k.a	$144$	$2$	144.k	16.e	$4$	$2$	$1$	$1.150$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(2\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+i)q^{2}+2iq^{4}+(1+i)q^{5}-2iq^{7}+\cdots\)
144.2.k.b	$144$	$2$	144.k	16.e	$4$	$8$	$4$	$1.150$	8.0.18939904.2	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+(-1-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
144.2.k.c	$144$	$2$	144.k	16.e	$4$	$8$	$4$	$1.150$	8.0.629407744.1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{4}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
144.2.l.a	$144$	$2$	144.l	48.k	$4$	$16$	$8$	$1.150$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{11}q^{2}-\beta _{7}q^{4}+\beta _{6}q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
144.2.s.a	$144$	$2$	144.s	36.h	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$1$	\(0\)	\(-3\)	\(-6\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
144.2.s.b	$144$	$2$	144.s	36.h	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1-\zeta_{6})q^{7}+\cdots\)
144.2.s.c	$144$	$2$	144.s	36.h	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1+\zeta_{6})q^{7}+\cdots\)
144.2.s.d	$144$	$2$	144.s	36.h	$6$	$2$	$1$	$1.150$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(-6\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots\)
144.2.s.e	$144$	$2$	144.s	36.h	$6$	$4$	$2$	$1.150$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{3}q^{3}+(1+\zeta_{12})q^{5}+(-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
144.2.u.a	$144$	$2$	144.u	144.u	$12$	$88$	$22$	$1.150$		$_{}$	None	None		$4$	$0$	\(-6\)	\(-4\)	\(-6\)	\(-4\)			$\mathrm{SU}(2)[C_{12}]$
144.2.x.a	$144$	$2$	144.x	144.x	$12$	$4$	$1$	$1.150$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(12\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
144.2.x.b	$144$	$2$	144.x	144.x	$12$	$4$	$1$	$1.150$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$2$	$1$	\(-2\)	\(-6\)	\(-8\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
144.2.x.c	$144$	$2$	144.x	144.x	$12$	$4$	$1$	$1.150$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(4\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
144.2.x.d	$144$	$2$	144.x	144.x	$12$	$4$	$1$	$1.150$	\(\Q(\zeta_{12})\)	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(2\)	\(-12\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+2\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
144.2.x.e	$144$	$2$	144.x	144.x	$12$	$72$	$18$	$1.150$		$_{}$	None	None		$4$	$0$	\(4\)	\(2\)	\(4\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
144.3.e.a	$144$	$3$	144.e	3.b	$2$	$2$	$2$	$3.924$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{5}-12q^{7}+4\beta q^{11}-8q^{13}+\cdots\)
144.3.e.b	$144$	$3$	144.e	3.b	$2$	$2$	$2$	$3.924$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+4q^{7}+4\beta q^{11}+8q^{13}+3\beta q^{17}+\cdots\)
144.3.g.a	$144$	$3$	144.g	4.b	$2$	$1$	$1$	$3.924$	\(\Q\)	$_{}$	\(\Q(\sqrt{-1}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+6q^{5}+10q^{13}+30q^{17}+11q^{25}+\cdots\)
144.3.g.b	$144$	$3$	144.g	4.b	$2$	$2$	$2$	$3.924$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-6q^{5}-\zeta_{6}q^{7}-3\zeta_{6}q^{11}-14q^{13}+\cdots\)
144.3.g.c	$144$	$3$	144.g	4.b	$2$	$2$	$2$	$3.924$	\(\Q(\sqrt{-3}) \)	$_{}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{7}+22q^{13}-2\zeta_{6}q^{19}-5^{2}q^{25}+\cdots\)
144.3.j.a	$144$	$3$	144.j	48.i	$4$	$32$	$16$	$3.924$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
144.3.m.a	$144$	$3$	144.m	16.f	$4$	$6$	$3$	$3.924$	6.0.399424.1	$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}+(-1-\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
144.3.m.b	$144$	$3$	144.m	16.f	$4$	$16$	$8$	$3.924$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{2}+(-1-\beta _{2})q^{4}+\beta _{8}q^{5}+(\beta _{11}+\cdots)q^{7}+\cdots\)
