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 87 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
289.2.a.a	$289$	$2$	289.a	1.a	$1$	$1$	$1$	$2.308$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots\)
289.2.a.b	$289$	$2$	289.a	1.a	$1$	$2$	$2$	$2.308$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots\)
289.2.a.c	$289$	$2$	289.a	1.a	$1$	$2$	$2$	$2.308$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots\)
289.2.a.d	$289$	$2$	289.a	1.a	$1$	$3$	$3$	$2.308$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-6\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
289.2.a.e	$289$	$2$	289.a	1.a	$1$	$3$	$3$	$2.308$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(6\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.a.f	$289$	$2$	289.a	1.a	$1$	$4$	$4$	$2.308$	\(\Q(\zeta_{16})^+\)	None	✓	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots\)
289.2.b.a	$289$	$2$	289.b	17.b	$2$	$2$	$2$	$2.308$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-q^{4}+iq^{5}+2iq^{7}-3q^{8}+\cdots\)
289.2.b.b	$289$	$2$	289.b	17.b	$2$	$4$	$4$	$2.308$	4.0.2048.2	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)
289.2.b.c	$289$	$2$	289.b	17.b	$2$	$4$	$4$	$2.308$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.b.d	$289$	$2$	289.b	17.b	$2$	$6$	$6$	$2.308$	6.0.419904.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{2}-\beta _{4})q^{4}+\cdots\)
289.2.c.a	$289$	$2$	289.c	17.c	$4$	$4$	$2$	$2.308$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}^{2}q^{2}+q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{3}q^{7}+\cdots\)
289.2.c.b	$289$	$2$	289.c	17.c	$4$	$8$	$4$	$2.308$	8.0.1871773696.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.c.c	$289$	$2$	289.c	17.c	$4$	$8$	$4$	$2.308$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{16}^{2}-\zeta_{16}^{3})q^{2}+(-\zeta_{16}+\zeta_{16}^{7})q^{3}+\cdots\)
289.2.c.d	$289$	$2$	289.c	17.c	$4$	$12$	$6$	$2.308$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{4}-\beta _{9})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\)
289.2.d.a	$289$	$2$	289.d	17.d	$8$	$4$	$1$	$2.308$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(-4\)	\(4\)	\(0\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.b	$289$	$2$	289.d	17.d	$8$	$4$	$1$	$2.308$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(4\)	\(-4\)	\(-4\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.c	$289$	$2$	289.d	17.d	$8$	$4$	$1$	$2.308$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(4\)	\(4\)	\(4\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.d	$289$	$2$	289.d	17.d	$8$	$8$	$2$	$2.308$	\(\Q(\zeta_{16})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots\)
289.2.d.e	$289$	$2$	289.d	17.d	$8$	$16$	$4$	$2.308$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\beta _{3}+\beta _{5})q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-2\beta _{8}+\cdots)q^{4}+\cdots\)
289.2.d.f	$289$	$2$	289.d	17.d	$8$	$24$	$6$	$2.308$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{8}]$
289.2.f.a	$289$	$2$	289.f	289.f	$17$	$384$	$24$	$2.308$		None		$2$	$0$	\(-13\)	\(-13\)	\(-43\)	\(-13\)			$\mathrm{SU}(2)[C_{17}]$
289.2.g.a	$289$	$2$	289.g	289.g	$34$	$384$	$24$	$2.308$		None		$2$	$0$	\(-17\)	\(-17\)	\(17\)	\(-17\)			$\mathrm{SU}(2)[C_{34}]$
289.2.h.a	$289$	$2$	289.h	289.h	$68$	$768$	$24$	$2.308$		None		$2$	$0$	\(-34\)	\(-34\)	\(-34\)	\(-34\)			$\mathrm{SU}(2)[C_{68}]$
289.2.i.a	$289$	$2$	289.i	289.i	$136$	$1600$	$25$	$2.308$		None		$2$	$0$	\(-64\)	\(-64\)	\(-68\)	\(-64\)			$\mathrm{SU}(2)[C_{136}]$
289.3.e.a	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(-8\)	\(-16\)	\(-8\)	\(-16\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-2-2\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.b	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(-8\)	\(-8\)	\(0\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.c	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(-8\)	\(8\)	\(-16\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.d	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(-8\)	\(8\)	\(0\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.e	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(-8\)	\(16\)	\(8\)	\(16\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(2+2\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.f	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(-8\)	\(-8\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots\)
289.3.e.g	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(24\)	\(16\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
289.3.e.h	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(8\)	\(8\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.i	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(8\)	\(-8\)	\(-16\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.j	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(8\)	\(-8\)	\(16\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.k	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(8\)	\(0\)	\(-16\)	\(40\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.l	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(8\)	\(0\)	\(16\)	\(-40\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.m	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(8\)	\(8\)	\(16\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.n	$289$	$3$	289.e	17.e	$16$	$8$	$1$	$7.875$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(8\)	\(8\)	\(-16\)	\(8\)		$1$	$\mathrm{SU}(2)[C_{16}]$	\(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.o	$289$	$3$	289.e	17.e	$16$	$16$	$2$	$7.875$	16.0.\(\cdots\).1	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{16}]$	\(q-\beta _{6}q^{2}+\beta _{11}q^{3}+3\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots\)
289.3.e.p	$289$	$3$	289.e	17.e	$16$	$32$	$4$	$7.875$		None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
289.3.e.q	$289$	$3$	289.e	17.e	$16$	$48$	$6$	$7.875$		None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
289.3.e.r	$289$	$3$	289.e	17.e	$16$	$96$	$12$	$7.875$		None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{16}]$
289.3.j.a	$289$	$3$	289.j	289.j	$272$	$6400$	$50$	$7.875$		None		$2$	$0$	\(-128\)	\(-128\)	\(-128\)	\(-128\)			$\mathrm{SU}(2)[C_{272}]$
289.4.a.a	$289$	$4$	289.a	1.a	$1$	$1$	$1$	$17.052$	\(\Q\)	None	✓	$1$	$0$	\(-3\)	\(8\)	\(-6\)	\(28\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+8q^{3}+q^{4}-6q^{5}-24q^{6}+\cdots\)
289.4.a.b	$289$	$4$	289.a	1.a	$1$	$3$	$3$	$17.052$	3.3.2636.1	None	✓	$1$	$0$	\(1\)	\(-4\)	\(8\)	\(-22\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
289.4.a.c	$289$	$4$	289.a	1.a	$1$	$4$	$4$	$17.052$	4.4.2555057.1	None	✓	$1$	$0$	\(1\)	\(-2\)	\(14\)	\(36\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
289.4.a.d	$289$	$4$	289.a	1.a	$1$	$4$	$4$	$17.052$	4.4.2555057.1	None	✓	$1$	$1$	\(1\)	\(2\)	\(-14\)	\(-36\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
289.4.a.e	$289$	$4$	289.a	1.a	$1$	$4$	$4$	$17.052$	4.4.4669632.2	None	✓	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+\cdots\)
289.4.a.f	$289$	$4$	289.a	1.a	$1$	$8$	$8$	$17.052$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(5-\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots\)
289.4.a.g	$289$	$4$	289.a	1.a	$1$	$12$	$12$	$17.052$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$2$	$1$	\(-8\)	\(0\)	\(0\)	\(0\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{5})q^{2}+\beta _{7}q^{3}+(2+2\beta _{1}+\cdots)q^{4}+\cdots\)