Embedded newform 567.1.d.b.244.1

• Label: 567.1.d.b.244.1
• Level: $567$
• Weight: $1$
• Character: 567.244
• Self dual: yes
• Analytic conductor: $0.283$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -7
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$567 = 3^{4} \cdot 7$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	567.d (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$0.282969862163$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.567.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.964467.1
Stark unit:	Root of $x^{6} - 249x^{5} - 9246x^{4} - 80993x^{3} - 9246x^{2} - 249x + 1$

Embedding invariants

Embedding label			244.1
Character	$\chi$	$=$	567.244

$q$-expansion

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{11} +1.00000 q^{14} -1.00000 q^{16} +1.00000 q^{22} -2.00000 q^{23} +1.00000 q^{25} -2.00000 q^{29} -1.00000 q^{37} -1.00000 q^{43} -2.00000 q^{46} +1.00000 q^{49} +1.00000 q^{50} +1.00000 q^{53} -1.00000 q^{56} -2.00000 q^{58} +1.00000 q^{64} -1.00000 q^{67} +1.00000 q^{71} -1.00000 q^{74} +1.00000 q^{77} -1.00000 q^{79} -1.00000 q^{86} -1.00000 q^{88} +1.00000 q^{98} +O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

(See $a_n$ instead)

$p$	$a_p$	$a_p / p^{(k-1)/2}$	$\alpha_p$			$\theta_p$
$2$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
			0.500000	+	0.866025i	$0.333333\pi$
$3$	0	0
			$5$	0	0	1.00000			$0$
−1.00000						$\pi$
$7$	1.00000	1.00000
			$11$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
0.500000	+	0.866025i				$0.333333\pi$
$13$	0	0	1.00000			$0$
			−1.00000			$\pi$
$17$	0	0	1.00000			$0$
			−1.00000			$\pi$
$19$	0	0	1.00000			$0$
			−1.00000			$\pi$
$23$	−2.00000	−2.00000	−1.00000			$\pi$
			−1.00000			$\pi$
$29$	−2.00000	−2.00000	−1.00000			$\pi$
			−1.00000			$\pi$
$31$	0	0	1.00000			$0$
			−1.00000			$\pi$
$37$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
			−0.500000	+	0.866025i	$0.666667\pi$
$41$	0	0	1.00000			$0$
			−1.00000			$\pi$
$43$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
			−0.500000	+	0.866025i	$0.666667\pi$
$47$	0	0	1.00000			$0$
			−1.00000			$\pi$

(See $a_n$ instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.1.d.b.244.1	yes	1
3.2	odd	2		567.1.d.a.244.1	✓	1
7.2	even	3		3969.1.m.a.325.1		2
7.3	odd	6		3969.1.m.a.1783.1		2
7.4	even	3		3969.1.m.a.1783.1		2
7.5	odd	6		3969.1.m.a.325.1		2
7.6	odd	2	CM	567.1.d.b.244.1	yes	1
9.2	odd	6		567.1.l.c.433.1		2
9.4	even	3		567.1.l.a.55.1		2
9.5	odd	6		567.1.l.c.55.1		2
9.7	even	3		567.1.l.a.433.1		2
21.2	odd	6		3969.1.m.b.325.1		2
21.5	even	6		3969.1.m.b.325.1		2
21.11	odd	6		3969.1.m.b.1783.1		2
21.17	even	6		3969.1.m.b.1783.1		2
21.20	even	2		567.1.d.a.244.1	✓	1
63.2	odd	6		3969.1.k.d.1648.1		2
63.4	even	3		3969.1.k.a.460.1		2
63.5	even	6		3969.1.t.a.2971.1		2
63.11	odd	6		3969.1.t.a.3106.1		2
63.13	odd	6		567.1.l.a.55.1		2
63.16	even	3		3969.1.k.a.1648.1		2
63.20	even	6		567.1.l.c.433.1		2
63.23	odd	6		3969.1.t.a.2971.1		2
63.25	even	3		3969.1.t.d.3106.1		2
63.31	odd	6		3969.1.k.a.460.1		2
63.32	odd	6		3969.1.k.d.460.1		2
63.34	odd	6		567.1.l.a.433.1		2
63.38	even	6		3969.1.t.a.3106.1		2
63.40	odd	6		3969.1.t.d.2971.1		2
63.41	even	6		567.1.l.c.55.1		2
63.47	even	6		3969.1.k.d.1648.1		2
63.52	odd	6		3969.1.t.d.3106.1		2
63.58	even	3		3969.1.t.d.2971.1		2
63.59	even	6		3969.1.k.d.460.1		2
63.61	odd	6		3969.1.k.a.1648.1		2

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.1.d.a.244.1	✓	1	3.2	odd	2
567.1.d.a.244.1	✓	1	21.20	even	2
567.1.d.b.244.1	yes	1	1.1	even	1	trivial
567.1.d.b.244.1	yes	1	7.6	odd	2	CM
567.1.l.a.55.1		2	9.4	even	3
567.1.l.a.55.1		2	63.13	odd	6
567.1.l.a.433.1		2	9.7	even	3
567.1.l.a.433.1		2	63.34	odd	6
567.1.l.c.55.1		2	9.5	odd	6
567.1.l.c.55.1		2	63.41	even	6
567.1.l.c.433.1		2	9.2	odd	6
567.1.l.c.433.1		2	63.20	even	6
3969.1.k.a.460.1		2	63.4	even	3
3969.1.k.a.460.1		2	63.31	odd	6
3969.1.k.a.1648.1		2	63.16	even	3
3969.1.k.a.1648.1		2	63.61	odd	6
3969.1.k.d.460.1		2	63.32	odd	6
3969.1.k.d.460.1		2	63.59	even	6
3969.1.k.d.1648.1		2	63.2	odd	6
3969.1.k.d.1648.1		2	63.47	even	6
3969.1.m.a.325.1		2	7.2	even	3
3969.1.m.a.325.1		2	7.5	odd	6
3969.1.m.a.1783.1		2	7.3	odd	6
3969.1.m.a.1783.1		2	7.4	even	3
3969.1.m.b.325.1		2	21.2	odd	6
3969.1.m.b.325.1		2	21.5	even	6
3969.1.m.b.1783.1		2	21.11	odd	6
3969.1.m.b.1783.1		2	21.17	even	6
3969.1.t.a.2971.1		2	63.5	even	6
3969.1.t.a.2971.1		2	63.23	odd	6
3969.1.t.a.3106.1		2	63.11	odd	6
3969.1.t.a.3106.1		2	63.38	even	6
3969.1.t.d.2971.1		2	63.40	odd	6
3969.1.t.d.2971.1		2	63.58	even	3
3969.1.t.d.3106.1		2	63.25	even	3
3969.1.t.d.3106.1		2	63.52	odd	6