144.3.m.c	$144$	$3$	144.m	16.f	$4$	$16$	$8$	$3.924$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{2}+(1-\beta _{1})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
144.3.o.a	$144$	$3$	144.o	36.f	$6$	$8$	$4$	$3.924$	8.0.856615824.2	$_{}$	None	None		$2$	$0$	\(0\)	\(-3\)	\(3\)	\(3\)		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
144.3.o.b	$144$	$3$	144.o	36.f	$6$	$8$	$4$	$3.924$	8.0.121550625.1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{1}-\beta _{7})q^{5}+\cdots\)
144.3.o.c	$144$	$3$	144.o	36.f	$6$	$8$	$4$	$3.924$	8.0.856615824.2	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}+\beta _{4})q^{3}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
144.3.q.a	$144$	$3$	144.q	9.d	$6$	$2$	$1$	$3.924$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(3\)	\(6\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(3-3\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
144.3.q.b	$144$	$3$	144.q	9.d	$6$	$4$	$2$	$3.924$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-3\)	\(9\)	\(1\)		$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3})q^{3}+(4-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
144.3.q.c	$144$	$3$	144.q	9.d	$6$	$4$	$2$	$3.924$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-18\)	\(-2\)		$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\beta _{1}-\beta _{3})q^{3}+(-3-3\beta _{1})q^{5}+\cdots\)
144.3.q.d	$144$	$3$	144.q	9.d	$6$	$4$	$2$	$3.924$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(12\)	\(6\)	\(6\)		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+3q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
144.3.q.e	$144$	$3$	144.q	9.d	$6$	$8$	$4$	$3.924$	8.0.\(\cdots\).9	$_{}$	None	None		$2$	$0$	\(0\)	\(-10\)	\(-6\)	\(-6\)		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
144.3.v.a	$144$	$3$	144.v	144.v	$12$	$184$	$46$	$3.924$		$_{}$	None	None		$4$	$0$	\(-2\)	\(-4\)	\(-2\)	\(-4\)			$\mathrm{SU}(2)[C_{12}]$
144.3.w.a	$144$	$3$	144.w	144.w	$12$	$184$	$46$	$3.924$		$_{}$	None	None		$4$	$0$	\(-6\)	\(-4\)	\(-6\)	\(0\)			$\mathrm{SU}(2)[C_{12}]$
144.4.a.a	$144$	$4$	144.a	1.a	$1$	$1$	$1$	$8.496$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-16\)	\(12\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{5}+12q^{7}+2^{6}q^{11}+58q^{13}+\cdots\)
144.4.a.b	$144$	$4$	144.a	1.a	$1$	$1$	$1$	$8.496$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(-14\)	\(24\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-14q^{5}+24q^{7}-28q^{11}-74q^{13}+\cdots\)
144.4.a.c	$144$	$4$	144.a	1.a	$1$	$1$	$1$	$8.496$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(16\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{5}+2^{4}q^{7}+12q^{11}+38q^{13}+\cdots\)
144.4.a.d	$144$	$4$	144.a	1.a	$1$	$1$	$1$	$8.496$	\(\Q\)	$_{}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-20\)	$-$	$1$	$N(\mathrm{U}(1))$	\(q-20q^{7}-70q^{13}-56q^{19}-5^{3}q^{25}+\cdots\)
144.4.a.e	$144$	$4$	144.a	1.a	$1$	$1$	$1$	$8.496$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-24\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-24q^{7}-44q^{11}+22q^{13}+\cdots\)
144.4.a.f	$144$	$4$	144.a	1.a	$1$	$1$	$1$	$8.496$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(16\)	\(12\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{5}+12q^{7}-2^{6}q^{11}+58q^{13}+\cdots\)
144.4.a.g	$144$	$4$	144.a	1.a	$1$	$1$	$1$	$8.496$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(0\)	\(18\)	\(-8\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+18q^{5}-8q^{7}+6^{2}q^{11}-10q^{13}+\cdots\)
144.4.c.a	$144$	$4$	144.c	12.b	$2$	$2$	$2$	$8.496$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-92q^{13}+11\beta q^{17}-37q^{25}+\cdots\)